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We extend the public CppTransport code to calculate the statistical properties of fluctuations in multiple-field inflationary models with curved field space. Our implementation accounts for all physical effects at tree-level in the 'in-in' diagrammatic expansion.
We measure the evolution of the X-ray luminosity-temperature (L_X-T) relation since z~1.5 using a sample of 211 serendipitously detected galaxy clusters with spectroscopic redshifts drawn from the XMM Cluster Survey first data release (XCS-DR1). This is the first study spanning this redshift range using a single, larg...
We extend the method of Flow Equations to the Effective Field Theory framework of inflation, in order to investigate the observable predictions of a very broad class of inflationary models. Focusing our attention on the gravitational-wave sector, we derive a general expression for the consistency relation for effectiv...
The physical processes affecting the thermalization of cosmic microwave background spectral distortions are very simple and well understood. This allows us to make precise predictions for the distortions signals caused by various energy release scenarios, where the theoretical uncertainty is largely dominated by the p...
We present measurements of the specific star-formation rate (SSFR)-stellar mass relation for star-forming galaxies. Our deep spectroscopic samples are based on the Redshift One LDSS3 Emission line Survey, ROLES, and European Southern Observatory, ESO, public spectroscopy at z=1, and on the Sloan Digital Sky Survey (SD...
We study the $TT\mu$ bispectrum, generated by correlations between Cosmic Microwave Background temperature (T) anisotropies and chemical potential ($\mu$) distortions, and we analyze its dependence on primordial local trispectrum parameters $g_{\rm NL}$ and $\tau_{\rm NL}$. We cross-check our results by comparing the ...
Modifications to General Relativity typically introduce a scalar degree of freedom. Experimental constraints require that the "fifth" force produced by this field must be screened in high density environments.
We examine the effects of photon-axion mixing on the CMB. We show that if there are very underdense regions between us and the last scattering surface which contain coherent magnetic fields (whose strength can be orders of magnitude weaker than the current bounds), then photon-axion mixing can induce observable deviat...
We study the ability of future weak lensing (WL) surveys to constrain primordial non-Gaussianity of the local type. We use a large ensemble of simulated WL maps with survey specifications relevant to Euclid and LSST.
We consider an appealing scenario for the production of purely gravitational dark matter in the background of warm inflation, a mechanism that maintains stable thermal bath during inflation. Through systematic investigation of various gravitational production channels, we reveal distinctive features compared to the st...
Primordial black holes (PBHs) are black holes which may have formed very early on during the radiation dominated era in the early universe. We present here a method by which the large scale perturbations in the density of primordial black holes may be used to place tight constraints on non-gaussianity if PBHs account ...
The ESA Planck satellite, launched on May 14th, 2009, is the third generation space mission dedicated to the measurement of the Cosmic Microwave Background (CMB), the first light in the Universe. Planck observes the full sky in nine frequency bands from 30 to 857 GHz and is designed to measure the CMB anisotropies wit...
We examine how much information measured broad-line widths add to virial BH mass estimates for flux limited samples of quasars. We do this by comparing the BH mass estimates to those derived by randomly reassigning the quasar broad-line widths to different objects and re-calculating the BH mass.
We explore the prospects of using the hyperfine transition of 3He+ as a probe of the intergalactic medium. The emission signal from ionized regions during reionization is expected to be anti-correlated with 21cm maps.
The possibility of explanation of accelerated expansion of the Universe by tachyonic scalar fields which homogeneously fill the world is discussed. The dependences of potential and kinetic term on scale factor are deduced for the case of quintessential and phantom dark energy with generalized linear barotropic equatio...
AMiBA is the largest hexapod astronomical telescope in current operation. We present a description of this novel hexapod mount with its main mechanical components -- the support cone, universal joints, jack screws, and platform -- and outline the control system with the pointing model and the operating modes that are ...
We have combined X-ray observations from Chandra with Sunyaev-Zel'dovich (SZ) effect data from Planck and Bolocam to measure intra-cluster medium pressure profiles from 0.03R$_{500}$ $\le$ R $\le$ 5R$_{500}$ for a sample of 21 low-$z$ galaxy clusters with a median redshift $\langle z \rangle = 0.08$ and a median ma...
