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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

Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

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Electromagnetically induced transparency : Optics in coherent media

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Table Of Integrals Series And Products

Modified Gravity and Cosmology

The energy conditions of general relativity permit one to deduce very powerful and general theorems about the behaviour of strong gravitational fields and cosmological geometries. However, the energy conditions these theorems are based on are beginning to look a lot less secure than they once seemed: (1) there are subtle quantum effects that violate all of the energy conditions, and more tellingly (2), there are also relatively benign looking classical systems that violate all the energy conditions. This opens up a Pandora's box of rather disquieting possibilities --- everything from negative asymptotic mass, to traversable wormholes, to warp drives, up to and including time machines.

Energy conditions and their cosmological implications

It is by now clear that the naive rule for the entropy of a black hole, {entropy} = 1/4 {area of event horizon}, is violated in many interesting cases. Indeed, several authors have recently conjectured that in general the entropy of a dirty black hole might be given purely in terms of some surface integral over the event horizon of that black hole. A formal proof of this conjecture, using Lorentzian signature techniques, has recently been provided by Wald. This note performs two functions. Firstly, a rather different proof of this result is presented --- a proof based on Euclidean signature techniques. The total entropy is S = 1/4 {k A_H / l_P~2} + \int_H {S} \sqrt{g} d~2x. The integration runs over a spacelike cross-section of the event horizon H. The surface entropy density, {S}, is related to the behaviour of the matter Lagrangian under time dilations. Secondly, I shall consider the specific case of Einstein-Hilbert gravity coupled to an effective Lagrangian that is an arbitrary function of the Riemann tensor (though not of its derivatives). In this case a more explicit result is obtained S = 1/4 {k A_H / l_P~2} + 4 pi {k/hbar} \int_H {partial L / partial R_{\mu\nu\lambda\rho}} g~\perp_{\mu\lambda} g~\perp_{\nu\rho} \sqrt{g} d~2x . The symbol $g~\perp_{\mu\nu}$ denotes the projection onto the two-dimensional subspace orthogonal to the event horizon.

Dirty black holes: Entropy as a surface term.

What is going on (as of August 2008) at the interface between theoretical general relativity, stringinspired models, and observational astrophysics? Quite a lot. In this mini-survey I will make a personal choice and focus on four specific questions: Do black holes “exist”? (For selected values of the word “exist”.) Is black hole formation and evaporation unitary? Can one mimic a black hole to arbitrary accuracy? Can one detect the presence of a horizon using local physics?

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Black holes in general relativity

The evaporation of black holes raises a number of conceptual issues, most of them related to the final stages of evaporation, where the interplay between the central singularity and Hawking radiation cannot be ignored. Regular models of black holes replace the central singularity with a nonsingular spacetime region, in which an effective classical geometric description is available. It has been argued that these models provide an effective, but complete, description of the evaporation of black holes at all times up to their eventual disappearance. However, here we point out that known models fail to be self-consistent: the regular core is exponentially unstable against perturbations with a finite timescale, while the evaporation time is infinite, therefore making the instability impossible to prevent. We also discuss how to overcome these difficulties, highlighting that this can be done only at the price of accepting that these models cannot be fully predictive regarding the final stages of evaporation.

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On the viability of regular black holes

Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide experimentally accessible models of curved-space quantum field theory. As such they mimic kinematic aspects of general relativity, though typically they do not mimic the dynamics. Although these analogue models are thereby limited in their ability to duplicate all the effects of Einstein gravity they nevertheless are extremely important—they provide black hole analogues (some of which have already been seen experimentally) and lead to tests of basic principles of curved-space quantum field theory. Currently these tests are still in the realm of gedanken-experiments, but there are plausible candidate models that should lead to laboratory experiments in the not too distant future.

Matt Visser

Papers

Energy conditions and their cosmological implications

Dirty black holes: Entropy as a surface term.

Black holes in general relativity

On the viability of regular black holes

Analogue Models of and for Gravity