We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

A simple cosmological model with only six parameters (matter density, Omega_m h^2, baryon density, Omega_b h^2, Hubble Constant, H_0, amplitude of fluctuations, sigma_8, optical depth, tau, and a slope for the scalar perturbation spectrum, n_s) fits not only the three year WMAP temperature and polarization data, but also small scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the best fit values for cosmological parameters for the power-law flat LCDM model are (Omega_m h^2, Omega_b h^2, h, n_s, tau, sigma_8) = 0.1277+0.0080-0.0079, 0.02229+-0.00073, 0.732+0.031-0.032, 0.958+-0.016, 0.089+-0.030, 0.761+0.049-0.048). The three year data dramatically shrink the allowed volume in this six dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, the WMAP data_alone_ require dark matter, and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n_s=1, r=0). Models that suppress large-scale power through a running spectral index or a large-scale cut-off in the power spectrum are a better fit to the WMAP and small scale CMB data than the power-law LCDM model: however, the improvement in the fit to the WMAP data is only Delta chi^2 = 3 for 1 extra degree of freedom. The combination of WMAP and other astronomical data yields significant constraints on the geometry of the universe, the equation of state of the dark energy, the gravitational wave energy density, and neutrino properties. Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps.

/pdf/wilkinson-microwave-anisotropy-probe-wmap-three-year-results-2l0o1lq78p.pdf

Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories that include higher-order curvature invariants, and specifically the particular class of $f(R)$ theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. Here $f(R)$ theories of gravity are reviewed in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented---metric, Palatini, and metric affine---and the following topics are discussed: motivation; actions, field equations, and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; and astrophysical applications.

f ( R ) theories of gravity

Modified Gravity and Cosmology

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.

/pdf/cosmology-and-fundamental-physics-with-the-euclid-satellite-1pi37a138r.pdf

Cosmology and Fundamental Physics with the Euclid Satellite

A relativistic theory of modified gravity has been recently proposed by Bekenstein. The tensor field in Einstein's theory of gravity is replaced by a scalar, a vector, and a tensor field which interact in such a way to give modified Newtonian dynamics (MOND) in the weak-field nonrelativistic limit. We study the evolution of the Universe in such a theory, identifying its key properties and comparing it with the standard cosmology obtained in Einstein gravity. The evolution of the scalar field is akin to that of tracker quintessence fields. We expand the theory to linear order to find the evolution of perturbations on large scales. The impact on galaxy distributions and the cosmic microwave background is calculated in detail. We show that it may be possible to reproduce observations of the cosmic microwave background and galaxy distributions with Bekenstein's theory of MOND.

/pdf/large-scale-structure-in-bekenstein-s-theory-of-relativistic-3lbghq66c1.pdf

Large Scale Structure in Bekenstein's Theory of Relativistic Modified Newtonian Dynamics

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Large Scale Structure in Bekenstein's Theory of Relativistic Modified Newtonian Dynamics