Nonsingular perturbations in a bouncing brane model

Abstract

The question of how perturbations evolve through a bounce in the Cyclic and Ekpyrotic models of the Universe remains a topical one. Issues concerning singularities at the background level and at the level of perturbation theory continue to be a matter of debate. In this report we hope to demonstrate a non singular collision between the boundary branes at the background level, and circumstances under which all perturbation variables remain bounded through the collision.As expected, we find most collisions to be singular even in the full 5-D formalism, where first order perturbation theory breaks down for at least one perturbation variable. Only in the case that the boundary branes approach each other with constant velocity shortly before the bounce, can a consistent, non singular solution be found. It is then possible to follow the perturbations explicitly until the actual collision. In this case, we find that if a scale invariant spectrum developed on the hidden brane, it will get transferred to the visible brane during the bounce.

Early universe dynamics in semi-classical loop quantum cosmology

“…One of the principle motivations for developing nonsingular bouncing cosmologies is that they provide an alternative to the inflationary scenario for the formation of large-scale structure in the universe. In principle, density perturbations on scales larger than the Hubble radius at the epoch of decoupling can be generated during a phase of decelerated contraction [67,68,13,69]. Since a number of issues regarding the propagation of perturbations through the bounce presently remain unresolved [70,71,72,73], it is important to develop non-singular bouncing models as these can provide a solvable framework for analyzing the evolution of perturbations.…”

Scale invariance in expanding and contracting universes from two-field models

“…Until now there have largely been three approaches to dealing with this problem. One can analyze the perturbations in higher dimensions [12,13,14] in the hope that higher dimensional effects will provide the requisite mixing between the growing and decaying modes. Alternatively one may hope that during the evolution through the bounce from contraction to expansion a similar effect occurs [15,16].…”

Nonlocal matching condition and scale-invariant spectrum in bouncing cosmology

“…It is also easy to verify that δϕ = O(k nΦ+2 ) and δϕ ′ = O(k nΦ+2 ) on theη =η − surface. Therefore the fluctuations on the O = constant surface take the same form as (27) and (28) up to the order we consider and hence the same matching condition (47) is resulted.…”

“…We can choose a different matching surface with O − (η, x) = constant for a different quantity O − . However as explained in the appendix B, the metric and scalar field fluctuations turns out to be the same as (27) and (28) up to the order we consider and leads to the same matching condition (47) below .…”

“…3. In [27] (see also [28]), matching conditions in the five dimensional context has been studied. In our analysis, we are free to choose the time of the matching η − so long as k/aH(η − ) ≪ 1.…”