In the next decade, radio telescopes like the Square Kilometer Array (SKA) will explore the Universe at high redshift, and particularly during the Epoch of Reionisation (EoR). The first structures emerged during this epoch, and their radiations have reionised the previously cold and neutral gas of the Universe creatin...
Most of the visible matter in the Universe is in a gaseous state, subject to hydrodynamic forces and galaxy formation processes that are much more complex to model than gravity. These baryonic effects can potentially bias the analyses of several cosmological probes, such as weak gravitational lensing.
This paper is a guide to the installation and use of the Python package PYESSENCE. PYESSENCE is designed to evolve linear perturbations to Coupled Quintessence models with a arbitrary number of cold dark matter (CDM) fluids and dark energy (DE) scalar fields as dictated by a given model.
A number of dwarf spheroidal (dSph) galaxies are known to contain a more extended, metal-poor population with a flattish velocity dispersion profile, and a more concentrated, metal-rich population with a velocity dispersion declining with radius. The two populations can be modelled with Michie-King distribution functi...
Weak-lensing measurements of the averaged shear profiles of galaxy clusters binned by some proxy for cluster mass are commonly converted to cluster mass estimates under the assumption that these cluster stacks have spherical symmetry. In this paper we test whether this assumption holds for optically selected clusters ...
The cosmic star formation rate, AGN activity, galaxy growth, mass assembly and morphological differentiation all culminate at redshift $\sim 2$. Yet, the redshift interval $1.4\lsim z\lsim 3$ is harder to explore than the closer and the more distant Universe.
We revisit for 714 SNeIa the discrepancy between the red-shift associated to the distance modulus $\mu$ and the spectroscopic red-shift. Previous work has shown that the total red-shift $z$ might be a combination of the expansion red-shift $z_{\rm C}$ and of a static, blue or red shift $z_{\rm LSV}(r)$, $r$ being the ...
Small and intermediate mass black holes should be expected in galactic nuclei as a result of stellar evolution, minor mergers and gravitational dynamical friction. If these minor black holes accrete as X-ray binaries or ultra-luminous X-ray sources, and are associated with star formation, they could account for observ...
Hydrostatic equilibrium (HE) is often used in observations to estimate galaxy clusters masses. We use a set of almost 300 simulated clusters from The Three Hundred Project, to estimate the cluster HE mass and the bias deriving from it.
Context: In the past decade, sensitive, resolved Sunyaev-Zel'dovich (SZ) studies of galaxy clusters have become common. Whereas many previous SZ studies have parameterized the pressure profiles of galaxy clusters, non-parametric reconstructions will provide insights into the thermodynamic state of the intracluster...
Of the many ways of detecting high redshift galaxies, the selection of objects due to their redshifted Ly-alpha emission has become one of the most successful. But what types of galaxies are selected in this way?
We describe the construction and general features of VIPERS, the VIMOS Public Extragalactic Redshift Survey. This `Large Programme' has been using the ESO VLT with the aim of building a spectroscopic sample of ~100,000 galaxies with i_{AB}<22.5 and 0.5<z<1.5.
We study the sensitivity of weak lensing surveys to the effects of catastrophic redshift errors - cases where the true redshift is misestimated by a significant amount. To compute the biases in cosmological parameters, we adopt an efficient linearized analysis where the redshift errors are directly related to shifts i...
From previous studies of the effect of primordial magnetic fields on early structure formation, we know that the presence of primordial magnetic fields during early structure formation could induce more perturbations at small scales (at present 1-10 Mpc/h) as compared to the usual LCDM theory. Matter power spectrum ov...
Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to ...
The existence of a cosmic neutrino background can be probed indirectly by CMB experiments, not only by measuring the background density of radiation in the universe, but also by searching for the typical signatures of the fluctuations of free-streaming species in the temperature and polarisation power spectrum. Previo...
Cosmological observations, e.g., cosmic microwave background, have precisely measured the spectrum of primordial curvature perturbation on larger scales, but smaller scales are still poorly constrained. Since primordial black holes (PBHs) could form in the very early Universe through the gravitational collapse of prim...
In the present paper, we study how the dark matter density profiles of dwarfs galaxies in the mass range $10^8-10^{10} M_{\odot}$ are modified by the interaction of the dwarf in study with the neighboring structures, and by changing baryon fraction in dwarfs. As already shown in Del Popolo (2009), the slope of density...
