Without making any assumption on the underlying geometry and metric of the local Universe, we provide a measurement of the expansion rate fluctuation field using the Cosmicflows-4 and Pantheon+ samples in the redshift range 0.01 < z < 0.1 (30 h(-1) Mpc < R < 300 h(-1) Mpc). The amplitude of the anisotropic fluctuations is found to be of order a few percent relative to the monopole of the expansion rate. We further decompose the expansion rate fluctuation field into spherical harmonic components and analyze their evolution with redshift across the studied redshift range. At low redshift, the dipole is clearly dominant, with an amplitude of similar to (2.2 +/- 0.15) & times; 10(-2), significantly larger than the higher-order modes. As redshift increases, the dipole amplitude steadily decreases, reaching roughly half its value in the highest redshift bin investigated. The quadrupole is also significant, at about half the dipole amplitude, and persists across all redshift bins, with no clear decreasing trend, although uncertainties grow at higher redshift. A nonzero octupole is detected at low redshift with a signal-to-noise ratio of similar to 3, but it becomes unconstrained at higher redshift. The dipole, quadrupole, and octupole components are found to be aligned, exhibiting axial symmetry around a common axis (l = 295 degrees, b = 5 degrees). We interpret the observed fluctuations in the expansion rate within the framework of covariant cosmography. Our results indicate that the multipoles of the expansion rate fluctuation field are primarily driven by a strong quadrupole in the covariant Hubble parameter, together with dipole and octupole contributions from the covariant deceleration parameter. These few parameters suffice to reconstruct the luminosity distance with high precision out to z similar to 0.1, in a manner that is model-independent, non-perturbative, and free from assumptions about peculiar velocities. Finally, we find that the CMB frame is not locally comoving with the matter fluid, and that a matter fluid element, roughly a spherical region of size in the range 38 less than or similar to R (Mpc) less than or similar to 100 centered on the observer position, moves relative to the CMB frame with a velocity of 188 +/- 22 km/s, along the axis of symmetry.

The spatial clustering of galaxies has long been a key probe of cosmology. Gravitational--wave (GW) sources, which provide direct luminosity--distance measurements, have recently emerged as a complementary tracer of large--scale structures. The cross--correlation of GW and galaxy catalogs offers a novel way to test cosmic expansion. We investigate the potential of tomographic GW--galaxy angular power spectra to constrain cosmological parameters, focusing on the Hubble constant and matter density, in the context of third--generation (3G) GW detectors combined with the Euclid survey. We constructed our forecasts using realistic GW source populations and error models calibrated on recent detector designs. We adopted a Fisher--matrix approach, marginalized over nuisance parameters including tracer biases, primordial spectrum parameters, and baryon density, and compared different survey configurations, binning schemes, and GW detector networks. We find that tomographic cross--correlation can constrain H_0 at a percent or sub--percent precision, depending on the binning strategy, network configuration, and observing time. Combining galaxy autocorrelations with GW--galaxy cross--correlations improves constraints by up to a factor of ∼10 relative to either probe alone. We further show that this performance requires multiple interferometers with accurate sky localization, and we discuss the added value of spectroscopic surveys and the detectability of GW clustering bias. Our results demonstrate that this technique, applied to 3G GW detectors in synergy with large galaxy surveys, can deliver competitive measurements of cosmic expansion, even when marginalizing over a wide range of astrophysical and cosmological nuisance parameters.

We investigate the non-Gaussian features in the distribution of the matter power spectrum multipoles. Using the COVMOS method, we generated 100 000 mock realisations of dark matter density fields in both real and redshift space across multiple redshifts and cosmological models. We derived an analytical framework linking the non-Gaussianity of the power spectrum distribution to higher-order statistics of the density field, including the trispectrum and pentaspectrum. We explored the e ffect of redshift-space distortions, the geometry of the survey, the Fourier binning, the integral constraint, and the shot noise on the skewness of the distribution of the power spectrum measurements. Our results demonstrate that the likelihood of the estimated matter power spectrum significantly deviates from a Gaussian assumption on non-linear scales, particularly at low redshift. This departure is primarily driven by the pentaspectrum contribution, which dominates over the trispectrum at intermediate scales. We also examined the impact of the finiteness of the survey geometry in the context of the Euclid mission, and we find that both the shape of the survey and the integral constraint amplify the skewness.

