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.

If dark energy interacts with dark matter, this gives a new approach to the coincidence problem. But interacting dark energy models can suffer from pathologies. We consider the case where the dark energy is modelled as a fluid with constant equation of state parameter w. Non-interacting constant-w models are well behaved in the background and in the perturbed universe. But the combination of constant w and a simple interaction with dark matter leads to an instability in the dark sector perturbations at early times: the curvature perturbation blows up on super-Hubble scales. Our results underline how important it is to carefully analyze the relativistic perturbations when considering models of coupled dark energy. The instability that we find has been missed in some previous work where the perturbations were not consistently treated. The unstable mode dominates even if adiabatic initial conditions are used. The instability also arises regardless of how weak the coupling is. This non-adiabatic instability is different from previously discovered adiabatic instabilities on small scales in the strong-coupling regime.PACS numbers: 95.36.+x, 98.70.Vc, 98.80.Cq

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 DGP brane-world model provides a simple alternative to the standard LCDM cosmology, with the same number of parameters. There is no dark energy -the late universe self-accelerates due to an infrared modification of gravity. We compute the joint constraints on the DGP model from supernovae, the cosmic microwave background shift parameter, and the baryon oscillation peak in the SDSS luminous red galaxy sample. Flat DGP models are within the joint 2 sigma contour, but the LCDM model provides a significantly better fit to the data. These tests are based on the background dynamics of the DGP model, and we comment on further tests that involve structure formation.PACS numbers: 95.36.+x, 98.80.-k, 98.80.Es THE DARK ENERGY PROBLEMThe acceleration of the late-time universe, as implied by observations of supernovae, cosmic microwave background anisotropies and the large-scale structure, poses one of the deepest theoretical problems facing cosmology [1]. Within the framework of general relativity, the acceleration originates from a dark energy field (or effective dark energy) with negative pressure (w ≡ p/ρ < − 1 3 ), such as vacuum energy (w = −1) or a slow-rolling scalar field ("quintessence", w > −1). So far, none of the available models has a natural explanation.For the simplest option of vacuum energy, i.e., the LCDM model, the incredibly small value of the cosmological constantcannot be explained by current particle physics. In addition, the value needs to be fine-tuned,which also has no natural explanation. Quintessence models attempt to address the fine-tuning problem, but do not produce a natural solution -and also cannot address the problem of how Λ is set exactly to 0. Alternatively, it is possible that there is no dark energy, but instead an infrared modification of general relativity, i.e., on very large scales, r > ∼ H −1 0 , that accounts for late-time acceleration. (Note that this does not remove the problem of explaining why the vacuum energy does not gravitate.) Schematically, we are modifying the geometric side of the field equations,rather than the matter side,as in general relativity. It is important that the modification is covariant and incorporates deviations from homogeneity and isotropy, so that one can compute not only the background dynamics, but also the perturbations. DGP MODIFIED GRAVITYOne of the simplest covariant modified-gravity models is based on the Dvali-Gabadadze-Porrati (DGP) braneworld model, as generalized to cosmology by Deffayet [2]. (It is worth noting that the original DGP model with a Minkowski brane was not introduced to explain acceleration -the generalization to a Friedman brane was subsequently found to be self-accelerating.) In this model, gravity leaks off the 4-dimensional brane universe into the 5-dimensional bulk spacetime at large scales. At small scales, gravity is effectively bound to the brane and 4D gravity is recovered to a good approximation, via the lightest modes of the 5D graviton -effectively via an ultralight metastable graviton in the 4D universe. The...

We use observations of cosmic microwave background anisotropies, supernova luminosities and the baryon acoustic oscillation signal in the galaxy distribution to constrain the cosmological parameters in a simple interacting dark energy model with a time-varying equation of state. Using a Monte Carlo Markov Chain technique we determine the posterior likelihoods. Constraints from the individual data sets are weak, but the combination of the three data sets confines the interaction constant $\Gamma$ to be less than 23% of the expansion rate of the Universe $H_0$; at 95% CL $-0.23 < \Gamma/H_0 < +0.15$. The CMB acoustic peaks can be well fitted even if the interaction rate is much larger, but this requires a larger or smaller (depending on the sign of interaction) matter density today than in the non-interacting model. Due to this degeneracy between the matter density and the interaction rate, the only observable effect on the CMB is a larger or smaller integrated Sachs-Wolfe (ISW) effect. While SN or BAO data alone do not set any direct constraints on the interaction, they exclude the models with very large matter density, and hence indirectly constrain the interaction rate when jointly analysed with the CMB data. To enable the analysis described in this paper, we present in a companion paper [arXiv:0907.4981] a new systematic analysis of the early radiation era solution to find the adiabatic initial conditions for the Boltzmann integration.Comment: 16 pages, 10 figures. V2: Improved typography (2-column format); References and a motivation of CPL parametrization added; Accepted by MNRA