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In an attempt to look for a viable mechanism leading to a present day accelerated expansion, we investigate the possibility that the observed cosmic speed up may be recovered in the framework of the Rastall's theory, relying on the non-conservativity of the stress-energy tensor, i.e. Tμv;μ 0. We derive the modified Friedmann equations and show that they correspond to Cardassian-like equations. We also show that, under suitable assumptions on the equation of state of the matter term sourcing the gravitational field, it is indeed possible to get an accelerated expansion, in agreement with the Hubble diagram of both Type Ia Supernovae (SNeIa) and Gamma Ray Bursts (GRBs). Unfortunately, to achieve such a result one has to postulate a matter density parameter larger than the typical ΩM ≊ 0.3 value inferred from cluster gas mass fraction data. As a further issue, we discuss the possibility to retrieve the Rastall's theory from a Palatini variational principle approach to f(R) gravity. However, such an attempt turns out to be unsuccessful.

We explore the predictions of a class of dark energy models, quinstant dark energy, concerning the structure formation in the Universe, both in the linear and non-linear regimes. Quinstant dark energy is considered to be formed by quin tessence and a negative cosmological con stant . We conclude that these models give good predictions for structure formation in the linear regime, but fail to do so in the non-linear one, for redshifts larger than one.

The future Euclid space satellite mission will offer an invaluable opportunity to constrain modifications to Einstein's general relativity at cosmic scales. We focus on modified gravity models characterised, at linear scales, by a scale-independent growth of perturbations while featuring different testable types of derivative screening mechanisms at smaller non-linear scales. We considered three specific models, namely JBD, a scalar-tensor theory with a flat potential, the nDGP gravity, a braneworld model in which our Universe is a four-dimensional brane embedded in a five-dimensional Minkowski space-time, and \\(k\\)-mouflage (KM) gravity, an extension of \\(k\\)-essence scenarios with a universal coupling of the scalar field to matter. In preparation for real data, we provide forecasts from spectroscopic and photometric primary probes by Euclid on the cosmological parameters and the additional parameters of the models, respectively, \\(\\omega_{\\rm BD}\\), \\(\\Omega_{\\rm rc}\\) and \\(\\epsilon_{2,0}\\). The forecast analysis employs the Fisher matrix method applied to weak lensing (WL); photometric galaxy clustering (GCph), spectroscopic galaxy clustering (GCsp) and the cross-correlation (XC) between GCph and WL. In an optimistic setting at 68.3\\% confidence interval, we find the following percentage relative errors with Euclid alone: for \\(\\log_{10}{\\omega_{\\rm BD}}\\), with a fiducial value of \\(\\omega_{\\rm BD}=800\\), 27.1\\% using GCsp alone, 3.6\\% using GCph+WL+XC and 3.2\\% using GCph+WL+XC+GCsp; for \\(\\log_{10}{\\Omega_{\\rm rc}}\\), with a fiducial value of \\(\\Omega_{\\rm rc}=0.25\\), we find 93.4\\%, 20\\% and 15\\% respectively; and finally, for \\(\\epsilon_{2,0}=-0.04\\), we find 3.4\\%, 0.15\\%, and 0.14\\%. (abridged)

The measurement of the absolute neutrino mass scale from cosmological large-scale clustering data is one of the key science goals of the Euclid mission. Such a measurement relies on precise modelling of the impact of neutrinos on structure formation, which can be studied with \\(N\\)-body simulations. Here we present the results from a major code comparison effort to establish the maturity and reliability of numerical methods for treating massive neutrinos. The comparison includes eleven full \\(N\\)-body implementations (not all of them independent), two \\(N\\)-body schemes with approximate time integration, and four additional codes that directly predict or emulate the matter power spectrum. Using a common set of initial data we quantify the relative agreement on the nonlinear power spectrum of cold dark matter and baryons and, for the \\(N\\)-body codes, also the relative agreement on the bispectrum, halo mass function, and halo bias. We find that the different numerical implementations produce fully consistent results. We can therefore be confident that we can model the impact of massive neutrinos at the sub-percent level in the most common summary statistics. We also provide a code validation pipeline for future reference.

