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.

No abstract

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.