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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ec1cc2c8bf5eadbd27ba7fcb56ee4b52ee038181 | subsection | 3 | 39 | Introduction | Formal aspects of the
model-building have been relegated to the appendices. In Section 3 we
analyse possible scenarios for reheating after inflation, including
constraints from possible overproduction of gravitinos and Big Bang
Nucleosynthesis (BBN). In addition, we estimate the effect that the
texture Goldstone bosons... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.06605672836303711,
0.00613558292388916,
0.... |
bf8e1fe5b560cfbd5bf1a6da97fd49fa6656ae90 | subsection | 4 | 39 | Superpotential and scalar potential | The model of SUSY hybrid inflation with global defects is implemented
by the superpotentialW = \kappa \, \widehat{S}\, \Big ( \widehat{X}_1
\widehat{X}_2\: -\: {M}^2\Big )
\,,with \widehat{X}_1=({\bf 2}) being a fundamental,
\widehat{X}_2=({\bf \overline{2}}) an identical anti-fundamental
representation of the global {... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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f4f5422007ee89a51ece886039a5ffb5babb4393 | subsection | 5 | 39 | Superpotential and scalar potential | In the following, we assume that {\rm SU}(2) is an exact symmetry,
while {\rm SU}(2)_X may be explicitly broken through the introduction
of new operators in addition to those arising from the superpotential.We note that the action of a \theta _3 rotation of {\bf X} is
equivalent to an U(1) transformation given by\wideh... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.... |
b188e8a69c15531fb06c4d69428cee29b2578aab | subsection | 6 | 39 | Identification of the scalar particle spectrum | In order to identify these modes and determine the vacuum manifold, we
first make use of the symmetries {\rm SU}(2) and {\rm U}(1)_X to
write the fields asX_1=
{\rm e}^{{\rm i}\left(\alpha _i \tau ^i +\beta \mathbb {1}_2\right)}
\left(\begin{array}{c}
{w}_1^+\\
0
\end{array}
\right)
\;
\textnormal {and}\;\;
X_2=
{\rm e... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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-0.... |
e8112b88a157458a8a4e51bba687b7b4dc398ec8 | subsection | 7 | 39 | Identification of the scalar particle spectrum | In this way, the
waterfall doublets X_{1,2} may be expressed asX_{1}=
\left(
\begin{array}{c}
{w}_1^+ +\frac{1}{\sqrt{2}}(X_{1R}^+ +{\rm i}X_{1I}^+)\\
\frac{1}{\sqrt{2}}(X_{1R}^- +{\rm i}X_{1I}^-)
\end{array}
\right)\;
\textnormal {and}\;\;
X_{2}=
\left(
\begin{array}{c}
{w}_2^+
+\frac{1}{\sqrt{2}}(X_{2R}^+ +{\rm i}X_{... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
-0.023908549919724464,
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-0.00572157371789217,
... |
44aaeedb6a7a305a68aa24a1837dc50218c40fb8 | subsection | 8 | 39 | Identification of the scalar particle spectrum | The modes of this type areH_0^R\!\!\!&=&\!\!\!\frac{1}{w} \left({w}_2^+ X_{1R}^- -
{w}_1^+ X_{2R}^- - {w}_2^- X_{1R}^+
\right)\,,\\
H_0^I\!\!\!&=&\!\!\!\frac{1}{{w}}\left({w}_2^+ X_{1I}^- + {w}_1^+ X_{2I}^-
-{w}_2^- X_{1I}^+ \right)\,,andH_g=
\frac{1}{w}\left(
-{w}_1^+ X_{1R}^+ + {w}_2^+ X_{2R}^+ -{w}_2^- X_{2R}^-
\rig... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
-0.02422822266817093,
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... |
42c3cd762ee9dc97d98c41a681b60d4c9c9ec5df | subsection | 9 | 39 | Lifting of the moduli | Unlike the Goldstone bosons (REF ), the moduli fields,
H_0^R, H_0^I and H_g, are not protected by the global symmetry
{\rm SU}(2)\times {\rm U}(1)_X and usually acquire non-zero masses if
soft SUSY-breaking terms are added to the potential which respect the
global symmetry. We refer to this mechanism as lifting. Some o... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1063,
"openalex_id": "",
"raw": "A. E. Nelson and N. Seiberg, “R symmetry breaking versus supersymmetry breaking,” Nucl. Phys. B 416 (1994) 46 [arXiv:hep-ph/9309299].",
"source_ref_id": "afe438ee565725ee79800343d0a35c5bd1bd5... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.001786838285624981,
-0.00... |
7819f02d300279251294f58f89bf1bde3191a209 | subsection | 10 | 39 | Lifting of the moduli | Although they break the accidental global {\rm U}(1)_X-symmetry, we show in Appendix , how
these d-terms can be absorbed in m_1^2 and m_2^2 after a field
redefinition of X_1 and X_2.Consequently, we will set both b=0 and d=0 in the subsequent
discussion and just allow m_{1,2}^2 to vary, that isV_{\rm lift} = m_1^2 |X_1... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.03226299211382866,
-0... |
724dc6695556b0c6054b6aa1f0e1bf12aec03dfe | subsection | 11 | 39 | Vacuum manifold and texture defects | We now determine the vacuum manifold of the scalar potential,
which arises as a combination of (REF ) and (REF ),V_{\rm global}=V_0+V_{\rm lift}\,.With the parameterisation (REF ),
we get the potentialV_{\rm global}({w}_1^+,{w}_2^+,{w}_2^-,\varphi _2^+)=
\kappa ^2\left({w}_1^+{w}_2^+e^{i\varphi _2^+} - {M}^2 \right)^2
... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
-0.025322293862700462,
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0.01395014300942421,
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0.044268250465393066,
0.00022667075973004103,
... |
f204c7b907d2eb9f9f120e75263d606feefc5547 | subsection | 12 | 39 | Cosmological and Astrophysical Implications | In this section, we outline possible scenarios for reheating after
inflation. In order to do so, we choose to consider couplings to the
Higgs-fields of the MSSM and the right-handed neutrino sector, such
that the inflationary energy can eventually be converted into
particles of the Standard Model (SM). Furthermore, we ... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
-0.030464068055152893,
-0.04111733287572861,
-0.02823573350906372,
0.021703358739614487,
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0.00892859697341919,
0.0066926321014761925,
0.... |
96a9b692edf3b42bb80df207afdbfe0eff294255 | subsection | 13 | 39 | Extended superpotential | We extend the superpotential (REF ) by adding the
termsW_{\rm RH} = \lambda \, \widehat{S} \widehat{H}_u
\widehat{H}_d\ +\ \frac{\rho _{ij}}{2} \widehat{S}\, \widehat{N}_i
\widehat{N}_j\,,where \widehat{H}_{u,d} denote the MSSM-Higgs doublets and \widehat{N}_i (i=1,2,3) are right-handed singlet neutrinos, which we assu... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 390,
"openalex_id": "",
"raw": "A. Pilaftsis, “Resonant \\tau leptogenesis with observable lepton number violation,” Phys. Rev. Lett. 95 (2005) 081602 [arXiv:hep-ph/0408103].",
"source_ref_id": "c022710c4ee59cbabcb0aa60d43a7... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
-0.03698030859231949,
0.02251771278679371,
-0.015324554406106472,
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0.04592026770114899,
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0.04378443956375122,
0.013135332614183426,
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0.026911413297057152,
-0.023509345948696136... |
aaff7489db5caccc131663e44a4d284613509b01 | subsection | 14 | 39 | Stellar cooling | It is straightforward to check that the coupling \lambda does not
