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

https://www.physics.rutgers.edu/grad/690/Padmanabhan-2003.pdf

Cosmological constant—the weight of the vacuum

We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies

Dark Energy

In canonical quantization of gravity, the state functional does not seem to depend on time. This hampers the physical interpretation of quantum gravity. I critically examine ten major attempts to circumvent this problem and discuss their shortcomings.

/pdf/time-and-interpretations-of-quantum-gravity-4dgucfqvgd.pdf

Time and interpretations of quantum gravity

The cosmological constant and general covariance

The theory of gravity is considered from the little group viewpoint. This leads to a theory with a constraint, which is equivalent to general relativity with an arbitrary cosmological term. With this framework (i) the cosmological constant cannot be put into the Lagrangian but it appears as an integration constant. (ii) The gravitational Lagrangian automatically takes the form of a finite polynomial of the metric. (iii) The so-called conformal factor is fixed, which removes an apparent difficulty in carrying out path integrals.

/pdf/the-exchange-of-massless-spin-two-particles-2yjutntyah.pdf

Yee Jack Ng

Papers

The exchange of massless spin-two particles

Theory of gravity and the cosmological term: the little group viewpoint