We investigate the cosmological constraints that can be expected from measurement of the cross-correlation of galaxies with cosmic voids identified in the Euclid spectroscopic survey, which will include spectroscopic information for tens of millions of galaxies over \\(15\\,000\\) deg\\(^2\\) of the sky in the redshift range \\(0.9\\leq z<1.8\\). We do this using simulated measurements obtained from the Flagship mock catalogue, the official Euclid mock that closely matches the expected properties of the spectroscopic data set. To mitigate anisotropic selection-bias effects, we use a velocity field reconstruction method to remove large-scale redshift-space distortions from the galaxy field before void-finding. This allows us to accurately model contributions to the observed anisotropy of the cross-correlation function arising from galaxy velocities around voids as well as from the Alcock-Paczynski effect, and we study the dependence of constraints on the efficiency of reconstruction. We find that Euclid voids will be able to constrain the ratio of the transverse comoving distance \\(D_{\\rm M}\\) and Hubble distance \\(D_{\\rm H}\\) to a relative precision of about \\(0.3\\%\\), and the growth rate \\(f\\sigma_8\\) to a precision of between \\(5\\%\\) and \\(8\\%\\) in each of four redshift bins covering the full redshift range. In the standard cosmological model, this translates to a statistical uncertainty \\(\\Delta\\Omega_\\mathrm{m}=\\pm0.0028\\) on the matter density parameter from voids, better than can be achieved from either Euclid galaxy clustering and weak lensing individually. We also find that voids alone can measure the dark energy equation of state to \\(6\\%\\) precision.

Undisturbed galaxy clusters are characterized by a massive and large elliptical galaxy at their center, i.e. the Brightest Cluster Galaxy (BCG). How these central galaxies form is still debated. According to most models, a typical epoch for their assembly is z~1-2. We have performed a detailed multi-wavelength analysis of the core of XDCPJ0044.0-2033 (XDCP0044), one of the most massive and densest galaxy clusters currently known at redshift z~1.6, whose central galaxy population shows high star formation compared to lower-z clusters and an X-ray AGN located close to its center. SINFONI J-, H- and KMOS YJ-, H- bands spectroscopic data have been analyzed, together with deep archival HST photometric data in F105W, F140W, and F160W bands, Chandra X-ray, radio JVLA data at 1-2 GHz, and ALMA band-6 observations. In the central region of the cluster (~70x70 kpc^2), 2 systems of interacting galaxies have been identified and studied (Complex A and B), with a total of 7 confirmed cluster members. These galaxies show perturbed morphologies and 3 of them show signs of AGN activity. In particular, 2 type-1 AGN with typical broad lines have been found at the center of each complex (both of them X-ray obscured and highly accreting; Eddington ratio ~0.5), while a type-2 AGN has been discovered in Complex A. The AGN at the center of Complex B is also detected in X-ray while the other 2 are spatially related to radio emission. The 3 AGN provide one of the closest AGN triple at z>1 revealed so far with a minimum(maximum) projected distance of ~10(40) kpc. The observation of high star formation, merger signatures and nuclear activity in the core of XDCP0044 suggests that all these processes are key ingredients in shaping the nascent BCG. According to our data, XDCP0044 could form a typical massive galaxy of 10^12 Msun, hosting a Black Hole of 2x10^8-10^9 Msun, in a time scale of the order of ~2.5 Gyrs.

Upcoming surveys will map the growth of large-scale structure with unprecented precision, improving our understanding of the dark sector of the Universe. Unfortunately, much of the cosmological information is encoded by the small scales, where the clustering of dark matter and the effects of astrophysical feedback processes are not fully understood. This can bias the estimates of cosmological parameters, which we study here for a joint analysis of mock Euclid cosmic shear and Planck cosmic microwave background data. We use different implementations for the modelling of the signal on small scales and find that they result in significantly different predictions. Moreover, the different nonlinear corrections lead to biased parameter estimates, especially when the analysis is extended into the highly nonlinear regime, with both the Hubble constant, \\(H_0\\), and the clustering amplitude, \\(\\sigma_8\\), affected the most. Improvements in the modelling of nonlinear scales will therefore be needed if we are to resolve the current tension with more and better data. For a given prescription for the nonlinear power spectrum, using different corrections for baryon physics does not significantly impact the precision of Euclid, but neglecting these correction does lead to large biases in the cosmological parameters. In order to extract precise and unbiased constraints on cosmological parameters from Euclid cosmic shear data, it is therefore essential to improve the accuracy of the recipes that account for nonlinear structure formation, as well as the modelling of the impact of astrophysical processes that redistribute the baryons.