induce any tree-level mixing between the Higgs bosons, the Goldstone
bosons and moduli. Hence, we do not expect related collider
phenomenology.We may now examine whether the same coupling induces effects that are
in contradiction with astrophysical obser... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1010,
"openalex_id": "",
"raw": "G. G. Raffelt, “Astrophysical methods to constrain axions and other novel particle phenomena,” Phys. Rept. 198 (1990) 1.",
"source_ref_id": "483e20572a259691589383ad0add093312f58cb4",
"... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.012175936251878... |
9014e85272fda05e80de688da5574cbd463189e5 | subsection | 15 | 39 | Reheating and gravitinos | We sketch two possible ways in which the inflationary vacuum energy
can be transferred to the MSSM degrees of freedom through
renormalisable interactions. One may alternatively consider
“gravity-mediated" reheating through non-renormalisable operators, a
possibility which we do not discuss here.For the first reheat sce... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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... |
520476e590db7155e5571c41f96670b31dbbc217 | subsection | 16 | 39 | Reheating delayed by stop VEV | Considering the scalar potential (REF ) and the interactions
arising from (REF ), it is clear that the oscillating fields S
and H_\kappa ^R can directly decay into Goldstone bosons, light
moduli and their superpartner fermions. Since these particles are only
weakly coupled to the MSSM degrees of freedom, higher tempera... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1540,
"openalex_id": "",
"raw": "M. Kawasaki and T. Moroi, “Gravitino production in the inflationary universe and the effects on big bang nucleosynthesis,” Prog. Theor. Phys. 93 (1995) 879 [arXiv:hep-ph/9403364].",
"source_r... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.... |
f7164ca19932c323e614d4a034a26b3661c6816f | subsection | 17 | 39 | Reheating delayed by stop VEV | This typically is below the upper bounds Y_{\widetilde{G}}
\stackrel{<}{{}_\sim }10^{-15} for a gravitino of mass m_{\widetilde{G}}\simeq 360~{\rm GeV} and Y_{\widetilde{G}}
\stackrel{<}{{}_\sim }10^{-14} for a gravitino of mass m_{\widetilde{G}}\simeq 600~{\rm GeV}, as imposed by constraints from
BBN , . Larger gravit... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 306,
"openalex_id": "",
"raw": "M. Kawasaki, K. Kohri and T. Moroi, “Hadronic decay of late-decaying particles and big-bang nucleosynthesis,” Phys. Lett. B 625 (2005) 7 [arXiv:astro-ph/0402490].",
"source_ref_id": "db64dc0fa... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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... |
828fe9bfc99d1322600c92cc44b906f83c321402 | subsection | 18 | 39 | Reheating delayed by stop VEV | In the weak basis
\left(H_u^*,H_d\right), the Higgs mass-square matrix may then be
written down as\left(
\begin{array}{cc}
\lambda ^2|S|^2+h^2 v_{\rm stop}^2 & -\kappa \lambda {M}^2\\
-\kappa \lambda {M}^2 & \lambda ^2 |S|^2
\end{array}
\right)\,,and the condition for it to be positive definite is|S|^2 >
\frac{-h^2 v_{... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 877,
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"raw": "M. Berkooz, D. J. H. Chung and T. Volansky, “Constraining modular inflation in the MSSM from giant Q-ball formation,” Phys. Rev. D 73 (2006) 063526 [arXiv:hep-ph/0507218].",
"source_ref_id": "... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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-... |
13d01fd32e1462e71f6a187f0e1f594d22e8e62f | subsection | 19 | 39 | Reheating via sneutrinos | If \lambda =0 and \rho \ge \kappa , decays into right handed
neutrinos and sneutrinos also take place. The decay rate is\Gamma _{\kappa \rho }=\frac{3}{32\pi }
\left(\kappa ^2+\rho ^2\right)\kappa {w}\,,and the reheat temperature within this sector is given byT_{\kappa \rho }=
\left(\frac{45}{4 \pi ^3 g_*^{\rm G}}\righ... | {
"cite_spans": [
{
"arxiv_id": "",
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"openalex_id": "",
"raw": "A. Pilaftsis, “CP violation and baryogenesis due to heavy Majorana neutrinos,” Phys. Rev. D 56 (1997) 5431 [arXiv:hep-ph/9707235].",
"source_ref_id": "7a7cebb6fe1efbc0a038587c51e730639603bb4d... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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aafe79a4595277bc5f786fd2e135c8fd693ef902 | subsection | 20 | 39 | Big bang nucleosynthesis and the new light fields | The number and the temperature of light relativistic species is
constrained by considerations from BBN, or even
more strongly by a combined analysis of CMB data and observations
of abundances of light nuclei, see for example
Ref. . This is because the results of BBN
are sensitive to the effective number of degrees of
f... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 231,
"openalex_id": "",
"raw": "V. Barger, J. P. Kneller, H. S. Lee, D. Marfatia and G. Steigman, “Effective number of neutrinos and baryon asymmetry from BBN and WMAP,” Phys. Lett. B 566 (2003) 8 [arXiv:hep-ph/0305075].",
"... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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353f9eeb484fb7c02e4fe6578df318b26832fad0 | subsection | 21 | 39 | Semi-Local Model | It is possible to promote the global symmetry to a semi-local one by
assigning opposite {\rm U}(1)_X gauge charges to X_1 and X_2.
In this case, the scalar-gauge Lagrangian is{\cal L}=-\frac{1}{4} F_{\mu \nu }F^{\mu \nu }
-|D_\mu X_1|^2-|D_\mu X_2|^2-V_0- V_{\rm lift} -\frac{1}{2} D^2\,.For the kinetic terms, we use th... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0... |
5e6fa843bdad7ce46c5b854c456748486e1264d8 | subsection | 22 | 39 | Semi-Local Model | Choosing again the parameterisation (REF ) and
using V_{\rm lift}, we minimiseV_{{w}}({w}_1^+,{w}_2^+,{w}_2^-,\varphi _2^+)&=&
\kappa ^2\left({w}_1^+{w}_2^+e^{i\varphi _2^+} - {M}^2 \right)^2
+m_1^2{{w}_1^+}^2+m_2^2{{w}_2^+}^2+m_2^2{{w}_2^-}^2\cr &+&\frac{g^2}{8}\left({{w}_1^+}^2-{{w}_2^+}^2-{{w}_2^-}^2-m_{\rm FI}^2\ri... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1278,
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"raw": "B. Garbrecht and A. Pilaftsis, “F(D)-term hybrid inflation with electroweak-scale lepton number violation,” Phys. Lett. B 636 (2006) 154 [arXiv:hep-ph/0601080].",
"source_ref_id": "73ab300b26... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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e509b3c2a7267aa261f3b204f0923f8a23b173f1 | subsection | 23 | 39 | Semi-Local Model | During the phase transition at the end of
inflation, {w} is evolving rapidly, such that the g-sector
particles are produced via preheating, which occurs due to their
non-adiabatically changing mass term. Even though approximate
D-parity holds due to the smallness of (),
from (REF ) and (REF ), we see that the g-sector
... | {
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{
"arxiv_id": "",
"doi": "",
"end": 617,
