Perturbations in a regular bouncing Universe

We consider a simple toy model of a regular bouncing universe. The bounce is caused by an extra time-like dimension, which leads to a sign flip of the $\rho^2$ term in the effective four dimensional Randall Sundrum-like description. We find a wide class of possible bounces: big bang avoiding ones for regular matter content, and big rip avoiding ones for phantom matter. Focusing on radiation as the matter content, we discuss the evolution of scalar, vector and tensor perturbations. We compute a spectral index of $n_s=-1$ for scalar perturbations and a deep blue index for tensor perturbations after invoking vacuum initial conditions, ruling out such a model as a realistic one. We also find that the spectrum (evaluated at Hubble crossing) is sensitive to the bounce. We conclude that it is challenging, but not impossible, for cyclic/ekpyrotic models to succeed, if one can find a regularized version.Comment: v3: 10 pages, 1 figure, section III revised, conclusions changed, references added, typos corrected; v4: numerics added, identical with version accepted in PR

Asymptotic Behavior of Perturbations in Randall-Sundrum Brane-World

The asymptotic behavior of metric perturbations in Randall-Sundrum infinite brane world is carefully investigated. Perturbations generated by matter fields on the brane are shown to be regular even at the future Cauchy horizon.Comment: 5 page

Fidelity and level correlations in the transition from regularity to chaos

Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities are identical. The result is compared with the susceptibility of chaotic systems against random perturbations. Regular systems are more susceptible against random perturbations than chaotic ones.Comment: 7 pages, 1 figur

A Note on Perturbations During a Regular Bounce

We point out an inconsistency in a method used in the literature for studying adiabatic scalar perturbations in a regular bouncing universe (in four dimensions). The method under scrutiny consists of splitting the Bardeen potential into two pieces with independent evolutions, in order to avoid a singular behavior at the boundaries of the region where the null energy condition (NEC) is violated. However, we argue that this method violates energy-momentum conservation. We then introduce a novel method which provides two independent solutions for the Bardeen potential around the boundaries, even in the case of adiabatic perturbations. The two solutions are well behaved and not divergent.Comment: 3 page

Scalar perturbations in regular two-component bouncing cosmologies

We consider a two-component regular cosmology bouncing from contraction to expansion, where, in order to include both scalar fields and perfect fluids as particular cases, the dominant component is allowed to have an intrinsic isocurvature mode. We show that the spectrum of the growing mode of the Bardeen potential in the pre-bounce is never transferred to the dominant mode of the post-bounce. The latter acquires at most a dominant isocurvature component, depending on the relative properties of the two fluids. Our results imply that several claims in the literature need substantial revision.Comment: 10 pages, 1 figur

Large Adiabatic Scalar Perturbations in a Regular Bouncing Universe

It has been shown that a contracting universe with a dust-like ($w \approx 0$) fluid may provide an almost scale invariant spectrum for the gravitational scalar perturbations. As the universe contracts, the amplitude of such perturbations are amplified. The gauge invariant variable $\Phi$ develops a growing mode which becomes much larger than the constant one around the bounce phase. The constant mode has its amplitude fixed by Cosmic Background Explorer (COBE) normalization, thus the amplitude of the growing mode can become much larger than 1. In this paper, we first show that this is a general feature of bouncing models, since we expect that general relativity should be valid in all scales away from the bounce. However, in the Newtonian gauge, the variable $\Phi$ gives the value of the metric perturbation $\phi$, raising doubts on the validity of the linear perturbative regime at the bounce. In order to address this issue, we obtain a set of necessary conditions for the perturbative series to be valid along the whole history of the model, and we show that there is a gauge in which all these conditions are satisfied, for a set of models, if the constant mode is fixed by COBE normalization. As a by-product of this analysis, we point out that there are sets of solutions for the perturbation variables where some gauge-fixing conditions are not well defined, turning these gauges prohibited for those solutions.Comment: 10 pages, revtex4, minor revision, version to appear in PR