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Asymptotic analysis of perturbed dust cosmologies to second order
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013). (Fysik)ORCID iD: 0000-0002-0906-8808
University of Waterloo, Canada.
2013 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 45, no 8, p. 1467-1492Article in journal (Refereed) Published
Abstract [en]

Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a cosmological constant Lambda>0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if Lambda>0 but logarithmic if Lambda=0 and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if Lambda>0 the decaying mode does not die a way, i.e.  it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (K=Lambda=0) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.

Place, publisher, year, edition, pages
Berlin: Springer , 2013. Vol. 45, no 8, p. 1467-1492
Keywords [en]
Cosmology
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-27133DOI: 10.1007/s10714-013-1559-0ISI: 000322177600001OAI: oai:DiVA.org:kau-27133DiVA, id: diva2:618816
Note

Paper available on arXiv:1303.4516

Available from: 2013-04-30 Created: 2013-04-30 Last updated: 2018-10-18Bibliographically approved

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