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"raw": "B. Garbrecht and A. Pilaftsis, “F(D)-term hybrid inflation with electroweak-scale lepton number violation,” Phys. Lett. B 636 (2006) 154 [arXiv:hep-ph/0601080].",
"source_ref_id": "73ab300b268... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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068b0cf28fd52787a5538544cf457525e66cc09b | subsection | 24 | 39 | Inflation and Impact on the CMB | We now discuss the predictions of our model for the amplitude A_{\rm s} of the primordial power spectrum produced during inflation and the
scalar spectral index n_{\rm s} that can be observed in the CMB. As
we discuss below, for given superpotential couplings, the symmetry
breaking scale M can be determined by imposing... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 512,
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"raw": "M. Cruz, N. Turok, P. Vielva, E. Martinez-Gonzalez and M. Hobson, “A Cosmic Microwave Background feature consistent with a cosmic texture,” Science 318, 1612 (2007) [arXiv:0710.5737 [astro-ph]].",
... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0... |
09665173c420dbf65d70a26a4926998f1ca28755 | subsection | 25 | 39 | Inflation and Impact on the CMB | \frac{1}{32\pi ^2}\, \Bigg \lbrace
2\kappa ^4\, \Bigg [ |S^2 + {M}^2|^2\,
\ln \Bigg (\frac{\kappa ^2 (|S|^2 +{M}^2)}{Q^2}\Bigg ) +\,
|S^2 - {M}^2|^2\,
\ln \Bigg (\frac{\kappa ^2 (|S|^2 - {M}^2)}{Q^2}\Bigg )\Bigg ]\\
&&\hspace{-4.83691pt} +\, 2\lambda ^4\, \Bigg [
|S^2 + {\textstyle \frac{\kappa }{\lambda }}\, {M}^2|^2... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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c5fd47b0e1a6a834007b8ed32a1ab795212c0f1c | subsection | 26 | 39 | Inflation and Impact on the CMB | When \langle S \rangle < {M}, the combination
of waterfall fields,\frac{1}{\sqrt{2}} \left(X_1+X_2\right)\,,develops a negative mass term which induces spontaneous breakdown of
{\rm SU}(2). In order for this instability to occur first in this
direction, rather than in any other direction, which involves the
N_i and H_{... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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-... |
43f6a18832a846e795d5fa8c51be96dc1d16a2d4 | subsection | 27 | 39 | Inflation and Impact on the CMB | The second observable we consider is the scalar spectral index
which is given byn_{\rm s}=
1-2\frac{m_{\rm Pl}^2}{8\pi }
\frac{\partial ^2V/\partial \sigma ^2}{V}
\Bigg |_{\sigma =\sigma _{\rm e}}\,.We can now compare the predictions of our F-term hybrid inflation
model with the best-fit value for M found in
Ref. . The... | {
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{
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"end": 316,
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"raw": "M. Cruz, N. Turok, P. Vielva, E. Martinez-Gonzalez and M. Hobson, “A Cosmic Microwave Background feature consistent with a cosmic texture,” Science 318, 1612 (2007) [arXiv:0710.5737 [astro-ph]].",
... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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104e4dbe2bff5dbd1048de6ea0b8711f33f3878c | subsection | 28 | 39 | Conclusions | The current CMB data shows hints for the presence of topological
defects of order the GUT energy scale M_{\rm GUT} \sim 10^{16} GeV.
First, fits to the CMB spectrum marginally favour models with a 10%
contribution to it that results from defects. Second, it has been
suggested that textures associated with GUT energies ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 394,
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"raw": "M. Cruz, N. Turok, P. Vielva, E. Martinez-Gonzalez and M. Hobson, “A Cosmic Microwave Background feature consistent with a cosmic texture,” Science 318, 1612 (2007) [arXiv:0710.5737 [astro-ph]].",
... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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d5b5406f063842af7fb761ba7e118ab679a4eed3 | subsection | 29 | 39 | Symmetries and Breaking Patterns | In this appendix, we present more details on the {\rm SU}(2)\times {\rm SU}(2)_X symmetry of the superpotential. | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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30848713bc0fa77cb5c888b0f5a4ce78e54bd3af | subsection | 30 | 39 | Symmetries and Breaking Patterns | In particular, we
discuss formal aspects of the spontaneous and the explicit breakdown
of the symmetry, such as counting of Goldstone modes and homotopy
groups of the vacuum manifold.The combined action of the symmetry transformations (REF )
and (REF ) can be compactly written in terms of a tensor-product
as\mathbf {X}... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0... |
ec768295c6e64c991fd2e684c28ea24d636f073d | subsection | 31 | 39 | Symmetries and Breaking Patterns | Using the parameterisation of the
VEVs (), it is useful to
distinguish two cases. An overview of arguments is presented in
Table REF .When w_1^+=w_2^+ (|X_1|=|X_2| is the reparameterization
invariant form), all 3 generators of {\rm SU}(2)
and {\rm SU}(2)_X have the same effect on the VEVs, which
means G_{\tau ^i}=G_{\s... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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... |
fa9ec277dc65d8ac37c5639245729349398f1625 | subsection | 32 | 39 | Symmetries and Breaking Patterns | When taking the flat direction H_g into account, the configuration
can change to |X_1|=|X_2|, such that the monopoles can
unwind. Hence, the monopoles are topologically unstable. In other
words, even though \pi _2\left({\rm SU}(2)\times {\rm SU}(2)_X/{\rm U}(1)_D\right)= \mathbb {Z}, for the full vacuum manifold {\cal ... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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079840d650177c63815f4371188d12c2537a3393 | subsection | 33 | 39 | Symmetries and Breaking Patterns | These terms explicitly break {\rm SU}(2)_X. The
symmetry breaking pattern is{\rm SU}(2)\times {\rm SU}(2)_X
\xrightarrow{}
{\rm SU}(2)\times {\rm U}(1)_X
\xrightarrow{}
{\rm U}(1)_D\,.Appendix:ExtraSymmetry.8
Again, there are 3 Goldstone bosons G_{\tau ^i} (i=1,2,3), out of
which G_{\tau ^3} is absorbed as a transverse... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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f0365fb38399e5c6f2d23d98ce37b70ba5091301 | subsection | 34 | 39 | Field Redefinitions and the Lifting Potential | When we include the d-term in the lifting potential (REF ),
it turns out that the minima (REF ) get shifted toAppendix:FieldRedef.0{Appendix:FieldRedef}.1a\endcsname
{w}_1^+\!\!\!&=&\!\!\!\sqrt{\frac{m_2}{m_1}{M}^2
\frac{1}{\sqrt{1-\frac{|d|^2}{m_1^2 m_2^2}}}-
\frac{m_2^2}{\kappa ^2}}
\,,\\
{w}_2^+\!\!\!&=&\!\!\!\sqr... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.007842588238418102,
0.001487650559283793,
0.00... |
83a3a51a24a57d4c34f5024bbd9b980eafeb222a | subsection | 35 | 39 | Field Redefinitions and the Lifting Potential | To see this, we make use
of the fact that field redefinitions according to {\rm SU}(2)_X have
the explicit effectAppendix:FieldRedef.0{Appendix:FieldRedef}.3a\endcsname
\hspace{-22.76228pt}
|X_1|^2\!\!\!&\xrightarrow{}&\!\!\!
