Looking Beyond Inflationary Cosmology

In spite of the phenomenological successes of the inflationary universe scenario, the current realizations of inflation making use of scalar fields lead to serious conceptual problems which are reviewed in this lecture. String theory may provide an avenue towards addressing these problems. One particular approach to combining string theory and cosmology is String Gas Cosmology. The basic principles of this approach are summarized.Comment: invited talk at "Theory Canada 1" (Univ. of British Columbia, Vancouver, Canada, June 2 - 4, 2005) (references updated

Hawking radiation of nonsingular black holes in two dimensions

In this letter we study the process of Hawking radiation of a black hole assuming the existence of a limiting physical curvature scale. The particular model is constructed using the Limiting Curvature Hypothesis (LCH) and in the context of two-dimensional dilaton gravity. The black hole solution exhibits properties of the standard Schwarzschild solution at large values of the radial coordinate. However, near the center, the black hole is nonsingular and the metric becomes that of de Sitter spacetime. The Hawking temperature is calculated using the method of complex paths. We find that such black holes radiate eternally and never completely evaporate. The final state is an eternally radiating relic, near the fundamental scale, which should make a viable dark matter candidate. We briefly comment on the black hole information loss problem and the production of such black holes in collider experiments.Comment: 8 pages, 4 figures; minor revisions; references added; version to appear in JHE

Towards a Stringy Resolution of the Cosmological Singularity

We study cosmological solutions to the low-energy effective action of heterotic string theory including possible leading order $\alpha'$ corrections and a potential for the dilaton. We consider the possibility that including such stringy corrections can resolve the initial cosmological singularity. Since the exact form of these corrections is not known the higher-derivative terms are constructed so that they vanish when the metric is de Sitter spacetime. The constructed terms are compatible with known restrictions from scattering amplitude and string worldsheet beta-function calculations. Analytic and numerical techniques are used to construct a singularity-free cosmological solution. At late times and low-curvatures the metric is asymptotically Minkowski and the dilaton is frozen. In the high-curvature regime the universe enters a de Sitter phase.Comment: 6 pages, 2 Figures; minor revisions; references added; REVTeX 4; version to appear in Phys. Rev.

T and S dualities and The cosmological evolution of the dilaton and the scale factors

Cosmologically stabilizing radion along with the dilaton is one of the major concerns of low energy string theory. One can hope that T and S dualities can provide a plausible answer. In this work we study the impact of S and T duality invariances on dilaton gravity. We have shown various instances where physically interesting models arise as a result of imposing the mentioned invariances. In particular S duality has a very privileged effect in that the dilaton equations partially decouple from the evolution of the scale factors. This makes it easy to understand the general rules for the stabilization of the dilaton. We also show that certain T duality invariant actions become S duality invariance compatible. That is they mimic S duality when extra dimensions stabilize.Comment: Corrected a misleading interpretation of the S duality transformation and a wrong comment on d=10. I thank A.Kaya for pointing this out to me in time. So the new version is dealing with d=10 only. Added references and corrected some typos. Minor re-editing. Omitted a section for elaboration in a further study. Corrected further typo

Linear Perturbations in Brane Gas Cosmology

We consider the effect of string inhomogeneities on the time dependent background of Brane Gas Cosmology. We derive the equations governing the linear perturbations of the dilaton-gravity background in the presence of string matter sources. We focus on long wavelength fluctuations and find that there are no instabilities. Thus, the predictions of Brane Gas Cosmology are robust against the introduction of linear perturbations. In particular, we find that the stabilization of the extra dimensions (moduli) remains valid in the presence of dilaton and string perturbations.Comment: 17 pages, 1 figur

Brane Gas Cosmology, M-theory and Little String Theory

We generalize the Brane Gas Cosmological Scenario to M-theory degrees of freedom, namely $M5$ and $M2$ branes. Without brane intersections, the Brandenberger Vafa(BV) arguments applied to M-theory degrees of freedom generically predict a large 6 dimensional spacetime. We show that intersections of $M5$ and $M2$ branes can instead lead to a large 4 dimensional spacetime. One dimensional intersections in 11D is related to (2,0) little strings (LST) on NS5 branes in type IIA. The gas regime of membranes in M-theory corresponds to the thermodynamics of LST obtained from holography. We propose a mechanism whereby LST living on the worldvolume of NS5 (M5)-branes wrapping a five dimensional torus, annihilate most efficiently in 3+1 dimensions leading to a large 3+1 dimensional spacetime. We also show that this picture is consistent with the gas approximation in M-theory.Comment: 8 page