Modified gravity (MG) theories have emerged as a promising alternative to explain the late-time acceleration of the Universe. However, the detection of MG in observations of the large-scale structure remains challenging due to the screening mechanisms that obscure any deviations from general relativity (GR) in high-density regions. The marked two-point correlation function, which is particularly sensitive to the surrounding environment, offers a promising approach to enhancing the discriminating power in clustering analyses and to potentially detecting MG signals. This work investigates novel marks based on large-scale environment estimates, which also that exploit the anti-correlation between objects in low- and high-density regions. This is the first time that the propagation of discreteness effects in marked correlation functions is investigated in depth. In contrast to standard correlation functions, the density-dependent marked correlation function estimated from catalogues is affected by shot noise in a non-trivial way. We assess the performance of various marks to distinguish GR from MG. This is achieved through the use of the ELEPHANT suite of simulations, which comprise five realisations of GR and two different MG theories: f(R) and nDGP. In addition, discreteness effects are thoroughly studied using the high-density Covmos catalogues. We have established a robust method to correct for shot-noise effects that can be used in practical analyses. This methods allows the recovery of the true signal, with an accuracy below 5% over the scales of 5 h-1 Mpc up to 150 h-1 Mpc. We find that such a correction is absolutely crucial to measure the amplitude of the marked correlation function in an unbiased manner. Furthermore, we demonstrate that marks that anti-correlate objects in low- and high-density regions are among the most effective in distinguishing between MG and GR; they also uniquely provide visible deviations on large scales, up to about 80 h-1 Mpc. We report differences in the marked correlation function between f(R) with |fR0| = 10-6 and GR simulations of the order of 3-5 sigma in real space. The redshift-space monopole of the marked correlation function in this MG scenario exhibits similar features and performance as the real-space marked correlation function. The combination of the proposed tanh-mark with shot-noise correction paves the way towards an optimal approach for the detection of MG in current and future spectroscopic galaxy surveys.

We present the official release of the EFfective Field theORy surrogaTe (Effort.jl), a novel and efficient emulator designed for the Effective Field Theory of Large-Scale Structure (EFTofLSS). This tool combines state-of-the-art numerical methods and clever preprocessing strategies to achieve exceptional computational performance without sacrificing accuracy. To validate the emulator reliability, we compare Bayesian posteriors sampled using Effort.jl via Hamiltonian MonteCarlo methods to the ones sampled using the widely-used pybird code, via the Metropolis-Hastings sampler. On a large-volume set of simulations, and on the BOSS dataset, the comparison confirms excellent agreement, with deviations compatible with MonteCarlo noise. Looking ahead, Effort.jl is poised to analyze next-generation cosmological datasets and to support joint analyses with complementary tools.

We design a new observable, the η expansion rate fluctuation, to characterize deviations from linearity and isotropy in the redshift-distance relationship in the local Universe. In order to better decipher the structure and symmetries of the anisotropies in the local expansion rate, we also show its decomposition into spherical harmonic coefficients using several public catalogs of redshift-independent distances, the Cosmicflows-3 and Pantheon data sets, covering the redshift range 0.01