|X_1|^2 \cos ^2\theta _1 + |X_2|^2 \sin ^2\theta _1
+{\rm i}\sin \theta _1\cos \theta _1
\lef... | {
"cite_spans": []
} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
"Richard A. Battye",
"Bjorn Garbrecht",
"Apostolos Pilaftsis"
] | [
"hep-ph",
"astro-ph",
"hep-th"
] | 2,008 | en | Physics | [
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0.028164373710751534,
... |
284e960d4c6bb80bb19105c40e0871ac9224b8e1 | subsection | 36 | 39 | Scalar Interaction Terms and | In this appendix, we present the expressions (REF )
and (REF ), from which the interactions within the scalar sector
can easily be inferred. It turns out that in the situation where
{w}_1^+ \approx {w}_2^+, the symmetry of the model is enhanced,
which has the consequence that certain interactions are
suppressed. These ... | {
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... | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
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"Bjorn Garbrecht",
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f2cb7d390d9b04ae3f842c7b9bdc06350e27aa1e | subsection | 37 | 39 | Scalar Interaction Terms and | On the other
hand, allowing for m_1\ne m_2 or, respectively, m_{\rm FI}\ne 0,
the smallness of {{w}_1^+}^2-{{w}_2^+}^2 allows to control the rate
of D-parity violating interactions, a feature which we make use of
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[Table: D-parities of the scalar masseigenstates.]In particular, we... | {
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} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
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1cdb15ef8cdca0df818e96c58f87e77cc7c42b59 | subsection | 38 | 39 | Scalar Interaction Terms and | Accordingly, the D-term (REF ) is{Appendix:DParities}.0\endcsname
D\!\!\!&=&\!\!\!-\frac{g}{2}m_{\rm FI}^2 +
\frac{g}{2}
\frac{{{w}_1^+}^4-{{w}_2^+}^4}{{{w}_1^+}^2+{{w}_2^+}^2}
\\
&&
+\frac{g}{\sqrt{2}}{w} H_g
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\left(
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} | 10.1088/1475-7516/2008/09/020 | 0807.1729 | Textures and Semi-Local Strings in SUSY Hybrid Inflation | [
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"Apostolos Pilaftsis"
] | [
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2679af05a17f539d21b3121498671c41f8f78036 | abstract | 0 | 4 | Abstract | We take advantage of the connection between the free carrier optical
conductivity and the glue function in the normal state, to reconstruct from the
infrared optical conductivity the glue-spectrum of ten different high-Tc
cuprates revealing a robust peak in the 50-60 meV range and a broad continuum
at higher energies f... | {
"cite_spans": []
} | 0807.1730 | Observation of a robust peak in the glue function of the high-Tc
cuprates in the 50-60 meV range | [
"E. van Heumen",
"E. Muhlethaler",
"A. B. Kuzmenko",
"D. van der Marel",
"H. Eisaki",
"M. Greven",
"W. Meevasana",
"Z. X. Shen"
] | [
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8222a039e8ab2de3ff6c2d8589ff987e58d34bf8 | subsection | 1 | 4 | Appendix | The inversion of Eq's 1 and 2 allows to extract \tilde{\Pi }(\omega ) from
experimental data of the optical conductivity, or related
optical spectra. The accuracy of the resulting \tilde{\Pi }(\omega ) spectrum
is in practice limited by the convolution with thermal factors
expressed by Eq's 1 and 2 . Microscopic
models... | {
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... | 0807.1730 | Observation of a robust peak in the glue function of the high-Tc
cuprates in the 50-60 meV range | [
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103cbd080b172b8cd76551d5f4d45a9d469320fb | subsection | 2 | 4 | Appendix | As the fitted curves are within the limits
of the experimental noise, further reduction of \chi ^2, while
in principle possible by fitting the statistical noise of the
data, can not improve the accuracy of the \tilde{\Pi }(\omega ) functions.
[Figure: Experimental reflectivity (red and blue lines) and fit curves (black... | {
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} | 0807.1730 | Observation of a robust peak in the glue function of the high-Tc
cuprates in the 50-60 meV range | [
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e1cbfcf04a112020389099bc9e162311c39bae80 | subsection | 3 | 4 | Appendix | A comparison of Fig. REF (a-d) shows
that the MMP model describes better the optical data then the
MFL model but that they give similar results if we add an extra
oscillator to these models. Panels SREF e-f show
the model independent results mentioned above and are very
similar to the modified MMP and MFL model. The mo... | {
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... | 0807.1730 | Observation of a robust peak in the glue function of the high-Tc
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39019cd58aceedec932342ba62a3745521549378 | abstract | 0 | 20 | Abstract | Accretion discs at sub-pc distances around supermassive black holes are
likely to cool rapidly enough that self-gravity results in fragmentation. Here,
we use high-resolution hydrodynamic simulations of a simplified disc model to
study how the outcome of fragmentation depends upon numerical resolution and
cooling time,... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
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dce715a55567ebef5464620823ff44c979cfad91 | subsection | 1 | 20 | Introduction | In recent years the topic of gravitational instabilities in accretion discs has been the subject of a great deal of theoretical and numerical research. Such gravitational instabilities have applications both to accretion disc theory, in terms of the transport of angular momentum, and also to theories of star and planet... | {
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df2af9eea73724fe3060c9525194a26e5d0ca37e | subsection | 2 | 20 | Numerical Method | The simulations presented in this paper use the publicly-available smoothed-particle hydrodynamics (SPH) code gadget2 . We have modified the code to include a simple cooling prescription (discussed below), which is representative of the cooling expected in a real accretion disc. We adopt the standard prescription for t... | {
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... | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
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9535481492733c372752e6035e3a83cf529d6727 | subsection | 3 | 20 | Numerical Method | With this set-up we are able to resolve the disc scale-height properly with only moderate numbers of SPH particles (see Section REF below), and can thus run simulations with much larger particle numbers (“over-resolving” the disc thickness) to study the fragmentation process in detail when the cooling time is short. | {
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} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
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b4d1485997492057fd8fd9f395a3aeb6ecc95296 | subsection | 4 | 20 | Initial Conditions | We adopt initial conditions similar to those that have been adopted in previous studies of disc fragmentation , , . We adopt a surface density profile\Sigma (r) \propto r^{-1}and a disk temperature that scales asT(r) \propto r^{-1/2} \, ,where r is the (cylindrical) radius. The disc sound speed c_s \propto T^{1/2} is n... | {
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cb1a919e31a1eb7f8a68e61919e4f6e8b3bffa25 | subsection | 5 | 20 | Cooling | The principle aim of this study is to investigate the effect of variable cooling rates on the fragmentation properties. At each time-step, we allow the internal energy of the ith particle, u_i, to cool as\left(\frac{du}{dt}\right)_{\mathrm {cool},i} = -\frac{u_i}{t_{\mathrm {cool}}} \, .The cooling time-scale t_{\mathr... | {
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dcf3a3fb01bbd5b4b89bb5071d766e9647353975 | subsection | 6 | 20 | Cooling | Thus, for 2-D collapse we havet_{\mathrm {D}} \propto h \propto \rho ^{-1} \, ,and we see that the cooling time-scale decreases with increasing density \rho . By contrast, in a collapsing spherical clump of mass m and radius h, we have \rho \simeq m/h^3, sot_{\mathrm {D}} \propto h^{-1} \propto \rho ^{1/3} \, ,and ther... | {
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55d17d44f6156bd2cb9fd18022d823434e3dcda7 | subsection | 7 | 20 | Cooling | The results of the MR runs are shown in Figs.REF –REF . Fig.REF shows the evolution of the disc surface density in the four different simulations, and it is clear that the cooling rate has a dramatic effect on the fragmentation process. Slow cooling leads to the formation of larger, more massive fragments with larger s... | {
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09dc460b6ef1e07767424bee8ac80f0be9af61ee | subsection | 8 | 20 | Cooling | The binary fraction is difficult to quantify due to the rapid merging of the binaries that form, but the differences are clearly seen in Fig.REF . With critical cooling (\tau =\infty ) most objects form as singles, and although some binaries form due to dynamical capture events the overall binary fraction is low. Howev... | {
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} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
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1b28a5c1daec0f941153846992ed94584ab053b6 | subsection | 9 | 20 | Cooling | The dotted line denotes the approximate (mass) resolution limit of 10N_{\mathrm {ngb}}m; all of our clumps are above this limit by at least a factor of 5–10. We see clearly that faster cooling results in a smaller characteristic mass, and a somewhat broader mass function.] | {
