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

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.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Superstring theoryをめぐって(放談室)

Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution

Tables of integrals

Traversable wormholes necessarily require violations of the averaged null energy condition, this being the definition of ``exotic matter.'' However, the theorems which guarantee the energy condition violation are remarkably silent when it comes to making quantitative statements regarding the ``total amount'' of energy condition violating matter in the spacetime. We develop a suitable measure for quantifying this notion and demonstrate the existence of spacetime geometries containing traversable wormholes that are supported by arbitrarily small quantities of exotic matter.

Traversable wormholes with arbitrarily small energy condition violations.

Lorentzian wormhole solutions are investigated in the context of the $D$-dimensional Einstein-Gauss-Bonnet theory of gravitation. These wormholes are found to have features depending on the dimensionality of the spacetime and the coupling coefficient $\ensuremath{\alpha}$ of the Gauss-Bonnet combination. In a large number of cases, the wormhole throat radius is constrained to have a value greater than a certain number depending on $D$ and $\ensuremath{\alpha}$. The possibility of obtaining solutions with normal and exotic matter limited to the vicinity of the throat is explored. Similar to the situation in general relativity, the violation of the weak energy condition persists for $\ensuremath{\alpha}g0$. For $\ensuremath{\alpha}l0$, this condition may or may not be violated depending on the nature of an inequality involving $|\ensuremath{\alpha}|$, $D$, the radius $r$, and the wormhole shape function $b(r)$.

Lorentzian wormholes in Einstein-Gauss-Bonnet theory.

We present a brief review on the Raychaudhuri equations. Beginning with a summary of the essential features of the original article by Raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the context of alternate non-Riemannian spacetimes as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion (Einstein-Cartan-Sciama-Kibble theory). Finally, we give an overview of some recent applications of these equations in general relativity, quantum field theory, string theory and the theory of relativisitic membranes. We conclude with a summary and provide our own perspectives on directions of future research.

The Raychaudhuri equations: A brief review

Scalar kinks propagating along the bulk in warped spacetimes provide a thick brane realisation of the braneworld. We consider here, a class of such exact solutions of the full Einstein-scalar system with a sine-Gordon potential and a negative cosmological constant. In the background of the kink and the corresponding warped geometry, we discuss the issue of localisation of spin half fermions (with emphasis on massive ones) on the brane in the presence of different types of kink-fermion Yukawa couplings. We analyse the possibility of quasi-bound states for large values of the Yukawa coupling parameter $\gamma_F$ (with $\nu$, the warp factor parameter kept fixed) using appropriate, recently developed, approximation methods. In particular, the spectrum of the low--lying states and their lifetimes are obtained, with the latter being exponentially enhanced for large $\nu \gamma_F$. Our results indicate quantitatively, within this model, that it is possible to tune the nature of warping and the strength and form of the Yukawa interaction to obtain trapped massive fermion states on the brane, which, however, do have a finite (but very small) probability of escaping into the bulk.

Scalar kinks and fermion localisation in warped spacetimes

Scalar kinks propagating along the bulk in warped spacetimes provide a thick brane realization of the braneworld. We consider here, a class of such exact solutions of the full Einstein-scalar system with a sine-Gordon potential and a negative cosmological constant. In the background of the kink and the corresponding warped geometry, we discuss the issue of localization of spin half fermions (with emphasis on massive ones) on the brane in the presence of different types of kink–fermion Yukawa couplings. We analyse the possibility of quasi-bound states for large values of the Yukawa coupling parameter ηF (with ν, the warp factor parameter, kept fixed) using appropriate, recently developed, approximation methods. In particular, the spectrum of the low-lying states and their lifetimes are obtained, with the latter being exponentially enhanced for large νηF. Our results indicate quantitatively, within this model, that it is possible to tune the nature of warping and the strength and form of the Yukawa interaction to obtain trapped massive fermion states on the brane, which, however, do have a finite (but very small) probability of escaping into the bulk.

https://iopscience.iop.org/article/10.1088/0264-9381/22/4/008/pdf

Sayan Kar

Papers

Traversable wormholes with arbitrarily small energy condition violations.

Lorentzian wormholes in Einstein-Gauss-Bonnet theory.

The Raychaudhuri equations: A brief review

Scalar kinks and fermion localisation in warped spacetimes

Scalar kinks and fermion localization in warped spacetimes