The data from the Euclid mission will enable the measurement of the photometric redshifts, angular positions, and weak lensing shapes for over a billion galaxies. This large dataset will allow for cosmological analyses using the angular clustering of galaxies and cosmic shear. The cross-correlation (XC) between these probes can tighten constraints and it is therefore important to quantify their impact for Euclid. In this study we carefully quantify the impact of XC not only on the final parameter constraints for different cosmological models, but also on the nuisance parameters. In particular, we aim at understanding the amount of additional information that XC can provide for parameters encoding systematic effects, such as galaxy bias or intrinsic alignments (IA). We follow the formalism presented in Euclid Collaboration: Blanchard et al. (2019) and make use of the codes validated therein. We show that XC improves the dark energy Figure of Merit (FoM) by a factor \\(\\sim 5\\), whilst it also reduces the uncertainties on galaxy bias by \\(\\sim 17\\%\\) and the uncertainties on IA by a factor \\(\\sim 4\\). We observe that the role of XC on the final parameter constraints is qualitatively the same irrespective of the galaxy bias model used. We also show that XC can help in distinguishing between different IA models, and that if IA terms are neglected then this can lead to significant biases on the cosmological parameters. We find that the XC terms are necessary to extract the full information content from the data in future analyses. They help in better constraining the cosmological model, and lead to a better understanding of the systematic effects that contaminate these probes. Furthermore, we find that XC helps in constraining the mean of the photometric-redshift distributions, but it requires a more precise knowledge of this mean in order not to degrade the final FoM. [Abridged]

Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities, in high-magnification regions. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. These effects cause significant biases in Omega_m, sigma_8, n_s, Omega_DE, w_0, and w_a of -0.53 sigma, 0.43 sigma, -0.34 sigma, 1.36 sigma, -0.68 sigma, and 1.21 sigma, respectively. We then show that these lensing biases interact with another systematic: the intrinsic alignment of galaxies. Accordingly, we develop the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant.

The statistics of peaks in weak lensing convergence maps is a promising tool to investigate both the properties of dark matter haloes and constrain the cosmological parameters. We study how the number of detectable peaks and its scaling with redshift depend upon the cluster dark matter halo profiles and use peak statistics to constrain the parameters of the mass - concentration (MC) relation. We investigate which constraints the Euclid mission can set on the MC coefficients also taking into account degeneracies with the cosmological parameters. To this end, we first estimate the number of peaks and its redshift distribution for different MC relations. We find that the steeper the mass dependence and the larger the normalisation, the higher is the number of detectable clusters, with the total number of peaks changing up to \\(40\\%\\) depending on the MC relation. We then perform a Fisher matrix forecast of the errors on the MC relation parameters as well as cosmological parameters. We find that peak number counts detected by Euclid can determine the normalization \\(A_v\\), the mass \\(B_v\\) and redshift \\(C_v\\) slopes and intrinsic scatter \\(\\sigma_v\\) of the MC relation to an unprecedented accuracy being \\(\\sigma(A_v)/A_v = 1\\%\\), \\(\\sigma(B_v)/B_v = 4\\%\\), \\(\\sigma(C_v)/C_v = 9\\%\\), \\(\\sigma(\\sigma_v)/\\sigma_v = 1\\%\\) if all cosmological parameters are assumed to be known. Should we relax this severe assumption, constraints are degraded, but remarkably good results can be restored setting only some of the parameters or combining peak counts with Planck data. This precision can give insight on competing scenarios of structure formation and evolution and on the role of baryons in cluster assembling. Alternatively, for a fixed MC relation, future peaks counts can perform as well as current BAO and SNeIa when combined with Planck.