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b2ff7ff45b6c99424d3f5c1b0edc76e242820e09 | subsection | 10 | 20 | Simulations | The issue of numerical resolution is critical when considering calculations of fragmentation, as insufficient resolution can result in spurious suppression or amplification of fragmentation. We have conducted a number of calculations using a range of numbers of SPH particles for different values of \tau (see Table REF ... | {
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e87e5421e6ca51fa77d3d6cda45503f6ac566495 | subsection | 11 | 20 | Simulations | Consequently our high-resolution simulations act not only as convergence tests, but also provide a means of studying the small-scale fragmentation that may occur in discs with short cooling times.In order to compare the fragmentation in different simulations we must first identify individual fragments (“clumps”) in our... | {
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} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
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"J. Cuadra"
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921cba8a221cdda093fcbf0eed10682d024bd6b7 | subsection | 12 | 20 | Numerical convergence | We first seek to compare our results at difference numerical resolutions, in order to test convergence in our simulations. The non-linear development of gravitational instabilities essentially amplifies seed fluctuations in the density field, and it is not possible to construct identical noise fields at different parti... | {
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... | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
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] | [
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1ade865513e4deee231b4cbc841bb5ffe4152581 | subsection | 13 | 20 | Numerical convergence | Thus in this case, as expected, we see that the LR simulation is slightly under-resolved (by a factor of approximately 2 in particle number), but both resolution requirements are satisfied comfortably in the MR and HR runs. Binary mergers are somewhat more significant in the MR simulation than in the HR simulation (aga... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
"R. D. Alexander",
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"J. Cuadra"
] | [
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5be7c9ed254f927d3b2983da51e7b2b370309498 | subsection | 14 | 20 | Discussion | Our simulations are robust and well-understood from a numerical perspective, but concerns remain when we consider the physical interpretation of our results. The most obviously unphysical aspect of our simulations is our “thin disc approximation”, using an artificial cooling law to allow fragmentation characteristic of... | {
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d27ef60520263f5ed9b4bbe4ea82607d803d50b5 | subsection | 15 | 20 | Discussion | Thus cooling is likely slower than predicted by our simulations in real fragmenting clumps. Models of core-collapse during star formation predict only moderate increases in temperature, however, so the uncertainly due to the temperature dependence of dust opacity is likely small. We note in passing that we also neglect... | {
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short cooling times | [
"R. D. Alexander",
"P. J. Armitage",
"J. Cuadra"
] | [
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] | 2,008 | en | Physics | [
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e9ea4ac1b96c8c3095e6ebcc55950cd438b686e0 | subsection | 16 | 20 | Discussion | Here, a better approach may be to “re-simulate” a small region of our computational domain at much higher resolution in order to study the inter-clump dynamics in more detail, but this is beyond the scope of this paper. | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
"R. D. Alexander",
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"J. Cuadra"
] | [
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cfc3847089e228500e7098ce65d25af6728a7552 | subsection | 17 | 20 | Application to the Galactic Centre | We now consider the implications of our results for the formation of stars near the Galactic Centre (GC). Many young, massive stars are known to exist close to the black hole at the centre of the Galaxy , , , , and many of the stars at \simeq 0.1pc are known to form a coherent ring or disc Note that there is some contr... | {
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... | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
"R. D. Alexander",
"P. J. Armitage",
"J. Cuadra"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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72345d12f1d10e08422df467272493fe1f267d5f | subsection | 18 | 20 | Application to the Galactic Centre | Systems of this type appear to be a plausible outcome of fast cooling in a fragmenting, self-gravitating accretion disc, and we suggest that such systems should be common if the stellar disc at the GC formed via fragmentation of a gaseous accretion disc. | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
"R. D. Alexander",
"P. J. Armitage",
"J. Cuadra"
] | [
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69cc36fe56c3256e7289d50740d24bbbef17e9af | subsection | 19 | 20 | Summary | We have used numerical hydrodynamic simulations to investigate the role of the cooling rate in the fragmentation of gravitationally unstable accretion discs. Our simulations make use of a simple cooling law, designed to mimic the behaviour of radiative cooling in an optically thick, geometrically thin disc. We performe... | {
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} | 10.1111/j.1365-2966.2008.13706.x | 0807.1731 | Binary formation and mass function variations in fragmenting discs with
short cooling times | [
"R. D. Alexander",
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9c43f29a9a2f2c83a97ea59aa85cd81d09e06729 | abstract | 0 | 21 | Abstract | We prove the impossibility of resonant decay of a metastable vacuum in a
theory of a scalar field coupled to a gauge field. Our result extends to gauge
theories of scalar fields a recent no go theorem for resonant tunneling in a
pure scalar field theory. | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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9807edc2c555b7e56ba12b0db4296f289a161e4f | subsection | 1 | 21 | Introduction | Understanding in detail the mobility patterns in the landscape is a challenging
problem. In fact rather little is known about it and thus even a study of what may seem
non generic paths is of interest. For example Tye ,
has suggested to apply the
phenomena of rapid tunneling ,,,, to shed a different light on the issue ... | {
"cite_spans": [
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... | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
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] | 2,008 | en | Physics | [
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2a9d8e1e8845345f482ecf00a76273a60143cce7 | subsection | 2 | 21 | Resonant tunneling: From QM to QFT | Quantum interference is typical in systems with a
degenerate set of classical trajectories.
In the double barrier potential V(x) in figure REF , in the semiclassical regime
a point particle with wave function localized
around the false vacuum x = x_+ will decay to the true vacuum
localized around x = x_-. The tunneling... | {
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"raw": "L.Chang, L. Esaki and R. Tsu, Appl. Phys. Lett. 24 (1974) 593.",
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"doi":... | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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53d0a342e0ddc77a1af91b2617afef9361f8ac2e | subsection | 3 | 21 | Resonant tunneling: From QM to QFT | In the semiclassical regime both S_{I}
and S_{III} are large numbers in \hbar units,
thus the condition S_I - S_{III} \sim 0 requires a large amount
of fine tuning for the shape of the potential V(x).[Figure: Double barrier decay in QFT.The field in a false vacuum \varphi = \varphi _{+} can decay trough quantum tunneli... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 563,
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"raw": "S. R. Coleman, “The Fate Of The False Vacuum. 1. Semiclassical Theory,” Phys. Rev. D 15, 2929 (1977) [Erratum-ibid. D 16, 1248 (1977)].",
"source_ref_id": "bb216ff9780c70d6d7b555f677c26491296c... | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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a65e290290a376177ea0cb392357a338795c6221 | subsection | 4 | 21 | Resonant tunneling: From QM to QFT | If this happens one is forced
to analytic continue the solution to real time t_E \rightarrow it_E = t at the point
\tilde{t}_E where \partial _{t_E}\varphi (\tilde{t}_E , \vec{x})=0.
Analytic continuation in \tilde{t}_E = \tilde{t} requires
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"s... | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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aeee6470f0ea217bee749c21bf9c39d8c9fd42de | subsection | 5 | 21 | Vacuum decay in a landscape potential and the question of quantum interference | As discussed at the end of the previous section,
in order to have quantum interference
in vacuum decay the existence of a
Lorentzian solution \varphi (t, \vec{x}) defined on a time interval [t_1 , t_2 ] with non-vanishing action satisfying eq. (REF ) is required.
