Starting from an initial classical four dimensional flat background of the heterotic or type II superstrings, we are able to determine at the string one-loop level the quantum corrections to the effective potential due to the spontaneous breaking of supersymmetry by "geometrical fluxes". Furthermore, considering a gas of strings at finite temperature, the full "effective thermal potential" is determined, giving rise to an effective non-trivial pressure. The backreaction of the quantum and thermal corrections to the space-time metric as well as to the moduli fields induces a cosmological evolution that depends on the early time initial conditions and the number of spontaneously broken supersymmetries. We show that for a whole set of initial conditions, the cosmological solutions converge at late times to two qualitatively different trajectories: They are either attracted to (i) a thermal evolution similar to a radiation dominated cosmology, implemented by a coherent motion of some moduli fields, or to (ii) a "Big Crunch" non-thermal cosmological evolution dominated by the non-thermal part of the effective potential or the moduli kinetic energy. During the attraction to the radiation-like era, periods of accelerated cosmology can occur. However, they do not give rise to enough inflation (e-fold < 0.2) for the models we consider, where N>1 supersymmetry is spontaneously broken to N=0.
We consider four dimensional heterotic string backgrounds for which supersymmetry is spontaneously broken via the Scherk-Schwarz mechanism on an internal spatial cycle and by finite temperature effects. We concentrate on initially flat backgrounds with N=4 and N=2 amount of supersymmetry. Thermal and quantum corrections give rise to a non-trivial cosmological evolution. We show that these corrections are under control and calculable due to the underlying no-scale structure of the effective supergravity theory. The effective Friedmann-Hubble equation involves a radiation term ~1/a^4 and a curva…
We review the recent developments in obtaining accelerating cosmologies and/or inflation from higher-dimensional gravitational theories, in particular superstring theories in ten dimensions and M-theory in eleven dimensions. We first discuss why it is difficult to obtain inflationary behavior in the effective low-energy theories of superstring/M-theory, i. e. supergravity theories. We then summarize interesting solutions including S-branes that give rise to accelerating cosmologies and inflationary solutions in M-theory with higher order corrections. Other approaches to inflation in the string…
We study aspects of the accelerating cosmologies obtained from the compactification of vacuum solution and S2-branes of superstring/M theories. Parameter dependence of the resulting expansion of our universe and internal space is examined for all cases. We find that accelerating expansions are obtained also from spherical internal spaces, albeit the solution enters into contracting phase eventually. The relation between the models of SM2- and SD2-branes are also discussed, and a potential problem with SD2-brane model is noted.
We review the cosmology induced by finite temperature and quantum effects on non-supersymmetric string models. We show the evolution is attracted to radiation-like solutions after the Hagedorn era and before the electroweak phase transition. This mechanism generates a hierarchy between the Planck mass and the supersymmetry breaking scale. A dynamical change of space-time dimension can take place.
We extend the analysis of the recently obtained stringy cosmological solutions induced by thermal and quantum effects, once space-time supersymmetry is spontaneously broken by geometrical fluxes. Cases in which more than one modulus participating in the supersymmetry breaking mechanism are investigated. The free energy is obtained at the full string level. In the intermediate cosmological region where the temperature and the supersymmetry breaking scale are sufficiently smaller than the Hagedorn temperature, the quantum and thermal corrections are under control and calculable. The reason is th…
We consider classical superstring theories on flat four dimensional space-times, and where N=4 or N=2 supersymmetry is spontaneously broken. We obtain the thermal and quantum corrections at the string one-loop level and show that the back-reaction on the space-time metric induces a cosmological evolution. We concentrate on heterotic string models obtained by compactification on a T^6 torus and on T^6/Z_2 orbifolds. The temperature T and the supersymmetry breaking scale M are generated via the Scherk-Schwarz mechanism on the Euclidean time cycle and on an internal spatial cycle respectively. Th…
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-Schw…
We study the cosmological implications of the one-loop terms in the string expansion. In particular, we find non-singular solutions which interpolate between a contracting universe and an expanding universe, and show that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies. In addition, we perform numerical calculations to show that the non-singular cosmologies do not require a careful choice of initial conditions, and estimate the likely magnitude of higher order terms in the string expansion.
