A new component of the cosmic medium, a light scalar field or ''quintessence,'' has been proposed recently to explain cosmic acceleration with a dynamical cosmological constant. Such a field is expected to be coupled explicitly to ordinary matter, unless some unknown symmetry prevents it. I investigate the cosmological consequences of a coupled quintessence ͑CQ͒ model, assuming an exponential potential and a linear coupling. This model is conformally equivalent to Brans-Dicke Lagrangians with any power-law potential. I evaluate the density perturbations on the cosmic microwave background and on the galaxy distribution at the present and derive bounds on the coupling constant from the comparison with observational data. A novel feature of CQ is that during the matter dominated era the scalar field has a finite and almost constant energy density. This epoch, denoted as MDE, is a saddle point in the dynamical phase space. The MDE is responsible of several differences with respect to uncoupled quintessence: the multipole spectrum of the microwave background is tilted at large angles, the acoustic peaks are shifted, their amplitude is changed, and the present 8 Mpc/h density variance is diminished. The present data constrain the dimensionless coupling constant to ͉␤͉р0.1 assuming ⍀ m ϭ0.3 and a primordial fluctuation slope n s ϭ1.

We derive the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. We show that the cosmological behavior of f (R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r, m) plane, where m ≡ Rf,RR/f,R and r ≡ −Rf,R/f with f,R ≡ df /dR. This allows us to classify the f (R) models into four general classes, depending on the existence of a standard matter epoch and on the final accelerated stage. The existence of a viable matter dominated epoch prior to a late-time acceleration requires that the variable m satisfies the conditions m(r) ≈ +0 and dm/dr > −1 at r ≈ −1. For the existence of a viable late-time acceleration we require instead either (i) m = −r − 1 , ( √ 3 − 1)/2 < m ≤ 1 and dm/dr < −1 or (ii) 0 ≤ m ≤ 1 at r = −2. These conditions identify two regions in the (r, m) space, one for the matter era and the other for the acceleration. Only models with a m(r) curve that connects these regions and satisfy the requirements above lead to an acceptable cosmology. The models of the type f (R) = αR −n and f = R + αR −n do not satisfy these conditions for any n > 0 and n < −1 and are thus cosmologically unacceptable. Similar conclusions can be reached for many other examples discussed in the text. In most cases the standard matter era is replaced by a cosmic expansion with scale factor a ∝ t 1/2 . We also find that f (R) models can have a strongly phantom attractor but in this case there is no acceptable matter era.

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.

Dark energy, the mysterious cause of the accelerating expansion of the universe, is one of the most important fields of research in astrophysics and cosmology today. Introducing the theoretical ideas, observational methods and results, this textbook is ideally suited to graduate courses on dark energy, and will also supplement advanced cosmology courses. Providing a thorough introduction to this exciting field, the textbook covers the cosmological constant, quintessence, k-essence, perfect fluid models, extra-dimensional models, and modified gravity. Observational research is reviewed, from the cosmic microwave background to baryon acoustic oscillations, weak lensing and cluster abundances. Every chapter ends with problems, with full solutions provided, and any calculations are worked through step-by-step.

A class of generalized non-minimal coupling theories is investigated, in search of scaling attractors able to provide an accelerated expansion at the present time. Solutions are found in the strong coupling regime and when the coupling function and the potential verify a simple relation. In such cases, which include power law and exponential functions, the dynamics is independent of the exact form of the coupling and the potential. The constraint from the time variability of G, however, limits the fraction of energy in the scalar field to less than 4% of the total energy density, and excludes accelerated solutions at the present.

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We introduce a convenient parameterization of dark energy models that is general enough to include several modified gravity models and generalized forms of dark energy. In particular we take into account the linear perturbation growth factor, the anisotropic stress and the modified Poisson equation. We discuss the sensitivity of large-scale weak lensing surveys like the proposed DUNE satellite to these parameters (assuming systematic errors can be controlled). We find that a large-scale weak lensing tomographic survey is able to easily distinguish the Dvali–Gabadadze–Porrati model from ΛCDM and to determine the perturbation growth index to an absolute error of 0.02–0.04.