The strongly lensed Supernova (SN) Encore at a redshift of $z = 1.949$, discovered behind the galaxy cluster MACS J0138$-$2155 at $z=0.336$, provides a rare opportunity for time-delay cosmography and studies of the SN host galaxy, where previously another SN, called SN Requiem, had appeared. To enable these studies, w...
We report 250 GHz (1.2 mm) observations of a sample of 20 QSOs at redshifts 5.8<z<6.5 from the the Canada-France High-z Quasar Survey (CFHQS), using the Max-Planck Millimeter Bolometer (MAMBO) array at the IRAM 30-metre telescope. A rms sensitivity <~ 0.6 mJy was achieved for 65% of the sample, and <~ 1.0 ...
Using N-body simulations and galaxy formation models, we study the galaxy stellar mass correlation and the two-point auto-correlation. The simulations are run with cosmological parameters from the WMAP first, third and seven year results, which mainly differ in the perturbation amplitude of \sigma_{8}.
We show that gravitational waves have the potential to unravel the microphysical properties of dark matter due to the dependence of the binary black hole merger rate on cosmic structure formation, which is itself highly dependent on the dark matter scenario. In particular, we demonstrate that suppression of small-scal...
High sensitivity observations of radio halos in galaxy clusters at frequencies lower than 330 MHz are still relatively rare, and very little is known compared to the classical 1.4 GHz images. The few radio halos imaged down to 150-240 MHz show a considerable spread in size, morphology and spectral properties.
According to a popular scenario supported by numerical models, the mass assembly and growth of massive galaxies, in particular the Early-Type Galaxies (ETGs), is, below a redshift of 1, mainly due to the accretion of multiple gas--poor satellites. In order to get observational evidence of the role played by minor dry ...
We present the preliminary analysis of clustering of a sample of 1157 radio-identified galaxies from Machalski & Condon (1999). We found that for separations $2-15 h^{-1}$Mpc their redshift space autocorrelation function $\xi
Radio halos and radio relics are diffuse synchrotron sources that extend over Mpc-scales and are found in a number of merger galaxy clusters. They are believed to form as a consequence of the energy that is dissipated by turbulence and shocks in the intra-cluster medium (ICM).
We report on our observations of the 79 and 119um doublet transitions of OH for 24 local (z<0.262) ULIRGs observed with Herschel-PACS as part of the Herschel ULIRG Survey (HERUS). Some OH119 profiles display a clear P-Cygni shape and therefore imply outflowing OH gas, other profiles are predominantly in absorption ...
We investigate the emergence of large, localized, pseudo-stable configurations (oscillons) from inflaton fragmentation at the end of inflation. We predict the number density of large oscillons, and the conditions necessary for their emergence in a class of inflationary models.
Context. Time delay lensing is a powerful tool to measure the Hubble constant $H_0$.
Under the commonly used assumption that clumped objects can be well described by a spherical top-hat matter density profile, we investigate the evolution of the cosmic growth index in clustering dark energy (CDE) scenarios on sub-horizon scales. We show that the evolution of the growth index $\gamma(z)$ strongly depen...
The large-scale distribution of neutral hydrogen in the Universe will be luminous through its 21 cm emission. Here, for the first time, we use the auto-power spectrum of 21 cm intensity fluctuations to constrain neutral hydrogen fluctuations at z~0.8.
Using new, highly accurate photometric redshifts from the MUSYC medium-band survey in the Extended Chandra Deep Field South (ECDF-S), we fit synthetic stellar population models to compare AGN host galaxies to inactive galaxies at 0.8 < z < 1.2. We find that AGN host galaxies are predominantly massive galaxies on...
The quasar sample of the fourteenth data release of the Sloan Digital Sky Survey (SDSS-IV DR14) is used to determine the cosmic homogeneity scale in the redshift range $0.80<z<2.24$. We divide the sample into 4 redshift bins, each one with $N_{\rm q} \geq 19,000$ quasars, spanning the whole redshift coverage of ...
IC 3418 is a dwarf irregular galaxy falling into the Virgo cluster, and a 17 kpc long trail is seen behind the galaxy, which is considered to have formed due to ram pressure stripping. The trail contains compact knots and diffuse blobs of ultraviolet and blue optical emission and, thus, it is a clear site of recent st...
