Construction of nonsingular pre-big-bang and ekpyrotic cosmologies and the resulting density perturbations

Abstract

We consider the construction of nonsingular Pre-Big-Bang and Ekpyrotic type cosmological models realized by the addition to the action of specific higher-order terms stemming from quantum corrections. We study models involving general relativity coupled to a single scalar field with a potential motivated by the Ekpyrotic scenario. We find that the inclusion of the string loop and quantum correction terms in the string frame makes it possible to obtain solutions of the variational equations which are nonsingular and bouncing in the Einstein frame, even when a negative exponential potential is present, as is the case in the Ekpyrotic scenario. This allows us to discuss the evolution of cosmological perturbations without the need to invoke matching conditions between two Einstein Universes, one representing the contracting branch, the second the expanding branch. We analyze the spectra of perturbations produced during the bouncing phase and find that the spectrum of curvature fluctuations in the model proposed originally to implement the Ekpyrotic scenario has a large blue tilt (nR = 3). Except for instabilities introduced on small scales, the result agrees with what is obtained by imposing continuity of the induced metric and of the extrinsic curvature across a constant scalar field (up to k 2 corrections equal to the constant energy density) matching surface between the contracting and the expanding Einstein Universes. We also discuss nonsingular cosmological solutions obtained when a Gauss-Bonnet term with a coefficient suitably dependent on the scalar matter field is added to the action in the Einstein frame with a potential for the scalar field present. In this scenario, nonsingular solutions are found which start in an asymptotically flat state, undergo a period of super-exponential inflation and end with a graceful exit. The spectrum of fluctuations is also calculated in this case.

Dilatonic ghost condensate as dark energy

“…In string theory we have other non-perturbative and loop corrections such as the Gauss-Bonnet curvature invariant [31,32,36]. It is certainly of interest to extend our analysis to such a direction.…”

“…Of course, there is a residual gauge freedom: a rescaling of the type ϕ → α ϕ, with α a positive number. The parameters of the scaling solutions change, accordingly, as Q → Q/α, λ → λ/α, β → β and formulas (32) and (34) are invariant under such a rescaling.…”

Realizing scale-invariant density perturbations in low-energy effective string theory

“…Although these perturbations correspond to the ones which are generated before the bounce, it was shown that these spectra are preserved even long after the bounce if α ′ curvature and derivative corrections are taken into account [32]. The reason why the spectrum is highly blue-tilted is that the system is dominated by the kinetic energy of the scalar field.…”

“…Moreover since c 2 R and c 2 T are constants, one can use the formula given in Eqs. (32), (34) and (27), namely…”

The phantom divide in string gas cosmology

“…The study of NEC-violating cosmologies was initiated in [17]; they are often singular [see [18] [19] for more recent references discussing the singular case], but the fact that they can be non-singular and asymptotically locally de Sitter was pointed out in [20], and this observation has been developed in various ways in [21] [22][23] [24][25] [26]. "Phantom cosmologies" involving true violations of the NEC encounter well-known objections [27], but these are avoided by more sophisticated models in which the violation is merely effective 2 : for example, in brane-world theories [29] [30], or through quantum effects [31] [32], or by considering string-motivated Gauss-Bonnet corrections [33] to the Einstein-Hilbert Lagrangian. String theory apparently permits true NEC violation in the very early Universe; specifically, there are in fact explicit NECviolating cosmologies which have been constructed within string theory: Kachru and McAllister [34] have given such an example in the context of a warped deformed conifold in a Calabi-Yau compactification of II B string theory 3 .…”