Analytic continuation of \varphi to Euclidean signature
... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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47035ac5d279f2b3981d88c7f3c52ee4494217ae | subsection | 6 | 21 | No resonant tunneling in a scalar field theory | Let us consider a scalar field theory in D = 1 + d space-time dimensions
with Lagrangian\mathcal {L} = \frac{1}{2} \partial _{\mu } \varphi \partial ^{\mu } \varphi - V(\varphi ),where V(\varphi ) is a generic potential with various metastable vacua.A necessary condition for the field \varphi to have non-vanishing acti... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
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ade43006ecf6c823bf1106af32cd9b00c957f4e4 | subsection | 7 | 21 | No resonant tunneling in a scalar field theory | Therefore I_{ii} can be computed at x_{i} = \infty ,
where it depends only on V(\varphi _+), since all the field derivatives
go to zero at infinityI_{ii} &=& \lim _{x_{i} \rightarrow \infty }
\int _{t_1}^{t_2}dx_0 \int \prod _{j \ne i}dx_{j} \cdot \\
&& \left( \frac{1}{2}(\partial _{0}\varphi )^2 +\frac{1}{2}(\partial ... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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0.00995364598929882,
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0.019388634711503983,
0.0417671762406826,
0.02567354217171669,
0.01926659792661667,
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-0.027397315949201584,
0.029548218473792076,
-0.0123... |
2ed5cfb6832db278b80b197770627889fd395f46 | subsection | 8 | 21 | No resonant tunneling in a scalar field theory | This shows that an intermediate analytic continuation to Lorentzian signature
is impossible, and the full tunneling event is described by instanton fields in Euclidean signature.
Thus one concludes that for the decaying of a metastable vacuum in a pure scalar field theory with a multi-vacua
potential there is no quantu... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 996,
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"raw": "P. M. Saffin, A. Padilla and E. J. Copeland, “Decay of an inhomogeneous state via resonant tunnelling,” arXiv:0804.3801 [hep-th].",
"source_ref_id": "9a8362e0363e04b590e76c8db132bec353b88354",... | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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0.... |
b11f0026dfd96f8726dc0012fd40a8ca2ac00d9a | subsection | 9 | 21 | No resonant tunneling in a scalar field theory | This is achieved when there is a large enough region of Euclidean space where the field acquires values
in classically allowed regions where V(\varphi ) < 0, such
as the regions \varphi _1 < \varphi < \varphi _2 and \varphi > \varphi _3
for the potential in figure (REF ). | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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-0... |
70a45f5214f1b9f59adf8ad34bb10c7ac9a7b5b1 | subsection | 10 | 21 | No quantum interference in the decay of a scalar field coupled to a gauge field | We study now whether a theory of a scalar field coupled to a gauge field
admits non-constant classical field solutions of Lorentzian time signature that can be
analiticaly continued to Euclidean signature in two separate occasions.We consider the Lagrangian\mathcal {L} = -\frac{1}{4}F^{a}_{\mu \nu }F^{a \mu \nu } + \fr... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
-0.07429877668619156,
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0.... |
25f5d587056be60534b6405087db88c70b0c67de | subsection | 11 | 21 | No quantum interference in the decay of a scalar field coupled to a gauge field | The Lorentzian classical solutions \varphi (t,\vec{x}) and A_{\mu }^{a}(t,\vec{x})
are then defined on the interval [t_1 , t_2 ], they dominate the path integral and
have both vanishing time derivative at t=t_1 and t=t_2, as required by
analytic continuation.
In order to check if there is a degeneracy of Lorentzian mot... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
-0.034994084388017654,
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0... |
dabbb8d8fc7318fb636d7f5e26505b23ae0061b5 | subsection | 12 | 21 | No quantum interference in the decay of a scalar field coupled to a gauge field | The conclusion will be that field paths describing the full tunneling
event are purely Euclidean and therefore there is no resonant decay.The overall T_{00} space integral is set to be equal to the total false vacuum energy V(\varphi _+)=0
that is our initial condition in time, therefore the space integral of T_{00} va... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
-0.04790598899126053,
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0... |
286d43501f8869589c8a2e57a7661b453ef78aa1 | subsection | 13 | 21 | Conclusions | We studied whether in a theory of a scalar field coupled to a gauge field
a homogeneous metastable vacuum can decay in a resonant fashion.
The answer turns out to be negative and thus our result
generalizes the no go theorem for resonant tunneling in a pure scalar field theory .
The proof follows the line of ,
appropri... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 279,
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"raw": "E. J. Copeland, A. Padilla and P. M. Saffin, “No resonant tunneling in quantum field theory,” arXiv:0709.0261 [hep-th].",
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"st... | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
-0.02044931799173355,
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ad2f1d5e229341b9e0f80830e7edbdd0748c9d71 | subsection | 14 | 21 | Tunneling through one barrier potential | Let us consider the tunneling problem represented in figure REF ,
the semiclassical wave function for a particle of unit mass with energy
E in region I is given by\Psi _{I}(x) = \alpha _{I}^{R}\frac{e^{iS_{0}(x)/\hbar }}{ (2(E - V(x)))^{1/4}} + \alpha _{I}^{L}\frac{e^{-iS_{0}(x)/\hbar }}{(2(E - V(x)))^{1/4}},whereS_{0}... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1284,
"openalex_id": "",
"raw": "E. Merzbacher, Chapter 7, Quantum Mechanics, 2nd Edition, John Wiley, 1970.",
"source_ref_id": "d40e2acfd88d518557f973b61b0d7b4e9e9a5102",
"start": 920
}
]
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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0.013805748894810677,
-0... |
117904930958418b21b0ce77b16fd6a64adf855d | subsection | 15 | 21 | Tunneling through one barrier potential | It turns out that the correct wave function inside the barrier
is given by summing the two contributions:\Psi _{II}(x) = e^{-\Theta } \left( \alpha _{I}^{R}e^{-i\pi /4} + \alpha _{I}^{L}e^{i\pi /4}\right) \frac{e^{-S_{0}^{^{\prime }}(x)/\hbar }}{(2(V(x) - E))^{1/4}} \\
+ e^{\Theta } \left( \alpha _{I}^{R}e^{i\pi /4} + ... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
0.037481408566236496,
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e4e69c0b94b3afd81b68cb2b75ba0571d32d1c79 | subsection | 16 | 21 | Tunneling through one barrier potential | The wave function in region III x > x_2 outside the barrier
is then given by\Psi _{III}(x) = \alpha _{III}^{R}\frac{e^{iS_{0}^{^{\prime \prime }}(x)/\hbar }}{ (2(E - V(x)))^{1/4}} + \alpha _{III}^{L}\frac{e^{-iS_{0}^{^{\prime \prime }}(x)/\hbar }}{(2(E - V(x)))^{1/4}},withS_{0}^{^{\prime \prime }}(x) = \frac{1}{\hbar }... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
0.0007371468236669898,
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b54dcba1489ff9151c2a7ee9587a525241ba3338 | subsection | 17 | 21 | Tunneling through a double barrier potential | For a double barrier tunneling (fig. | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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... |
a0c29369c40ce8117f3049f2390047386cd49c1d | subsection | 18 | 21 | Tunneling through a double barrier potential | REF )
one can compute the full "rotation" matrix which rotates the wave function of region I
into the wave function of region V\vec{\alpha }_{out} = \mathcal {R}_{\Theta _1}\mathcal {R}_{\delta }\mathcal {R}_{\Theta _2}\vec{\alpha }_{in},where \mathcal {R}_{\Theta _1}\mathcal {R}_{\delta }\mathcal {R}_{\Theta _2}
is gi... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
-0.013429543934762478,
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97952ea0a9ad64ad5037303f793a58953103c401 | subsection | 19 | 21 | Tunneling through a double barrier potential | For \delta = 0 the two hyperbolic
angles \Theta _1 and \Theta _2
sum together giving the sum of the rotations.