Small-field inflation typically requires rather special initial conditions to commence. It is proposed that in models where the inflaton is an axionlike field, with a periodic contribution to the potential, there is a possibility of significantly enhancing the chances of inflation without any fine-tuning of initial co...
We describe the construction of an all-sky galaxy catalogue, using SuperCOSMOS scans of Schmidt photographic plates from the UKST and POSS2 surveys. The photographic photometry is calibrated using SDSS data, with results that are linear to 2% or better.
We investigate the feasibility of using the velocity acoustic oscillations (VAO) features on the Cosmic Dawn 21 cm power spectrum to probe small-scale density fluctuations. In the standard cold dark matter (CDM) model, Pop III stars form in minihalos and affect the 21 cm signal through Ly$\alpha$ and X-ray radiation.
The observational evidence for the recent acceleration of the universe demonstrates that canonical theories of cosmology and particle physics are incomplete (or possibly incorrect) and that new physics is out there, waiting to be discovered. A crucial task for the next generation of astrophysical facilities is to sear...
We examine the HI+H_2 content of blue-sequence E/S0s -- a recently identified population of galaxies that are morphologically early type, but reside alongside spiral galaxies in color vs. stellar mass space. We test the idea that the majority of low-to-intermediate mass blue-sequence E/S0s may be settled products of p...
Using a recently proposed gauge invariant formulation of light-cone averaging, together with adapted "geodesic light-cone" coordinates, we show how an "induced backreaction" effect emerges, in general, from correlated fluctuations in the luminosity distance and covariant integration measure. Considerin...
We investigate whether future measurements of high redshift standard candles (HzSCs) will be a powerful probe of dark energy, when compared to other types of planned dark energy measurements. Active galactic nuclei and gamma ray bursts have both been proposed as potential HzSC candidates.
We report on sensitive dual-frequency (1.7 and 5 GHz) European VLBI Network observations of the central region of nine Seyfert galaxies. These sources are among the faintest and least luminous members of a complete sample of nearby (d<22 Mpc) low luminosity AGNs.
We present a regular cubic lattice solution to Einstein field equations that is exact at second order in a small parameter. We show that this solution is kinematically equivalent to the Friedmann-Lemaître-Robertson-Walker (FLRW) solution with the same averaged energy density.
We use here a family of scaling transformations, that scale key rates in the evolution equations, to analytically understand constraints on light relics from cosmic microwave background (CMB) maps, given cosmological models of varying degrees of complexity. We describe the causes of physical effects that are fundament...
We combine time-dependent multi-waveband flux and linear polarization observations with sub-milliarcsecond-scale polarimetric images at lambda=7mm of the BL Lacertae-type blazar OJ287 to locate the gamma-ray emission in prominent flares in the jet of the source >14pc from the central engine. We demonstrate a highly...
We study the primordial bispectrum of curvature perturbation in the uniform- density slicing generated by the interaction between the inflaton and isotropic background gauge fields. We derive the action up to cubic order in perturbation and take into account all the relevant effects in the leading order of slow-roll e...
Typically the fluctuations generated from a decaying field during inflation do not contribute to the large scale structures. In this paper we provide an example where it is possible for a field which slowly rolls and then decays during inflation to create all the matter perturbations with a slightly red-tilted spectra...
I describe a fast algorithm for the identification of connected sets of points where the point-wise connections are determined by a fixed spatial distance - a task commonly referred to in the cosmological simulation community as Friends-of-Friends (FOF) group finding. This technique sorts particles into fine cells suf...
We use a combined 120 ks Chandra exposure to analyze X-ray edges produced by non-hydrostatic gas motions (sloshing) from galaxy collisions, and cavities formed by AGN activity. Evidence for gas sloshing is seen in the spiral morphology and multiple cold front edges in NGC 5846's X-ray surface brightness distributi...
In axion gauge field inflation an axion-like particle driving cosmic inflation is coupled to the Chern-Simons density of an Abelian or non-Abelian gauge group. In the case of a non-Abelian gauge group, this can lead to the formation of a stable, homogeneous and isotropic gauge field background.
