Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Euclid is a European Space Agency medium-class mission selected for launch in 2019 within the Cosmic Vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis.This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

If the accelerated expansion of the Universe at the present epoch is driven by a dark energy scalar field, there may well be a non-trivial coupling between the dark energy and the cold dark matter (CDM) fluid. Such interactions give rise to new features in cosmological structure growth, like an additional long-range attractive force between CDM particles, or variations of the dark matter particle mass with time. We have implemented these effects in the N-body code GADGET-2 and present results of a series of high-resolution N-body simulations where the dark energy component is directly interacting with the CDM. As a consequence of the new physics, CDM and baryon distributions evolve differently both in the linear and in the nonlinear regime of structure formation. Already on large scales, a linear bias develops between these two components, which is further enhanced by the non-linear evolution. We also find, in contrast with previous work, that the density profiles of CDM haloes are less concentrated in coupled dark energy cosmologies compared with CDM, and that this feature does not depend on the initial conditions setup, but is a specific consequence of the extra physics induced by the coupling. Also, the baryon fraction in haloes in the coupled models is significantly reduced below the universal baryon fraction. These features alleviate tensions between observations and the CDM model on small scales. Our methodology is ideally suited to explore the predictions of coupled dark energy models in the fully non-linear regime, which can provide powerful constraints for the viable parameter space of such scenarios.

We present a new massively parallel code for N-body and cosmological hydrodynamical simulations of modified gravity models. The code employs a multigrid-accelerated Newton-Gauss-Seidel relaxation solver on an adaptive mesh to efficiently solve for perturbations in the scalar degree of freedom of the modified gravity model. As this new algorithm is implemented as a module for the p-gadget3 code, it can at the same time follow the baryonic physics included in p-gadget3, such as hydrodynamics, radiative cooling and star formation. We demonstrate that the code works reliably by applying it to simple test problems that can be solved analytically, as well as by comparing cosmological simulations to results from the literature. Using the new code, we perform the first non-radiative and radiative cosmological hydrodynamical simulations of an f (R)-gravity model. We also discuss the impact of AGN feedback on the matter power spectrum, as well as degeneracies between the influence of baryonic processes and modifications of gravity.

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We present the first suite of cosmological N-body simulations that simultaneously include the effects of two different and theoretically independent extensions of the standard ΛCDM cosmological scenario -namely an f (R) theory of Modified Gravity (MG) and a cosmological background of massive neutrinos -with the aim to investigate their possible observational degeneracies. We focus on three basic statistics of the large-scale matter distribution, more specifically the nonlinear matter power spectrum, the halo mass function, and the halo bias. Our results show that while these two extended models separately determine very prominent and potentially detectable features in all the three statistics, when we allow them to be simultaneously at work these features are strongly suppressed. In particular, when an f (R) gravity model with f R0 = −1 × 10 −4 is combined with a total neutrino mass of Σ i m νi = 0.4 eV, the resulting matter power spectrum, halo mass function, and bias at z = 0 are found to be consistent with the standard model's predictions at the 10%, 20%, and 5% accuracy levels, respectively. Therefore, our results imply an intrinsic theoretical limit to the effective discriminating power of present and future observational data sets with respect to these widely considered extensions of the standard cosmological scenario.

We present a complete numerical study of cosmological models with a time‐dependent coupling between the dark energy component driving the present accelerated expansion of the Universe and the cold dark matter (CDM) fluid. Depending on the functional form of the coupling strength, these models show a range of possible intermediate behaviours between the standard ΛCDM background evolution and the widely studied case of interacting dark energy models with a constant coupling. These different background evolutions play a crucial role in the growth of cosmic structures and determine strikingly different effects of the coupling on the internal dynamics of non‐linear objects. By means of a suitable modification of the cosmological N‐body code gadget‐2, we have performed a series of high‐resolution N‐body simulations of structure formation in the context of interacting dark energy models with variable couplings. Depending on the type of background evolution, the halo density profiles are found to be either less or more concentrated with respect to ΛCDM, contrarily to what happens for constant coupling models where concentrations can only decrease. However, for some specific choice of the interaction function, the reduction in halo concentrations can be larger than in constant coupling scenarios. We also find that different types of coupling evolution determine specific features in the growth of large‐scale structures, like peculiar distortions of the matter power spectrum shape or different time‐evolutions of the halo mass function. Furthermore, also for time‐dependent couplings, baryons and CDM develop a bias already on large scales, which is progressively enhanced for smaller and smaller scales, and the effect can be significantly larger compared to constant coupling scenarios. The same happens to the baryon fraction of haloes, which can be more significantly reduced below its universal value in variable coupling models with respect to constant coupling cosmologies. In general, we find that time‐dependent interactions between dark energy and CDM can in some cases determine stronger effects on structure formation as compared to the constant coupling case, with a significantly weaker impact on the background evolution of the universe, and might therefore provide a more viable possibility to alleviate the tensions between observations and the ΛCDM model on small scales than the constant coupling scenario.

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