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

Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

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The Cosmological Constant and Dark Energy

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

/pdf/the-observation-of-gravitational-waves-from-a-binary-black-58srpupgg9.pdf

The Observation of Gravitational Waves from a Binary Black Hole Merger

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

We consider the scenario emerging from the dynamics of a generalized Born-Infeld theory. The equation of state describing this system is given in terms of the energy density $\ensuremath{\rho}$ and pressure p by the relationship $p=\ensuremath{-}A/{\ensuremath{\rho}}^{\ensuremath{\alpha}},$ where A is a positive constant and $0l\ensuremath{\alpha}l~1.$ We discuss the conditions under which homogeneity arises and show that this equation of state describes the evolution of a universe evolving from a phase dominated by nonrelativistic matter to a phase dominated by a cosmological constant via an intermediate period where the effective equation of state is given by $p=\ensuremath{\alpha}\ensuremath{\rho}.$

Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification

The equation of motion for massive particles in f(R) modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, R, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak-field limit. Connections with MOND and with the Pioneer anomaly are further discussed.

Extra force in f(R) modified theories of gravity

Dark energy–dark matter interaction and putative violation of the equivalence principle from the Abell cluster A586

Recent studies of type Ia supernovas with redshifts up to about $z\ensuremath{\lesssim}1$ reveal evidence for a cosmic acceleration in the expansion of the Universe. The most straightforward explanation to account for this acceleration is a cosmological constant dominating the recent history of our Universe; however, a more interesting suggestion is to consider an evolving vacuum energy. Several proposals have been put forward along these lines, most of them in the context of general relativity. In this work we analyze the conditions under which the dynamics of a self-interacting Brans-Dicke field can account for this accelerated expansion of the Universe. We show that accelerated expanding solutions can be achieved with a quadratic self-coupling of the Brans-Dicke field and a negative coupling constant \ensuremath{\omega}.

http://cds.cern.ch/record/403889/files/9910056.pdf

Nonminimal coupling and quintessence

A Brans-Dicke theory is considered with a scalar-field-dependent cosmological term. Solutions of the field equations in a homogeneous and isotropic space-time are obtained and discussed.

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Orfeu Bertolami

Papers

Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification

Extra force in f(R) modified theories of gravity

Dark energy–dark matter interaction and putative violation of the equivalence principle from the Abell cluster A586

Nonminimal coupling and quintessence

Time-dependent cosmological term