skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Perturbations in a regular bouncing universe

Abstract

We consider a simple toy model of a regular bouncing universe. The bounce is caused by an extra timelike dimension, which leads to a sign flip of the {rho}{sup 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{sub 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.

Authors:
 [1];  [2]
  1. Physics Department, Brown University, Providence, Rhode Island 02912 (United States)
  2. University of Wisconsin, Madison, Wisconsin 53706 (United States)
Publication Date:
OSTI Identifier:
20782647
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.064013; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; DISTURBANCES; EVOLUTION; INDEXES; MATTER; SCALARS; UNIVERSE; VECTORS

Citation Formats

Battefeld, T.J., and Geshnizjani, G. Perturbations in a regular bouncing universe. United States: N. p., 2006. Web. doi:10.1103/PHYSREVD.73.064013.
Battefeld, T.J., & Geshnizjani, G. Perturbations in a regular bouncing universe. United States. doi:10.1103/PHYSREVD.73.064013.
Battefeld, T.J., and Geshnizjani, G. Wed . "Perturbations in a regular bouncing universe". United States. doi:10.1103/PHYSREVD.73.064013.
@article{osti_20782647,
title = {Perturbations in a regular bouncing universe},
author = {Battefeld, T.J. and Geshnizjani, G.},
abstractNote = {We consider a simple toy model of a regular bouncing universe. The bounce is caused by an extra timelike dimension, which leads to a sign flip of the {rho}{sup 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{sub 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.},
doi = {10.1103/PHYSREVD.73.064013},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • An exact model for a relativistic gaseous sphere (i.e., one whose density rho vanishes at the outer boundary of the nonstatic sphere together with the pressure rho) is given. The model has a bounce: The collapsing sphere comes momentarily to rest when the boundary is still outside the Schwarzschild radius of the matter sphere, then there is a macroscopic bounce, and the matter of the expanding sphere spreads all over the universe. This bouncing solution of Einstein's field equations is physically valid at any moment, i.e., the pressure and the density are positive inside the fluid sphere, and there respectivemore » gradients are negative. The mass function is positive, and the circumference is an increasing function of radial coordinate. This solution may represent an easily surveyable model for a supernova explosion where the explosion is so violent that no remnant whatsoever is left.« less
  • We reconsider the toy model studied by Gordon and Turok of a spatially closed Friedmann-Lemaire universe, driven by a massive scalar field, which deflates quasiexponentially, bounces, and then enters a period of standard inflation. We find that the equations for the matter density perturbations can be solved analytically, at least at lowest order in some 'slow-roll' parameter. We can therefore give, in that limit, the explicit spectrum of the postbounce perturbations in terms of their prebounce initial spectrum. Our result is twofold. If the prebounce growing and decaying modes are of the same order of magnitude at the bounce, thenmore » the spectrum of the prebounce growing mode is carried over to the postbounce decaying mode. On the other hand, if, more likely, the prebounce growing mode dominates, then resolution at next order indicates that its spectrum is nicely carried over, with reduced amplitude, to the postbounce growing mode.« less
  • 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 nonsingular 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 5D formalism, where first order perturbation theory breaks down for at least one perturbationmore » variable. Only in the case that the boundary branes approach each other with constant velocity shortly before the bounce, can a consistent, nonsingular 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.« less
  • For bouncing cosmologies such as the ekpyrotic/cyclic scenarios we show that it is possible to make predictions for density perturbations which are independent of the details of the bouncing phase. This can be achieved, as in inflationary cosmology, thanks to the existence of a dynamical attractor, which makes local observables equal to the unperturbed solution up to exponentially small terms. Assuming that the physics of the bounce is not extremely sensitive to these corrections, perturbations can be evolved even at the nonlinear level. The resulting spectrum is not scale invariant and thus incompatible with experimental data. This can be explicitlymore » shown in synchronous gauge where, contrary to what happens in the commonly used Newtonian gauge, all perturbations remain small going towards the bounce and the existence of the attractor is manifest.« less
  • No abstract prepared.