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

We present cosmological parameter forecasts for the Euclid 6x2pt statistics, which include the galaxy clustering and weak lensing main probes together with previously neglected cross-covariance and cross-correlation signals between imaging/photometric and spectroscopic data. The aim is understanding the impact of such terms on the Euclid performance. We produce 6x2pt cosmological forecasts, considering two different techniques: the so-called harmonic and hybrid approaches, respectively. In the first, we treat all the different Euclid probes in the same way, i.e. we consider only angular 2pt-statistics for spectroscopic and photometric clustering, as well as for weak lensing, analysing all their possible cross-covariances and cross-correlations in the spherical harmonic domain. In the second, we do not account for negligible cross-covariances between the 3D and 2D data, but consider the combination of their cross-correlation with the auto-correlation signals. We find that both cross-covariances and cross-correlation signals, have a negligible impact on the cosmological parameter constraints and, therefore, on the Euclid performance. In the case of the hybrid approach, we attribute this result to the effect of the cross-correlation between weak lensing and photometric data, which is dominant with respect to other cross-correlation signals. In the case of the 2D harmonic approach, we attribute this result to two main theoretical limitations of the 2D projected statistics implemented in this work according to the analysis of official Euclid forecasts: the high shot noise and the limited redshift range of the spectroscopic sample, together with the loss of radial information from subleading terms such as redshift-space distortions and lensing magnification. Our analysis suggests that 2D and 3D Euclid data can be safely treated as independent, with a great saving in computational resources.

We extend the evolution-mapping approach, introduced in the first paper of this series to describe non-linear matter density fluctuations, to statistics of the cosmic velocity field. This framework classifies cosmological parameters into shape parameters, which determine the shape of the linear matter power spectrum, PL(k,z), and evolution parameters, which control its amplitude at any redshift. Evolution-mapping leverages the fact that density fluctuations in cosmologies with identical shape parameters but different evolution parameters exhibit similar non-linear evolutions when expressed as a function of clustering amplitude. We analyse a suite of N-body simulations sharing identical shape parameters but spanning a wide range of evolution parameters. Using a method for estimating the volume-weighted velocity field based on the Voronoi tessellation of simulation particles, we study the non-linear evolution of the velocity divergence power spectrum, P-theta theta(k), and its cross-power spectrum with the density field, P-delta theta(k). We demonstrate that the evolution-mapping relation applies accurately to P-theta theta(k) and P-delta theta(k). While this breaks down in the strongly non-linear regime, deviations can be modelled in terms of differences in the suppression factor, g(a)=D(a)/a, similar to those for the density field. Such modelling describes the differences in P-theta theta(k) between models with the same linear clustering amplitude to better than 1 per cent accuracy at all scales and redshifts considered. Evolution-mapping simplifies the description of the cosmological dependence of non-linear density and velocity statistics, streamlining the sampling of large cosmological parameter spaces for cosmological analysis

We validate the COVMOS method introduced in Baratta et al. (2019) allowing for the fast simulation of catalogues of different cosmological field tracers (e.g. dark matter particles, halos, galaxies, etc.). The power spectrum and one-point probability distribution function of the underlying tracer density field are set as inputs of the method and are arbitrarily chosen by the user. In order to evaluate the validity domain of COVMOS at the level of the produced two-point statistics covariance matrix, we choose to target these two input statistical quantities from realistic $N$-body simulation outputs. In particular, we perform this cloning procedure in a $\Lambda$CDM and in a massive neutrino cosmologies, for five redshifts in the range $z\in[0,2]$. First, we validate the output real-space two-point statistics (both in configuration and Fourier space) estimated over $5,000$ COVMOS realisations per redshift and per cosmology, with a volume of $1\ [\mathrm{Gpc}/h]^3$ and $10^8$ particles each. Such a validation is performed against the corresponding $N$-body measurements, estimated from 50 simulations. We find the method to be valid up to $k\sim 0.2h/$Mpc for the power spectrum and down to $r~\sim 20$ Mpc$/h$ for the correlation function. Then, we extend the method by proposing a new modelling of the peculiar velocity distribution, aiming at reproducing the redshift-space distortions both in the linear and mildly non-linear regimes. After validating this prescription, we finally compare and validate the produced redshift-space two-point statistics covariance matrices in the same range of scales. We release on a public repository the Python code associated with this method, allowing the production of tens of thousands of realisations in record time. COVMOS is intended for any user involved in large galaxy-survey science requiring a large number of mock realisations.

