General Relativity and the ΛCDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications.All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature.We list the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research.

Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy component, and the addition of neutrinos changing structures on small scales. Here we study Horndeski theories of gravity, the most general minimally coupled scalar-tensor theories of second order. While the cosmological background evolution can be described by an effective equation of state, the perturbations are characterised by four free functions of time. We consider a specific parametrisation of these functions tracing the dark energy component. The likelihood of the full parameter set resulting from combining cosmic microwave background primary anisotropies including their gravitational lensing signal, tomographic angular galaxy clustering and weak cosmic shear, together with all possible non-vanishing cross-correlations is evaluated; both with the Fisher-formalism as well as without the assumption of a specific functional form of the posterior through Monte-Carlo Markov-chains (MCMCs). Our results show that even complex cosmological models can be constrained and could exclude variations of the effective Newtonian gravitational coupling larger than 10% over the age of the Universe. In particular, we confirm strong correlations between parameter groups. Furthermore, we find that the expected contours from MCMC are significantly larger than those from the Fisher analysis even with the vast amount of signal provided by stage IV experiments, illustrating the importance of a proper treatment of non-Gaussian likelihoods and the high level of precision needed for unlocking the sensitivity on gravitational parameters.

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The Fisher matrix is a widely used tool to forecast the performance of future experiments and approximate the likelihood of large data sets. Most of the forecasts for cosmological parameters in galaxy clustering studies rely on the Fisher matrix approach for large-scale experiments like DES, Euclid, or SKA. Here we improve upon the standard method by taking into account three effects: the finite window function, the correlation between redshift bins, and the uncertainty on the bin redshift. The first two effects are negligible only in the limit of infinite surveys. The third effect, on the contrary, is negligible for infinitely small bins. Here we show how to take into account these effects and what the impact on forecasts of a Euclid-type experiment will be. The main result of this article is that the windowing and the bin cross-correlation induce a considerable change in the forecasted errors, of the order of 10-30% for most cosmological parameters, while the redshift bin uncertainty can be neglected for bins smaller than ∆z = 0.1 roughly.

We present constraints on Horndeski gravity from a combined analysis of cosmic shear, galaxy-galaxy lensing and galaxy clustering from 450 deg 2 of the Kilo-Degree Survey (KiDS) and the Galaxy And Mass Assembly (GAMA) survey. The Horndeski class of dark energy/modified gravity models includes the majority of universally coupled extensions to ΛCDM with one scalar field in addition to the metric. We study the functions of time that fully describe the evolution of linear perturbations in Horndeski gravity. Our results are compatible throughout with a ΛCDM model. By imposing gravitational wave constraints, we fix the tensor speed excess to zero and consider a subset of models including e.g. quintessence and f (R) theories. Assuming proportionality of the Horndeski functions α B and α M (kinetic braiding and the Planck mass run rate, respectively) to the dark energy density fraction Ω DE (a) = 1 − Ω m (a), we find for the proportionality coefficientsα B = 0.20 +0.20 −0.33 andα M = 0.25 +0.19 −0.29 . Our value of S 8 ≡ σ 8√ Ω m /0.3 is in better agreement with the Planck estimate when measured in the enlarged Horndeski parameter space than in a pure ΛCDM scenario. In our joint three-probe analysis we report a downward shift of the S 8 best fit value from the Planck measurement of ∆S 8 = 0.016 +0.048 −0.046 in Horndeski gravity, compared to ∆S 8 = 0.059 +0.040 −0.039 in ΛCDM. Our constraints are robust to the modelling uncertainty of the non-linear matter power spectrum in Horndeski gravity. Our likelihood code for multi-probe analysis in both ΛCDM and Horndeski gravity is publicly available at https://github.com/alessiospuriomancini/KiDSHorndeski.

We present a tomographic weak lensing analysis of the Kilo Degree Survey Data Release 4 (KiDS-1000), using a new pseudo angular power spectrum estimator (pseudo-Cℓ) under development for the ESA Euclid mission. Over 21 million galaxies with shape information are divided into five tomographic redshift bins, ranging from 0.1 to 1.2 in photometric redshift. We measured pseudo-Cℓ using eight bands in the multipole range 76 < ℓ < 1500 for auto- and cross-power spectra between the tomographic bins. A series of tests were carried out to check for systematic contamination from a variety of observational sources including stellar number density, variations in survey depth, and point spread function properties. While some marginal correlations with these systematic tracers were observed, there is no evidence of bias in the cosmological inference. B-mode power spectra are consistent with zero signal, with no significant residual contamination from E/B-mode leakage. We performed a Bayesian analysis of the pseudo-Cℓ estimates by forward modelling the effects of the mask. Assuming a spatially flat ΛCDM cosmology, we constrained the structure growth parameter S8 = σ8(Ωm/0.3)1/2 = 0.754−0.029+0.027. When combining cosmic shear from KiDS-1000 with baryon acoustic oscillation and redshift space distortion data from recent Sloan Digital Sky Survey (SDSS) measurements of luminous red galaxies, as well as the Lyman-α forest and its cross-correlation with quasars, we tightened these constraints to S8 = 0.771−0.032+0.006. These results are in very good agreement with previous KiDS-1000 and SDSS analyses and confirm a ∼3σ tension with early-Universe constraints from cosmic microwave background experiments.

We present CosmoPower, a suite of neural cosmological power spectrum emulators providing orders-of-magnitude acceleration for parameter estimation from two-point statistics analyses of Large-Scale Structure (LSS) and Cosmic Microwave Background (CMB) surveys. The emulators replace the computation of matter and CMB power spectra from Boltzmann codes; thus, they do not need to be re-trained for different choices of astrophysical nuisance parameters or redshift distributions. The matter power spectrum emulation error is less than $0.4{{\ \rm per\ cent}}$ in the wavenumber range k ∈ [10−5, 10] Mpc−1, for redshift z ∈ [0, 5]. CosmoPower emulates CMB temperature, polarisation and lensing potential power spectra in the 5σ region of parameter space around the Planck best fit values with an error $\lesssim 10{{\ \rm per\ cent}}$ of the expected shot noise for the forthcoming Simons Observatory. CosmoPower is showcased on a joint cosmic shear and galaxy clustering analysis from the Kilo-Degree Survey, as well as on a Stage IV Euclid-like simulated cosmic shear analysis. For the CMB case, CosmoPower is tested on a Planck 2018 CMB temperature and polarisation analysis. The emulators always recover the fiducial cosmological constraints with differences in the posteriors smaller than sampling noise, while providing a speed-up factor up to O(104) to the complete inference pipeline. This acceleration allows posterior distributions to be recovered in just a few seconds, as we demonstrate in the Planck likelihood case. CosmoPower is written entirely in Python, can be interfaced with all commonly used cosmological samplers and is publicly available.

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