The term in \sin \delta is the effect of the quantum interference,
and it depends on the difference between \Theta _1 and \Theta _2.The tunneling probability can be closed to one in the resonant condition\delt... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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0.00... |
04fea8e508e65cb784779f62d69f9dc1ee9ac19c | subsection | 20 | 21 | Tunneling through | Given N barriers separated by N-1 classically allowed regions,
the matrix which connects the wave functions on the two regions extending to infinity
is given by \mathcal {R}_N = \prod _{k=1}^{N}\mathcal {R}_{\Theta _{k}}\mathcal {R}_{\delta _{k}}\mathcal {R}_N = \prod _{k=1}^{N}
\begin{pmatrix}
\cosh \Theta _k & -i \si... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/09/077 | 0807.1732 | Absence of resonant decay for metastable vacua in gauge theories of
scalar fields | [
"M. Cardella",
"S. Elitzur",
"E. Rabinovici"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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ecf7e9f7eb2bd5270dd0260b27e33f1a998d0ba8 | abstract | 0 | 43 | Abstract | The nonlinear perturbation theory of gravitational instability is extended to
include effects of both biasing and redshift-space distortions, which are
inevitable in predicting observable quantities in galaxy surveys. The precise
determination of scales of baryon acoustic oscillations is crucial to
investigate the natu... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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a0fbccd623b111ecbc9313ca436bf083b129a1b5 | subsection | 1 | 43 | Introduction | The nonlinear perturbation theory of gravitational instability has
recently attracted renewed interest. As precision measurements of the
large-scale structure of the universe become possible, theoretically
accurate modeling is essential to interpret the observational data. It
is recognized that the linear perturbation ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 825,
"openalex_id": "",
"raw": "P. J. E. Peebles and J. T. Yu, 162, 815 (1970); R. A. Sunyaev and Y. B. Zel'dovich, Astrophys. Space Sci.7, 3 (1970); J. R. Bond and G. Efstathiou, Astrophys. J. Letters, 285, L45 (1984); J. R. Bond... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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... |
f72c81407d9f6e29034c3968c4f7976032e2865c | subsection | 2 | 43 | Introduction | Extending the
linear formula of Eq. (REF ) to include nonlinear effects is
far from trivial. A straightforward application of the nonlinear
perturbation theory , , , with a local biasing
scheme has been studied so far
, , , . In the local biasing scheme, the
number density of biased objects is a local function of the s... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 227,
"openalex_id": "",
"raw": "R. Juszkiewicz, Mon. Not. R. Astron. Soc., 197, 931 (1981); E. T. Vishniac, Mon. Not. R. Astron. Soc., 203, 345 (1983); J. N. Fry, , 279, 499 (1984); B. Jain and E. Bertschinger, , 431, 495 (1994)."... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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... |
b3fa658ddd25c7fb60cf21a86d4d6e7725d01c7f | subsection | 3 | 43 | Introduction | However, the dynamical evolution of haloes is more naturally
described in the Lagrangian picture . It is not
straightforward to obtain an analytically useful formalism which
combines the LPT and the halo approach. A main obstacle is that the
observable quantities reside in Eulerian space, while the calculations
in LPT ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 98,
"openalex_id": "",
"raw": "P. Catelan, F. Lucchin, S. Matarrese, and C. Porciani, Mon. Not. R. Astron. Soc., 297, 692 (1998); P. Catelan, S. Matarrese, and C. Porciani, Astrophys. J. Letters, 502, L1 (1998).",
"source_re... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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f4e5c7717f1ffc4420a77b62ce4e4b0258d62bee | subsection | 4 | 43 | Nonlinear power spectrum with a local Lagrangian bias | In this section, we develop a method to track nonlinear evolution of
the Lagrangian bias. Our method in this section is not restricted to
the halo bias model, and is applicable to any bias defined by a local
function of linear density field in Lagrangian space.In the Lagrangian approach to track dynamical evolution of
... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 2367,
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"raw": "H. J. Mo and S. D. M. White, Mon. Not. R. Astron. Soc., 282, 347 (1996).",
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"start": 2263
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... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.022751973941922188,
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0.007442840840667486,
-0.00232326495461165... |
562fe1071410a568f77533ff2b81f174918cfe41 | subsection | 5 | 43 | Nonlinear power spectrum with a local Lagrangian bias | The locality of bias in
Lagrangian space does not mean locality in Eulerian space, because of
evolutionary effects. Therefore our biasing scheme does not fall into
the category of the local biasing scheme in a usual context of EPT.
The local Lagrangian bias is nonlocal in Eulerian space.Thus, we introduce a Lagrangian ... | {
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distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.048073671758174896,
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0... |
27fb54b344eebf31849acc369600164cec7e52f2 | subsection | 6 | 43 | Nonlinear power spectrum with a local Lagrangian bias | Our convention of the power spectrum is
given by\left\langle \tilde{\delta }_{\rm obj}({k})
\tilde{\delta }_{\rm obj}({k}^{\prime })
\right\rangle =
(2\pi )^3 \delta ^3_{\rm D}({k} + {k}^{\prime }) P_{\rm obj}({k}),where\tilde{\delta }_{\rm obj}({k}) =
\int d^3x\, e^{-i{k}\cdot {x}}
\left[
\frac{\rho ^{\rm E}_{\rm obj}... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 788,
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"raw": "S.-K. Ma, Statistical Mechanics (World Scientific, Singapore, 1985), Sec. 12",
"source_ref_id": "00e22d8af5de40b738a83d3eb15345c838aaa36e",
"start": 507
},
{
"arxiv_id": ""... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.001... |
b0d3038391cd55cf7191452ec12b91598a062cae | subsection | 7 | 43 | Nonlinear power spectrum with a local Lagrangian bias | (REF ) thus reduces to\left\langle e^{i[
\lambda _1\delta _R({q}_1)
+ \lambda _2\delta _R({q}_2) ]
-i{k}\cdot [
{\Psi }({q}_1) - {\Psi }({q}_2) ]
}
\right\rangle \\
=
\exp \left[
\sum _{n_1 + n_2 + m_1 + m_2 \ge 1}
\frac{i^{n_1 + n_2 + m_1 + m_2}}{n_1!n_2!m_1!m_2!}
{\lambda _1}^{n_1} {\lambda _2}^{n_2}
B^{n_1 n_2}_{m_1... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.056086890399456024,
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0.022916896268725395,
0.02396966889500618,
0.01139741763472557,
0.02058248408138752,
0.0230084415525198,
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0.045070912688970566,
-0.027250049635767937,
0.041... |
1c627b65cde4e6faa1f7c4b8236bfc67bc0ec214 | subsection | 8 | 43 | Nonlinear power spectrum with a local Lagrangian bias | (REF ) is symmetric with respect to its
indices:B^{n_1 n_2}_{m_1 m_2}({k},{q}) =
B^{n_2 n_1}_{m_2 m_1}({k},{q}).When the initial density field is random Gaussian, which is assumed
throughout this paper, the Equation (REF ) of m_1=m_2=0
survives only when n_1 + n_2 = 2:B^{n_1 n_2}_{00}({k}, {q})
=
{\left\lbrace \begin{a... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.057279519736766815,
0.03176770359277725,
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0.015540541149675846,
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0.015151455998420715,
0.013579854741692543,
-0... |
