In a class of non-singular cosmologies derived from higher-order corrections to the low-energy bosonic string action, we derive evolution equations for the most general cosmological scalar, vector and tensor perturbations. In the large scale limit, the evolutions of both scalar and tensor perturbations are characterised by conserved quantities, the usual curvature perturbation in the uniform-field gauge and the tensor-type perturbed metric. The vector perturbation is not affected, being described by the conservation of the angular momentum of the fluid component in the absence of any additional dissipative process. For the scalar-and tensor-type perturbations, we show how, given a background evolution during kinetic driven inflation of the dilaton field, we can obtain the final power spectra generated from the vacuum quantum fluctuations of the metric and the dilaton field during the inflation.PACS numbers: 98.80.Hw

We re-examine the graceful exit problem in the pre-Big Bang scenario of string cosmology, by considering the most general time-dependent classical correction to the Lagrangian with up to four derivatives. By including possible forms for quantum loop corrections we examine the allowed region of parameter space for the coupling constants which enable our solutions to link smoothly the two asymptotic low-energy branches of the pre-Big Bang scenario, and observe that these solutions can satisfy recently proposed entropic bounds on viable singularity free cosmologies.

We investigate both analytically and numerically the evolution of scalar perturbations generated in models which exhibit a smooth transition from a contracting to an expanding Friedmann universe. If the perturbation equations are formulated as second order equations for either the Bardeen potential Ψ or the curvature perturbation on uniform comoving hypersurfaces ζ, at best one of them can stay regular during the transition. We find that the resulting spectral index in the late radiation dominated universe depends on which of these two variables passes regularly through the transition. The results can be parametrized by the exponent q defining the rate of contraction of the universe, or equivalently through the equation of state w = (2 − q)/3q of the background fluid. For q − 1 2 we find that there are no stable cases where both Ψ and ζ are regular during the transition. In particular, for 0 < q ≪ 1, we find that the resulting spectral index is close to scale invariant if Ψ is regular, whereas it has a steep blue behavior if ζ is regular. We also show that as long as q 1, perturbations remain small during contraction in the sense that there exists a gauge in which all the metric and matter perturbation variables are small. This work has important implications for the current debate concerning the nature of perturbations evolving through a collapsing regime into an expanding one: it shows that if in the ekpyrotic model, where 0 < q ≪ 1, the Bardeen potential passes regularly through the transition, this leads to a nearly scale invariant spectrum with n = 1 − 2q, whereas in the case of dilaton-driven string cosmology we have the opposite situation. There it is assumed that ζ passes regularly through the transition, leading to a very blue spectrum of highly suppressed perturbations.

We study the evolution of tensor metric fluctuations in a class of non-singular models based on the string effective action, by including in the perturbation equation the higher-derivative and loop corrections needed to regularise the background solutions. We discuss the effects of such higher-order corrections on the final graviton spectrum, and we compare the results of analytical and numerical computations. *

We study braneworlds in a five-dimensional bulk, where cosmological expansion is mimicked by motion through AdS5. We show that the five-dimensional graviton reduces to the four-dimensional one in the late time approximation of such braneworlds. Inserting a fixed regulator brane far from the physical brane, we investigate quantum graviton production due to the motion of the brane. We show that the massive Kaluza-Klein modes decouple completely from the massless mode and they are not generated at all in the limit where the regulator brane position goes to infinity. In the low energy limit, the massless four-dimensional graviton obeys the usual 4D equation and is therefore also not generated in a radiation-dominated universe