Asymptotics of linearized cosmological perturbations
Abstract
In cosmology an important role is played by homogeneous and isotropic solutions of the EinsteinEuler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the approach to the initial singularity of the background model and at late times. The main equation of interest is a linear hyperbolic equation whose coefficients depend only on time. Expansions for the solutions are obtained in both asymptotic regimes. In both cases it is shown how general solutions with a linear equation of state can be parametrized by certain functions which are coefficients in the asymptotic expansion. For some nonlinear equations of state it is found that the latetime asymptotic behaviour is qualitatively different from that in the linear case.
 Publication:

arXiv eprints
 Pub Date:
 June 2009
 arXiv:
 arXiv:0906.2517
 Bibcode:
 2009arXiv0906.2517A
 Keywords:

 Mathematics  Analysis of PDEs;
 General Relativity and Quantum Cosmology;
 35Q75
 EPrint:
 24 pages