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.

The Effective Field Theory of Large-Scale Structure is a formalism that allows us to predict the clustering of Cosmological Large-Scale Structure in the mildly non-linear regime in an accurate and reliable way. After validating our technique against several sets of numerical simulations, we perform the analysis for the cosmological parameters of the DR12 BOSS data. We assume ΛCDM, a fixed value of the baryon/dark-matter ratio, Ω b /Ω c , and of the tilt of the primordial power spectrum, n s , and no significant input from numerical simulations. By using the one-loop power spectrum multipoles, we measure the primordial amplitude of the power spectrum, A s , the abundance of matter, Ω m , and the Hubble parameter, H 0 , to about 13%, 3.2% and 3.2% respectively, obtaining ln(10 10 A s ) = 2.72 ± 0.13, Ω m = 0.309 ± 0.010, H 0 = 68.5 ± 2.2 km/(s Mpc) at 68% confidence level. If we then add a CMB prior on the sound horizon, the error bar on H 0 is reduced to 1.6%. These results are a substantial qualitative and quantitative improvement with respect to former analyses, and suggest that the EFTofLSS is a powerful instrument to extract cosmological information from Large-Scale Structure.

We explore the impact of a ΛWDM cosmological scenario on the clustering properties large-scale structure in the Universe. We do this by extending the halo model. The new development is that we consider two components to the mass density: one arising from mass in collapsed haloes, and the second from a smooth component of uncollapsed mass. Assuming that the nonlinear clustering of dark matter haloes can be understood, then from conservation arguments one can precisely calculate the clustering properties of the smooth component and its cross-correlation with haloes. We then explore how the three main ingredients of the halo calculations, the halo mass function, bias and density profiles are affected by WDM. We show that, relative to CDM, the halo mass function is suppressed by 50%, for masses ∼ 100 times the free-streaming mass-scale M fs . Consequently, the bias of low mass haloes can be boosted by as much as ∼ 20% for 0.25 keV WDM particles. Core densities of haloes will also be suppressed relative to the CDM case. We also examine the impact of relic thermal velocities on the density profiles, and find that these effects are constrained to scales r < 1 h −1 kpc, and hence of little importance for dark matter tests, owing to uncertainties in the baryonic physics. We use our modified halo model to calculate the non-linear matter power spectrum, and find that there is significant small-scale power in the model. However, relative to the CDM case the power is suppressed. The amount of suppression depends on the mass of the WDM particle, but can be of order 10% at k ∼ 1 h Mpc −1 for particles of mass 0.25 keV. We then calculate the expected signal and noise that our set of ΛWDM models would give for a future weak lensing mission. We show that the models should in principle be separable at high significance. Finally, using the Fisher matrix formalism we forecast the limit on the WDM particle mass for a future full-sky weak lensing mission like Euclid or LSST. With Planck priors and using only multipoles l < 5000, we find that a lower limit of 2.6 keV should be easily achievable.