Unconventional Cosmology

I review two cosmological paradigms which are alternative to the current inflationary scenario. The first alternative is the "matter bounce", a non-singular bouncing cosmology with a matter-dominated phase of contraction. The second is an "emergent" scenario, which can be implemented in the context of "string gas cosmology". I will compare these scenarios with the inflationary one and demonstrate that all three lead to an approximately scale-invariant spectrum of cosmological perturbations.Comment: 45 pages, 10 figures; invited lectures at the 6th Aegean Summer School "Quantum Gravity and Quantum Cosmology", Chora, Naxos, Greece, Sept. 12 - 17 2012, to be publ. in the proceedings; these lecture notes form an updated version of arXiv:1003.1745 and arXiv:1103.227

On the Generation of a Scale-Invariant Spectrum of Adiabatic Fluctuations in Cosmological Models with a Contracting Phase

In Pre-Big-Bang and in Ekpyrotic Cosmology, perturbations on cosmological scales today are generated from quantum vacuum fluctuations during a phase when the Universe is contracting (viewed in the Einstein frame). The backgrounds studied to date do not yield a scale invariant spectrum of adiabatic fluctuations. Here, we present a new contracting background model (neither of Pre-Big-Bang nor of the Ekpyrotic form) involving a single scalar field coupled to gravity in which a scale-invariant spectrum of curvature fluctuations and gravitational waves results. The equation of state of this scalar field corresponds to cold matter. We demonstrate that if this contracting phase can be matched via a nonsingular bounce to an expanding Friedmann cosmology, the scale-invariance of the curvature fluctuations is maintained. We also find new background solutions for Pre-Big-Bang and for Ekpyrotic cosmology, which involve two scalar fields with exponential potentials with background values which are evolving in time. We comment on the difficulty of obtaining a scale-invariant spectrum of adiabatic fluctuations with background solutions which have been studied in the past.Comment: 8 pages, revised version without the section on perturbations, matching the version published on Phys. Rev. D. For cosmological perturbations in the two field model see astro-ph/021127

Inflation and Brane Gases

We investigate a new way of realizing a period of cosmological inflation in the context of brane gas cosmology. It is argued that a gas of co-dimension one branes, out of thermal equilibrium with the rest of the matter, has an equation of state which can - after stabilization of the dilaton - lead to power-law inflation of the bulk. The most promising implementation of this mechanism might be in Type IIB superstring theory, with inflation of the three large spatial dimensions triggered by ``stabilized embedded 2-branes''. Possible applications and problems with this proposal are discussed.Comment: 7 pages, uses REVTeX, version to appear in Phys. Rev.

Stabilization of Extra Dimensions and The Dimensionality of the Observed Space

We present a simple model for the late time stabilization of extra dimensions. The basic idea is that brane solutions wrapped around extra dimensions, which is allowed by string theory, will resist expansion due to their winding mode. The momentum modes in principle work in the opposite way. It is this interplay that leads to dynamical stabilization. We use the idea of democratic wrapping \cite{art5}-\cite{art6}, where in a given decimation of extra dimensions, all possible winding cases are considered. To simplify the study further we assumed a symmetric decimation in which the total number of extra dimensions is taken to be $Np$ where N can be called the order of the decimation. We also assumed that extra dimensions all have the topology of tori. We show that with these rather conservative assumptions, there exists solutions to the field equations in which the extra dimensions are stabilized and that the conditions do not depend on $p$. This fact means that there exists at least one solution to the asymmetric decimation case. If we denote the number of observed space dimensions (excluding time) by $m$, the condition for stabilization is $m\geq 3$ for pure Einstein gravity and $m\leq 3$ for dilaton gravity massaged by string theory parameters.Comment: Final versio