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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.

The Effective Field Theory of Large-Scale Structure (EFTofLSS) 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 \\(\\Lambda\\)CDM, a fixed value of the baryon/dark-matter ratio, \\(\\Omega_b/\\Omega_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, \\(\\Omega_m\\), and the Hubble parameter, \\(H_0\\), to about \\(13\\%\\), \\(3.2\\%\\) and \\(3.2\\%\\) respectively, obtaining \\(\\ln(10^{10}As)=2.72\\pm 0.13\\), \\(\\Omega_m=0.309\\pm 0.010\\), \\(H_0=68.5\\pm 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.

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 redshifts 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.