We analyse the clustering of matter on large scales in an extension of the concordance model that allows for spatial curvature. We develop a consistent approach to curvature and wide-angle effects on the galaxy 2-point correlation function in redshift space. In particular we derive the Alcock-Paczynski distortion of $f\sigma_{8}$, which differs significantly from empirical models in the literature. A key innovation is the use of the `Clustering Ratio', which probes clustering in a different way to redshift-space distortions, so that their combination delivers more powerful cosmological constraints. We use this combination to constrain cosmological parameters, without CMB information. In a curved Universe, we find that $\Omega_{{\rm m}, 0}=0.26\pm 0.04$ (68\% CL). When the clustering probes are combined with low-redshift background probes -- BAO and SNIa -- we obtain a CMB-independent constraint on curvature: $\Omega_{K,0} = 0.0041\,_{-0.0504}^{+0.0500}$. We find no Bayesian evidence that the flat concordance model can be rejected. In addition we show that the sound horizon at decoupling is $r_{\rm d} = 144.57 \pm 2.34 \; {\rm Mpc}$, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat $\Lambda$CDM and a standard sound horizon, leading to a small value of $H_{0}$, {\em without} assuming any CMB information. Clustering Ratio measurements produce the only low-redshift clustering data set that is not in disagreement with the CMB, and combining the two data sets we obtain $\Omega_{K,0}= -0.023 \pm 0.010$.

We provide an accurate comparison, against large cosmological N-body simulations, of different prescriptions for modelling nonlinear matter power spectra in the presence of massive neutrinos and dynamical dark energy. We test the current most widely used approaches: fitting functions (HALOFIT and HMcode), the halo-model reaction (ReACT) and emulators (baccoemu and EuclidEmulator2). Focussing on redshifts z <= 2 and scales k less than or similar to 1 h/Mpc (where the simulation mass resolution provides similar to 1% accuracy), we find that HMcode and ReACT considerably improve over the HALOFIT prescriptions of Smith and Takahashi (both combined with the Bird correction), with an overall agreement of 2% for all the cosmological scenarios considered. Concerning emulators, we find that, especially at low redshifts, EuclidEmulator2 remarkably agrees with the simulated spectra at. 1% level in scenarios with dynamical dark energy and massless neutrinos, reaching a maximum difference of similar to 2% at z = 2. baccoemu has a similar behaviour as EuclidEmulator2, except for a couple of dark energy models. In cosmologies with massive neutrinos, at z = 0 all the nonlinear prescriptions improve their agreement with respect to the massless neutrino case, except for the Bird and TakaBird models which, however, are not tailored to w(0)-w(a) models. At z > 0 we do not find a similar improvement when including massive neutrinos, probably due to the lower impact of neutrino free-streaming at higher redshifts; rather at z = 2 EuclidEmulator2 exceeds 2% agreement for some dark energy equation of state. When considering ratios between the matter power spectrum computed in a given cosmological model and its Lambda CDM counterpart, all the tested prescriptions agree with simulated data, at sub-percent or percent level, depending on z. Finally, we also test how nonlinear prescriptions compare against simulations when computing cosmic shear and angular galaxy clustering spectra. For the former, we find a 2-3% agreement for HMcode, baccoemu, EuclidEmulator2 and ReACT; for the latter, due to the minimum stellar mass of the simulated galaxies, shot noise highly affects the signal and makes the discrepancies as high as 5%.

We revisit the case of fast Monte Carlo simulations of galaxy positions for a non-Gaussian field. More precisely, we address the question of generating a 3D field with a given one-point function (e.g. log-normal) and some power spectrum fixed by cosmology. We highlight and investigate a problem that occurs in the log-normal case when the field is filtered, and we identify a regime where this approximation still holds. However, we show that the filtering is unnecessary if aliasing effects are taken into account and the discrete sampling step is carefully controlled. In this way we demonstrate a sub-percent precision of all our spectra up to the Nyquist frequency. We extend the method to generate a full light cone evolution, comparing two methods for this process, and validate our method with a tomographic analysis. We analytically and numerically investigate the structure of the covariance matrices obtained with such simulations which may be useful for future large and deep surveys.

