String cosmology

In this review, we discuss various cosmological issues related to our Universe from a string theoretic perspective. We analyse the pre-big bang cosmological scenario which appears naturally in this context due to the existence of scale factor duality symmetry in string theory. We then discuss some of the attractive and problematic features of this scenario. Finally, we introduce a method which is powerful enough to search for cosmological solutions in various low energy limits of string theories.     

On climbing scalars in String Theory

In string models with “brane supersymmetry breaking” exponential potentials emerge at (closed-string) tree level but are not accompanied by tachyons. Potentials of this type have long been a source of embarrassment in flat space, but can have interesting implications for Cosmology. For instance, in ten dimensions the logarithmic slope |V^′/V|$|V^{\prime }/V|$ lies precisely at a “critical” value where the Lucchin–Matarrese attractor disappears while the scalar field is forced to climb up the potential when it emerges from the Big Bang. This type of behavior is in principle perturbative in the string coupling, persists after compactification, could have trapped scalar fields inside potential wells as a result of the cosmological evolution and could have also injected the inflationary phase of our Universe.     

Letter: String Cosmology in Brane World Scenarios

We present exact solutions of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I & V geometry and string dust as the matter source. We assume the Weyl tensor in the bulk has vanishing projection on the brane and examine the different equations of state, for the string dust system. Exact analytic solutions are possible only in few cases.     

String cosmology in inhomogeneous cylindrically symmetric spacetime

String-dust cosmology in an inhomogeneous cylindrically symmetric model is considered. Solutions are obtained only for geometric string with the separability assumption for metric coefficients.     

Letter: Anisotropic Born-Infeld Cosmologies

Anisotropic cosmological spacetimes are constructed from spherically symmetric solutions to Einstein's equations coupled to nonlinear electrodynamics and a positive cosmological constant. This is accomplished by finding solutions in which the roles of r and t are interchanged for all r > 0 (i.e. r becomes timelike and t becomes spacelike). Constant time hypersurfaces have topology R× S ² and in all the spacetimes considered the radius of the two sphere vanishes as t goes to zero. The scale factor of the other dimension diverges as t goes to zero in some solutions and vanishes (or goes to a constant) in other solutions. At late times local observers would see the universe to be homogeneous and isotropic.     

Plane Symmetric Cosmological Macro Models in Self-creation Theory of Gravitation

We have constructed a class of plane symmetric macro models in Barber's second self-creation theory, when the source of the gravitational field is a macro matter field representing perfect fluid and satisfying the gamma-law equation of state p=(-1), where =4/3 and 3/2. The solutions of the field equations are derived and their physical aspects are studied.     

String cosmology in higher dimensional spherically symmetric space-time

Some cosmological solutions for string model are derived in higher dimensional spherically symmetric space-time, following the techniques used by Letelier. The equations of state for strings have been used for different solutions. Also polynomial relation between the metric coefficients has been assumed in some cases.     

String theory as a theory of quantum gravity: a status report

We review the status of string theory as a quantum theory of gravity. Our emphasis is on outstanding questions and remaining challenges rather then on well-established results and successes.     

Long-Wavelength Approximation for String Cosmology with Barotropic Perfect Fluid

The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded by the number of spatial gradients. In the zero order, a quasi-isotropic solution is presented and compared with the general solution of the pure dilaton gravity. Possible cosmological models are analyzed from the point of view of the pre-big bang scenario. The second order solutions are found and their growing and decaying parts are studied.     

Five Dimensional Axially Symmetric String Cosmological Models with Bulk Viscous Fluid

Bulk viscous fluid distribution with massive strings in LRS Bianchi type-1 space time is studied. The exact solutions of the field equations are obtained by using the equation of state ρ=−λ and ρ=λ. We observed that the bulk viscous fluid does not survive for ρ=−λ whereas it survives for ρ=λ. Some physical and geometrical properties of the models are discussed.     

String theory and cosmological singularities

In general relativity space-like or null singularities are common: they imply that ‘time’ can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches.      

String cosmology in Bianchi I space-time

Some cosmological solutions of massive strings are obtained in Bianchi I space-time following the techniques used by Letelier and Stachel. A class of solutions corresponds to string cosmology associated with/without a magnetic field and the other class consists of pure massive strings, obeying the Takabayashi equation of stateρ=(1+W)λ.     

Brane Cosmology From Heterotic String Theory

We consider brane cosmologies within the context of five-dimensional effective actions with higher curvature corrections. The actions are compatible with bulk string amplitude calculations from heterotic string theory. We find wrapped solutions that satisfy the field equations in an approximate but acceptable manner given their complexity, where the internal, four-dimensional, scale factor is naturally inflating, having an exponential De-Sitter form. The temporal dependence of the metric components is nontrivial so that this metric cannot be factored as in a conformally flat case. The effective Planck mass is finite and the brane solutions can localize four-dimensional gravity while the four-dimensional gravitational constant varies with time. The Hubble constant can be freely specified through the initial value of the scalar field, to conform with recent data.     

String theory triplets and higher-spin curvatures

Unconstrained local Lagrangians for higher-spin gauge theories are bound to involve auxiliary fields, whose integration in the partition function generates geometric, effective actions expressed in terms of curvatures. When applied to the triplets, emerging from the tensionless limit of open string field theory, the same procedure yields interesting alternative forms of geometric Lagrangians, expressible for both bosons and fermions as squares of field-strengths. This shows that higher-spin curvatures might play a role in the dynamics, regardless of whether the Fronsdal–Labastida constraints are assumed or forgone.     

Letter: Quantum Kaluza-Klein Cosmologies

In the No-boundary Universe with d = 11 supergravity, under the S _n × S _11–n Kaluza-Klein ansatz, the only seed instanton for the universe creation is a S ₇ × S ₄ space. It is proven that for the Freund-Rubin, Englert and Awada-Duff-Pope models the macroscopic universe in which we are living must be 4- instead of 7-dimensional without appealing to the anthropic principle.     

Integrable Scalar Cosmologies I. Foundations and links with String Theory

We build a number of integrable one-scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non-integrable ones. These include the impossibility for the scalar to emerge from the initial singularity descending along asymptotically exponential potentials with logarithmic slopes exceeding a critical value (“climbing phenomenon”) and the inevitable collapse in a Big Crunch whenever the scalar tries to settle at negative extrema of the potential. We also elaborate on the links between these types of potentials and “brane supersymmetry breaking”, a mechanism that ties together string scale and scale of supersymmetry breaking in a class of orientifold models.     

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous, and conjecturing that this distribution should follow a fractal pattern, in the sense of having a power-law type average density profile, in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts by reviewing the argument concerning the possibility that the galaxy distribution follows such a scale invariant pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that in order to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist.     

String theory in five dimensional cosmological models

A study on string theory has been done in five dimensional flat space-time. Barotropic equation of state andp-string model are discussed. Also a polynomial relation between the two scale factors is assumed. In some special cases the solution reduces to generalized Kasner metric. Further diminision of extra dimension with the evolution of universe is exhibited. A detailed study of phase-space analysis is done for geometric string model.