Aspects of superstring cosmology are reviewed with an emphasis on the cosmological implications of duality symmetries in the theory The string effective actions are summarized and toroidal compactification to four dimensions reviewed Global symmetries that arise in the compactification are discussed and the duality relationships between the string effective actions are then highlighted Higher-dimensional Kasner cosmologies are presented and interpreted in both string and Einstein frames, and then given in dimensionally reduced forms String cosmologies containing both non-trivial Neveu-Schwarz/Neveu-Schwarz and Ramond-Ramond fields are derived by employing the global symmetries of the effective actions Anisotropic and inhomogeneous cosmologies in four-dimensions are also developed The review concludes with a detailed analysis of the pre-big bang inflationary scenario The generation of primordial spectra of cosmological perturbations in such a scenario is discussed Possible future directions offered in the Horava-Witten theory are outlined

Superstring Cosmology

This paper investigates the predictions of an inflationary phase starting from a homogeneous and anisotropic universe of the Bianchi I type. After discussing the evolution of the background spacetime, focusing on the number of e-folds and the isotropization, we solve the perturbation equations and predict the power spectra of the curvature perturbations and gravity waves at the end of inflation. The main features of the early anisotropic phase is (1) a dependence of the spectra on the direction of the modes, (2) a coupling between curvature perturbations and gravity waves and (3) the fact that the two gravity wave polarizations do not share the same spectrum on large scales. All these effects are significant only on large scales and die out on small scales where isotropy is recovered. They depend on a characteristic scale that can, but a priori must not, be tuned to some observable scale. To fix the initial conditions, we propose a procedure that generalizes the one standardly used in inflation but that takes into account the fact that the WKB regime is violated at early times when the shear dominates. We stress that there exist modes that do not satisfy the WKB condition during the shear-dominated regime and for which the amplitude at the end of inflation depends on unknown initial conditions. On such scales, inflation loses its predictability. This study paves the way for the determination of the cosmological signature of a primordial shear, whatever the Bianchi I spacetime. It thus stresses the importance of the WKB regime to draw inflationary predictions and demonstrates that, when the number of e-folds is large enough, the predictions converge toward those of inflation in a Friedmann–Lemaitre spacetime but that they are less robust in the case of an inflationary era with a small number of e-folds.

Predictions from an anisotropic inflationary era

This article is a review of interpretations which have been given to some well known solutions of the vacuum equations. Special attention is paid to those of Schwarzschild, Curzon and Kerr, and it is argued that the bizarre topologies they have been endowed with are physically unrealistic. Among others discussed are the two-centres solution of Bach and Weyl, the NUT solution, and solutions for an infinite line-mass, both static and rotating.

Physical interpretation of vacuum solutions of Einstein's equations. Part I. Time-independent solutions

Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de Sitter spacetimes. On the interpretation and characterization of metrics. The choice of solutions. The outline] 2) The Schwarzschild solution [Spherically symmetric spacetimes. The Schwarzschild metric and its role in the solar system. Schwarzschild metric outside a collapsing star. The Schwarzschild-Kruskal spacetime. The Schwarzschild metric as a case against Lorentz-covariant approaches. The Schwarzschild metric and astrophysics] 3) The Reissner- Nordstrom solution [Reissner-Nordstrom black holes and the question of cosmic censorship. On extreme black holes, d-dimensional black holes, string theory and "all that"] 4) The Kerr metric [Basic features. The physics and astrophysics around rotating black holes. Astrophysical evidence for a Kerr metric] 5) Black hole uniqueness and multi-black hole solutions 6) Stationary axisymmetric fields and relativistic disks [Static Weyl metrics. Relativistic disks as sources of the Kerr metric and other stationary spacetimes. Uniformly rotating disks] 7) Taub-NUT space [A new way to the NUT metric. Taub-NUT pathologies and applications] 8) Plane waves and their collisions [Plane-fronted waves. New developments and applications. Colliding plane waves] 9) Cylindrical waves [Cylindrical waves and the asymptotic structure of 3-dimensional general relativity. Cylindrical waves and quantum gravity. Cylindrical waves: a miscellany] 10) On the Robinson-Trautman solutions 11) The boost-rotation symmetric radiative spacetimes 12) The cosmological models [Spatially homogeneous cosmologies. Inhomogeneous models] 13) Concluding remarks

Selected Solutions of Einsteins Field Equations: Their Role in General Relativity and Astrophysics

The Siklos class of solutions of Einstein's field equations is investigated by analytical methods. By studying the behaviour of free particles we reach the conclusion that the spacetimes represent exact gravitational waves propagating in the anti-de Sitter universe. The presence of a negative cosmological constant implies that the `background' space is not asymptotically flat and requires `rotating' reference frames in order to fully simplify and view the behaviour of nearby test particles. The Kaigorodov spacetime, which is the simplest representative of the Siklos class, is analysed in more detail. It is argued that it may serve as a `cosmological' analogue of the well known homogeneous pp-waves in the flat universe.

http://iopscience.iop.org/article/10.1088/0264-9381/15/3/019/pdf

Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe

An exact formalism is developed for describing cosmological models with strong, long wavelength gravitational waves of general polarization, propagating over backgrounds corresponding to Bianchi types I through VII. A new metric which exhibits the appropriate symmetries of two equivalent independent polarizations of gravitational waves is introduced and discussed. The formalism is applied to an empty type I cosmology, and it is shown how the original z-dependent chaotic singularity structure transforms itself into gravitational radiation propagating along the z-axis in a Bianchi I background.

D. I. Levine

Papers

Inhomogeneous cosmology - Gravitational radiation in Bianchi backgrounds