The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the galaxy positions and the expected galaxy density field. The expected field is commonly specified using a Monte-Carlo sampling of the volume covered by the survey and, to minimize additional sampling errors, this random catalog has to be much larger than the data catalog. Correlation function estimators compare data–data pair counts to data–random and random–random pair counts, where random–random pairs usually dominate the computational cost. Future redshift surveys will deliver spectroscopic catalogs of tens of millions of galaxies. Given the large number of random objects required to guarantee sub-percent accuracy, it is of paramount importance to improve the efficiency of the algorithm without degrading its precision. We show both analytically and numerically that splitting the random catalog into a number of subcatalogs of the same size as the data catalog when calculating random–random pairs and excluding pairs across different subcatalogs provides the optimal error at fixed computational cost. For a random catalog fifty times larger than the data catalog, this reduces the computation time by a factor of more than ten without affecting estimator variance or bias.

Techniques to classify galaxies solely based on photometry will be necessary for future large cosmology missions, such as Euclid or LSST. However, the precision of classification is always lower in photometric surveys and can be systematically biased with respect to classifications based upon spectroscopic data. We verified how precisely the detailed classification scheme introduced by Siudek et al. (2018, hereafter: S1) for galaxies at z~0.7 could be reproduced if only photometric data are available. We applied the Fisher Expectation-Maximization (FEM) unsupervised clustering algorithm to 54,293 VIPERS galaxies working in a parameter space of reliable photometric redshifts and 12 corresponding rest-frame magnitudes. The FEM algorithm distinguishes four main groups: (1) red, (2) green, (3) blue, and (4) outliers. Each group is further divided into 3, 3, 4, and 2 subclasses, respectively. The accuracy of reproducing galaxy classes using spectroscopic data is high: 92%, 84%, 96% for red, green, and blue classes, respectively, except for dusty star-forming galaxies. The presented verification of the photometric classification demonstrates that large photometric samples can be used to distinguish different galaxy classes at z > 0.5 with an accuracy provided so far only by spectroscopic data except for particular galaxy classes.

We use the unparalleled statistics of the VIPERS survey to investigate the relation between the surface mean stellar mass density Sigma = M/(2 pi R-e(2)) of massive passive galaxies (MPGs, M >= 10(11) M-circle dot) and their local environment in the redshift range 0.5 <= z <= 0.8. Passive galaxies were selected on the basis of their NUVrK colors (similar to 900 objects), and the environment was defined as the galaxy density contrast, delta, using the fifth nearest-neighbor approach. The analysis of Sigma versus delta was carried out in two stellar mass bins. In galaxies with M <= 2 x 10(11) M-circle dot, no correlation between Sigma and delta is observed. This implies that the accretion of satellite galaxies, which is more frequent in denser environments (groups or cluster outskirts) and efficient in reducing the galaxy Sigma, is not relevant in the formation and evolution of these systems. Conversely, in galaxies with M > 2 x 10(11) M-circle dot, we find an excess of MPGs with low Sigma and a deficit of high-Sigma MPGs in the densest regions with respect to other environments. We interpret this result as due to the migration of some high-Sigma MPGs (<1% of the total population of MPGs) into low-Sigma MPGs, probably through mergers or cannibalism of small satellites. In summary, our results imply that the accretion of satellite galaxies has a marginal role in the mass-assembly history of most MPGs. We have previously found that the number density of VIPERS massive star-forming galaxies (MSFGs) declines rapidily from z = 0.8 to z = 0.5, which mirrors the rapid increase in the number density of MPGs. This indicates that the MSFGs at z >= 0.8 migrate to the MPG population. Here, we investigate the Sigma-delta relation of MSFGs at z >= 0.8 and find that it is consistent within 1 sigma with that of low-Sigma MPGs at z <= 0.8. Thus, the results of this and our previous paper show that MSFGs at z >= 0.8 are consistent in terms of number and environment with being the progenitors of low-Sigma MPGs at z < 0.8.