Domain walls are topological defects produced by the spontaneous symmetry-breaking of discrete symmetry during cosmological phase transitions. The horizon-size domain wall can significantly contribute to the energy density in the late-evolution stage.
Filaments are one of the most prominent features visible in the galaxy distribution. Considering the Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey Data Release Seven (SDSS DR7), we have analyzed the filamentarity in 11 nearly two dimensional (2D) sections through a volume limited subsample of this data....
It is often said that detecting a spectrum of primordial gravitational waves via observing B-mode polarization of the Cosmic Microwave Background is the "Holy Grail" of inflation. The purpose of this short note is to point out that it is indeed of immense scientific interest to search for a signal of gravitati...
We study the clustering Generalized Chaplygin Gas (GCG) as a possible candidate for dark matter-dark energy unification. The vanishing speed of sound ($c_{s}^2 = 0$) for the GCG fluid can be obtained by incorporating higher derivative operator in the original K-essence Lagrangian.
A new empirical formulae is given for estimating the masses of black holes in AGNs from the H beta velocity dispersion and the continuum luminosity at 5100 Angstroms. It is calibrated to reverberation-mapping and stellar-dynamical estimates of black hole masses.
We derive semi-analytic formulae for the power spectra of two-field inflation assuming an arbitrary potential and non-canonical kinetic terms, and we use them both to build phenomenological intuition and to constrain classes of two-field models using WMAP data. Using covariant formalism, we first develop a framework f...
We present cosmological constraints using the abundance of weak-lensing shear-selected galaxy clusters in the Hyper Suprime-Cam (HSC) Subaru Strategic Program. The clusters are selected on the mass maps constructed using the three-year (Y3) weak-lensing data with an area of $\approx500~$deg$^2$, resulting in a sample ...
We revisit how super-Hubble cosmological fluctuations induce, at any time in the cosmic history, a non-vanishing spatial curvature of the local background metric. The random nature of these fluctuations promotes the curvature density parameter to a stochastic quantity for which we derive novel non-perturbative express...
We present NuSTAR hard X-ray observations of two X-ray weak broad absorption line (BAL) quasars, PG 1004+130 (radio loud) and PG 1700+518 (radio quiet). Many BAL quasars appear X-ray weak, probably due to absorption by the shielding gas between the nucleus and the accretion-disk wind.
We present the calibration of the Dark Energy Survey Year 1 (DES Y1) weak lensing source galaxy redshift distributions from clustering measurements. By cross-correlating the positions of source galaxies with luminous red galaxies selected by the redMaGiC algorithm we measure the redshift distributions of the source ga...
In previous works we proposed the Reverse Zeldovich Approximation (RZA) method, which can be used to estimate the cosmological initial conditions underlying the galaxy distribution in the Local Universe using peculiar velocity data. In this paper, we apply the technique to run constrained cosmological simulations from...
We present the large-scale 3-point correlation function (3PCF) of the SDSS DR12 CMASS sample of $777,202$ Luminous Red Galaxies, the largest-ever sample used for a 3PCF or bispectrum measurement. We make the first high-significance ($4.5\sigma$) detection of Baryon Acoustic Oscillations (BAO) in the 3PCF.
We present the results of a comparison between the environments of 1) a complete sample of 46 southern 2Jy radio galaxies at intermediate redshifts (0.05 < z < 0.7),
We investigate a class of rapidly growing emission line galaxies, known as "Green Peas", first noted by volunteers in the Galaxy Zoo project because of their peculiar bright green colour and small size, unresolved in SDSS imaging. Their appearance is due to very strong optical emission lines, namely [O III] 50...
We present a measurement of two-dimensional (2D) redshift-space power spectrum for the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 CMASS galaxies in the North Galactic Cap (NGC) based on the method developed by Jing & Borner (2001). In this method, we first measure the 2D redshift-space correlat...
We investigate cosmological consequences of an inflationary model which incorporates a generic seesaw extension (types I and II) of the Standard Model of Particle Physics. A non-minimal coupling between the inflaton field and the Ricci scalar is considered as well as radiative corrections at one loop order.
The recent Madala hypothesis, a conjecture that seeks to explain anomalies within Large Hadron Collider (LHC) data (particularly in the transverse momentum of the Higgs boson), is interesting for more than just a statistical hint at unknown and unpredicted physics. This is because the model itself contains additional ...