5ec8abeac5bdc294d3ce5bc416e4af57947c46fa | subsection | 9 | 43 | Nonlinear power spectrum with a local Lagrangian bias | (REF ), we obtain an expression,P_{\rm obj}({k}) =
\exp \left[
2 \sum _{m=1}^\infty \frac{(-1)^m}{(2m)!}
A_{2m}({k})
\right]
\int d^3q\, e^{-i{k}\cdot {q}}
\exp \left[
\sum _{m_1, m_2 \ge 1}^\infty \frac{ i^{m_1 + m_2}}{m_1!m_2!}
B_{m_1 m_2}({k}, {q})
\right]
\\ \times \int _{-\infty }^\infty \frac{d\lambda _1}{2\pi } ... | {
"cite_spans": [
{
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"doi": "",
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"raw": "T. Matsubara, , 77, 063530 (2008) (paper I).",
"source_ref_id": "4326df28d4135c560a4a2389e1317f62fd6e035d",
"start": 938
}
]
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.0690288245677948,
0.021071797236800194,
-0.04418821632862091,
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0.0185... |
c20ef1cc4f6c0fc0168407e847989a4086a07c51 | subsection | 10 | 43 | Nonlinear power spectrum with a local Lagrangian bias | In the integrand of \lambda _1 and \lambda _2, we expand
the last exponential factor, keeping the exponential prefactor which
involves \sigma _R^2. In a large-scale limit, \sigma _R^2 \gg \xi _R(|{q}|) because |{q}| is large, and \sigma _R^2 \gg B^{n_1 n_2}_{m_1 m_2} (m_1 + m_2 \ge 1) because |{k}| is
small. Therefore,... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0... |
be7c0a47aa51aa094996e663e41f0eab26eeb8b1 | subsection | 11 | 43 | Nonlinear power spectrum with a local Lagrangian bias | In our derivation, we have used an approximation \sigma _R^2
\gg \xi _R(|{q}|), which means our equations are valid on larger
scales than the smoothing radius of the Lagrangian bias: k \ll R^{-1}. In particular, the smoothing kernel W(kR) in final
expressions of our perturbation theory is replaced by unity, for
consist... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.009907778352499008,
0.031851332634687424,
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0.010167104192078114,
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0.04301760718226433,
-0.017512131482362747,
... |
5413e94d7731a4a58eba6fd7ddbef9851b682012 | subsection | 12 | 43 | Biased power spectrum from Lagrangian perturbation
theory | We evaluate the general Eq. (REF ) via the LPT as outlined in
the previous section. Details of derivations by the one-loop
perturbation theory are given in the Appendix. In this subsection, we
summarize basic assumptions made in the derivations.As explained above, we need to evaluate the cumulants
B_{m_1m_2}^{n_1n_2}({... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1074,
"openalex_id": "",
"raw": "F. Bernardeau, S. Colombi, E. Gaztañaga, and R. Scoccimarro, Phys. Rep., 367, 1 (2002).",
"source_ref_id": "b93944a6cfe6a7a397e6130a748d56e680d26e26",
"start": 945
},
{
"a... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.058336302638053894,
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-0.004811753053218126,
-0.016698041930794716,... |
f9584613b90a5c6d8fba16c37f496be99ec9db3b | subsection | 13 | 43 | Biased power spectrum from Lagrangian perturbation
theory | With those
approximations, order-by-order linear transformations of displacement
fields become particularly simple: {\Psi }^{{\rm s}(n)} = R^{(n)}
{\Psi }^{(n)}, where R^{(n)} is a 3\times 3 matrix whose
components are given by Eq. (REF ).Keeping the one-loop LPT exact, the integrand of Eq. (REF )
turns out to be a str... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.00949176400899887,
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0.005772121716290712,
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0... |
caca733fe014f0a70b68984dde634c3ed06e5b28 | subsection | 14 | 43 | The linear power spectrum in real space and in redshift space | Expanding Eq. (REF ) and keeping only linear terms in P_{\rm L}(k), we obtain the biased power spectrum in linear perturbation
theory. The result in real space is simply given by a linear term of
Eq. (REF ) with a substitution f=0,P_{\rm obj}(k) =
\left( 1 + \langle F^{\prime } \rangle \right)^2
P_{\rm L}(k).Since the ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 768,
"openalex_id": "",
"raw": "H. J. Mo and S. D. M. White, Mon. Not. R. Astron. Soc., 282, 347 (1996).",
"source_ref_id": "ab47d1498ac4381a82e7bccfbe76d88412e0a0e6",
"start": 587
},
{
"arxiv_id": "",
... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.01581171341240406,
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0.01900... |
fea64de31b8741aeb7408c9f2c23bb897311162b | subsection | 15 | 43 | The linear power spectrum in real space and in redshift space | Again, it is
interesting to notice that we have derived the Kaiser's formula in the
presence of any nonlinear local bias in Lagrangian space: the Kaiser's
formula with a scale-independent bias is a general consequence of a
large-scale limit even in this framework. | {
"cite_spans": []
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.03316532075405121,
0.048237692564725876,
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0... |
f3cc72dbc87e1649ebbbe1f745f94f91da794f92 | subsection | 16 | 43 | One-loop corrections to the biased power spectrum | The formal expression of Eq. (REF ) is evaluated by applying
the LPT. The derivation of one-loop corrections to the power spectrum
is detailed in the Appendix. The power spectrum in real
space with one-loop corrections is given by putting f=0 in
Eq. (REF ). The result is&P_{\rm obj}(k) =
\exp \left[-\left(k/k_{\rm NL}\... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1617,
"openalex_id": "",
"raw": "Y. Suto, M. Sasaki, , 66, 264 (1991); N. Makino, M. Sasaki, and Y. Suto, , 46, 585 (1992).",
"source_ref_id": "b71f5501616bb8d6c8f4fc76f4324763512db779",
"start": 1442
},
{
... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.07410801947116852,
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0.003145699156448245,
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0.018771182745695114,
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0.013... |
a1d28505e6d29152315d8d47bfdffca5b5614796 | subsection | 17 | 43 | One-loop corrections to the biased power spectrum | (REF ):&P^{\rm (s)}_{\rm obj}({k}) =
\exp \left\lbrace -\left[1 + f(f+2)\mu ^2\right]
\left(k/k_{\rm NL}\right)^2 \right\rbrace
\\
&\quad \times \left[
\left( 1 + \langle F^{\prime } \rangle + f\mu ^2 \right)^2
P_{\rm L}(k)
+ \sum _{n,m} \mu ^{2n} f^m E_{nm}(k)
\right],where E_{nm}(k) is given by Eqs. (REF )–(REF ).
W... | {
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{
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"doi": "",
"end": 470,
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"raw": "T. Matsubara, , 77, 063530 (2008) (paper I).",
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"start": 319
},
{
"arxiv_id": "",
"doi": "",
"end": ... | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.0... |
47f3761fa069fabfa456f301ad30fb3804035bb1 | subsection | 18 | 43 | One-loop corrections to the biased power spectrum | (REF )–(REF ) in the Appendix. All
of these functions but Q_{13}(k) vanish in a large-scale limit k
\rightarrow 0. The function Q_{13}(k) contributes only when
\langle F^{\prime \prime }\rangle \ne 0. Thus, the one-loop contributions are
present even in a large-scale limit through Q_{13}(k) when \langle F^{\prime \prim... | {
"cite_spans": [
{
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"doi": "",
"end": 1288,
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"raw": "R. J. Scherrer and D. H. Weinberg, , 504, 607 (1998)",
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"start": 1212
}
]
} | 10.1103/PhysRevD.78.083519 10.1103/PhysRevD.78.109901 | 0807.1733 | Nonlinear perturbation theory with halo bias and redshift-space
distortions via the Lagrangian picture | [
"Takahiko Matsubara"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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