Exact cosmological solutions for effective actions in D dimensions inspired by the tree-level superstring action are studied. For a certain range of free parameters existing in the model, nonsingular bouncing solutions are found. Among them, of particular interest can be open hyperbolic models, in which, without any fine tuning, the internal scale factor and the dilaton field (connected with string coupling in string theories) tend to constant values at late times. A cosmological singularity is avoided due to nonminimal dilaton-gravity coupling and, for D > 11, due to pure imaginary nature of …
We are presenting the basic ingredients of a stringy mechanism able to resolve both the Hagedorn instabilities of finite temperature superstrings as well as the initial singularity of the induced cosmology in arbitrary dimensions. These are shown to be generic in a large class of (4,0) type II superstring vacua, where non-trivial "gravito-magnetic" fluxes lift the Hagedorn instabilities of the thermal ensemble and the temperature duality symmetry is restored. This symmetry implies a universal maximal critical temperature. In all such models there are three characteristic regimes, each with a d…
We study the cosmology of perturbative heterotic superstring theory during the radiation-like era for semi-realistic backgrounds with initial $\N=1$ supersymmetry. This analysis is valid for times after the Hagedorn era (or alternatively inflation era) but before the electroweak symmetry breaking transition. We find an attraction to a radiation-like era with the ratio of the supersymmetry breaking scale to temperature stabilized. This provides a dynamical mechanism for setting the supersymmetry breaking scale and its corresponding hierarchy with the Planck scale. For the internal space, we fin…
We study cosmological implications of the duality ($PSL(2,{\bf Z})$) invariant potential for the compactification radius $T$, arising in a class of superstring vacua. We show that in spite of having only one minimum in the fundamental domain of the $T$ field there are two types of non-supersymmetric domain walls: one is associated with the discrete Peccei-Quinn symmetry $T\to T+i$, analogous to the axionic domain wall, and another one associated with the noncompact symmetry $T\to 1/T$, analogous to the $Z_2$ domain walls. The first one is bound by stringy cosmic strings. The scale of such doma…
The modified Gauss-Bonnet gravity can be motivated by a number of physical reasons, including: the uniqueness of a gravitational Lagrangian in four and higher dimensions and the leading order $α^\prime$ corrections in superstring theory. Such an effective theory of scalar-tensor gravity has been modeled in the recent past to explain both the initial cosmological singularity problem and the observationally supported cosmological perturbations. Here I present an overview of the recent developments in the use of modified Gauss-Bonnet gravity to explain current observations, touching on key cosmol…
The potential during inflation must be very flat in, at least, the direction of the inflaton. In renormalizable global supersymmetry, flat directions are ubiquitous, but they are not preserved in a generic supergravity theory. It is known that at least some of them are preserved in no-scale supergravity, and simple generalizations of it. We here study a more realistic generalization, based on string-derived supergravity, using the linear supermultiplet formalism for the dilaton. We consider a general class of hybrid inflation models, where a Fayet-Illiopoulos $D$ term drives some fields to lar…
We present a new class of non-singular string cosmologies in d space-time dimensions. At very early times, τ<< τ_c, the Universe is described by a flat σ-model metric, a constant maximal temperature T_c and super-weak string interactions, g_str << 1. During the evolution, the metric remains flat up to τ_c, while the string coupling grows and reaches a critical value g*_str at τ_c. This phase is characterized by a uniform temporal distribution of spacelike branes. At later times, τ> τ_c, the Universe enters in a new phase of expansion, with radiation. The string coupling decreases due to the di…
In this paper we pursue further a programme initiated in a previous work and aimed at the construction, classification and property investigation of time dependent solutions of supergravity (superstring backgrounds) through a systematic exploitation of U-duality hidden symmetries. This is done by first reducing to D=3 where the bosonic part of the theory becomes a sigma model on E_{8(8)}/SO(16), solving the equations through an algorithm that produces general integrals for any chosen regular subalgebra G_r of E_{8(8)} and then oxiding back to D=10. Different oxidations and hence different phys…
In this work, we review the results of Refs [1]-[5] dedicated to the description of the early Universe cosmology induced by quantum and thermal effects in superstring theories. The present evolution of the Universe is described very accurately by the standard Lambda-CDM scenario, while very little is known about the early cosmological eras. String theory provides a consistent microscopic theory to account for such missing epochs. In our framework, the Universe is a torus filled with a gas of superstrings. We first show how to describe the thermodynamical properties of this system, namely energ…
The existence of non-singular string cosmologies is established in a class of two-dimensional supersymmetric Hybrid models at finite temperature. The left-moving sector of the Hybrid models gives rise to 16 real (N_4=4) spacetime supercharges as in the usual superstring models. The right-moving sector is non-supersymmetric at the massless level, but is characterized by MSDS symmetry, which ensures boson/fermion degeneracy of the right-moving massive levels. Finite temperature configurations, which are free of Hagedorn instabilities, are constructed in the presence of non-trivial "gravito-magne…
In a superstring framework, the free energy density, F, can be determined unambiguously at the full string level once supersymmetry is spontaneously broken via geometrical fluxes. We show explicitly that only the moduli associated to the supersymmetry breaking may give relevant contributions. All other spectator moduli μ_I give exponentially suppressed contributions for relatively small (as compared to the string scale) temperature, T, and supersymmetry breaking scale, M. More concisely, for μ_I > T and M, F takes the form F(T,M; μ_I)=F(T,M)+O[exp(- {μ_I\over T}), exp(- {μ_I\over M})] We study…