We perform a model-independent reconstruction of the angular diameter distance ($D_{A}$) using the Multi-Task Gaussian Process (MTGP) framework with DESI-DR1 BAO and DES-SN5YR datasets. We calibrate the comoving sound horizon at the baryon drag epoch $r_d$ to the Planck best-fit value, ensuring consistency with early-...
We study the detailed evolution of the fine-structure constant $\alpha$ in the string-inspired runaway dilaton class of models of Damour, Piazza and Veneziano. We provide constraints on this scenario using the most recent $\alpha$ measurements and discuss ways to distinguish it from alternative models for varying $\al...
So far, the standard attitude to solve the Friedmann equations in the simultaneous presence of radiation $R$, matter $M$ and cosmological constant ${\Lambda}$ is to find solutions $R_R (t)$, $R_M (t)$ and $R_{\Lambda} (t)$ separately for each individual component alone, and next to join them together, thereby obtaining...
Next-generation radio telescopes will provide unprecedented data volumes of the neutral hydrogen (HI) distribution across cosmic time. Combining weak lensing surveys with spatial and kinematic observations of HI could help constrain key properties of dark matter, such as its mass, clustering behavior, and spatial dist...
We analyze the clustering properties of quasars simulated using a semianalytic model built on the Millennium Simulation, with the goal of testing scenarios in which black hole accretion and quasar activity are triggered by galaxy mergers. When we select quasars with luminosities in the range accessible by current obse...
Absorption signatures in the spectra of QSOs are one of our most powerful tools for studying galactic and intergalactic environments at high redshifts. With the discovery of QSOs out to z > 7, QSO absorption lines are now tracing the end stages of reionization on multiple fronts using the hydrogen Lyman-$\alpha$ fo...
Blazars radiate from relativistic jets launched by a supermassive black hole along our line of sight; the subclass of FSRQs exhibits broad emission lines, a telltale sign of a gas-rich environment and high accretion rate, contrary to the other subclass of the BL Lacertae objects. We show that this dichotomy of the sou...
We propose a dipole modulation model for the Cosmic Microwave Background Radiation (CMBR) polarization field. We show that the model leads to correlations between l and l+1 multipoles, exactly as in the case of temperature.
To exploit the power of next-generation large-scale structure surveys, ensembles of numerical simulations are necessary to give accurate theoretical predictions of the statistics of observables. High-fidelity simulations come at a towering computational cost.
Context. The determination of accurate photometric redshifts (photo-zs) in large imaging galaxy surveys is key for cosmological studies.
We use two subsets of 2000 and 1000 \textsc{Quijote} simulations to build two power spectrum emulators, allowing for fast computations of the non-linear matter power spectrum. The first emulator works on scales $k \in [0.015,1.8]\,h/ \rm{Mpc^{-1}}$ in terms of seven cosmological parameters: the matter and baryon fract...
The Atlas3D project is a multi-wavelength survey combined with a theoretical modeling effort. The observations span from the radio to the millimeter and optical, and provide multi-colour imaging, two-dimensional kinematics of the atomic (HI), molecular (CO) and ionized gas (Hbeta, [OIII] and [NI]), together with the k...
We report on the discovery of a very distant galaxy cluster serendipitously detected in the archive of the XMM-Newton mission, within the scope of the XMM-Newton Distant Cluster Project (XDCP). XMMUJ0044.0-2033 was detected at a high significance level (5sigma) as a compact, but significantly extended source in the X-...
The baryon acoustic oscillation (BAO) scale acts as a standard ruler for measuring cosmological distances and has therefore emerged as a leading probe of cosmic expansion history. However, any physical effect that alters the length of the ruler can lead to a bias in our determination of distance and expansion rate.
Source galaxy images are distorted not only by a static gravitational potential, but also by frame-dragging induced by massive rotating objects like clusters of galaxies. Such effect is well understood theoretically, it is therefore of great interest to estimate its detectability for future surveys.
Measurements of the thermal Sunyaev-Zel'dovich (tSZ) effect have long been recognized as a powerful cosmological probe. Here we assess the importance of relativistic temperature corrections to the tSZ signal on the power spectrum analysis of the Planck Compton-$y$ map, developing a novel formalism to account for t...