We estimate the velocity field in a large set ofN-body simulations including massive neutrino particles, and measure the auto-power spectrum of the velocity divergence field as well as the cross-power spectrum between the cold dark matter density and the velocity divergence. We perform these measurements at four different redshifts and within four different cosmological scenarios, covering a wide range in neutrino masses. We find that the nonlinear correction to the velocity power spectra largely depends on the degree of nonlinear evolution with no specific dependence on the value of neutrino mass. We provide a fitting formula based on the value of the rms of the matter fluctuations in spheres of 8 h−1Mpc, describing the nonlinear corrections with 3% accuracy on scales belowk = 0.7 h Mpc−1.

We use growth of structure data to constrain the effective field theory of dark energy. Considering as case study Horndeski theories with the speed of gravitational waves equal to that of light, we show how constraints on the free parameters and the large-scale structure phenomenological functions can be improved by two ingredients: firstly by complementing the set of redshift-space distortions data with the three recent measurements of the growth rate f and the amplitude of matter fluctuations σ8 from the VIPERS and SDSS collaborations; secondly by applying a local Solar System bound on the variation of the Newton constant. This analysis allows us to conclude that: i) despite firmly restricting the predictions of weaker gravity, the inclusion of the Solar System bound does not prevent suppressed growth relative to the standard model ΛCDM at low redshifts; ii) the same bound in conjunction with the growth of structure data strongly restricts the redshift evolution of the gravitational slip parameter to be close to unity and the present value is constrained to one at the 10−3 level; iii) the growth of structure data favours a fifth force contribution to the effective gravitational coupling at low redshifts and at more than {two} sigma at present time.

The VIPERS galaxy survey has measured the clustering of 0.5 < z < 1.2 galaxies, enabling a number of measurements of galaxy properties and cosmological redshift-space distortions (RSD). Because the measurements were made using one-pass of the VIMOS instrument on the Very Large Telescope (VLT), the galaxies observed only represent approximately 47% of the parent target sample, with a distribution imprinted with the pattern of the VIMOS slitmask. Correcting for the effect on clustering has previously been achieved using an approximate approach developed using mock catalogues. Pairwise inverse probability (PIP) weighting has recently been proposed to correct for missing galaxies, and we apply it to mock VIPERS catalogues to show that it accurately corrects the clustering for the VIMOS effects, matching the clustering measured from the observed sample to that of the parent. We then apply PIP-weighting to the VIPERS data, and fit the resulting monopole and quadrupole moments of the galaxy two-point correlation function with respect to the line-of-sight, making measurements of RSD. The results are close to previous measurements, showing that the previous approximate methods used by the VIPERS team are sufficient given the errors obtained on the RSD parameter.

Various galaxy classification schemes have been developed so far to constrain the main physical processes regulating evolution of different galaxy types. In the era of a deluge of astrophysical information and recent progress in machine learning, a new approach to galaxy classification becomes imperative. We employ a Fisher Expectation-Maximization unsupervised algorithm working in a parameter space of 12 rest-frame magnitudes and spectroscopic redshift. The model (DBk) and the number of classes (12) were established based on the joint analysis of standard statistical criteria and confirmed by the analysis of the galaxy distribution with respect to a number of classes and their properties. This new approach allows us to classify galaxies based just on their redshifts and UV-NIR spectral energy distributions. The FEM unsupervised algorithm has automatically distinguished 12 classes: 11 classes of VIPERS galaxies and an additional class of broad-line AGNs. After a first broad division into blue, green and red categories we obtained a further sub-division into three red, three green, and five blue galaxy classes. The FEM classes follow the galaxy sequence from the earliest to the latest types that is reflected in their colours (which are constructed from rest-frame magnitudes used in classification procedure) but also their morphological, physical, and spectroscopic properties (not included in the classification scheme). We demonstrate that the members of each class share similar physical and spectral properties. In particular, we are able to find three different classes of red passive galaxy populations. Thus, we demonstrate the potential of an unsupervised approach to galaxy classification and we retrieve the complexity of galaxy populations at z 0.7, a task that usual simpler colour-based approaches cannot fulfil.