The Effects of Gravitational Back-Reaction on Cosmological Perturbations

Because of the non-linearity of the Einstein equations, the cosmological fluctuations which are generated during inflation on a wide range of wavelengths do not evolve independently. In particular, to second order in perturbation theory, the first order fluctuations back-react both on the background geometry and on the perturbations themselves. I this paper, the gravitational back-reaction of long wavelength (super-Hubble) scalar metric fluctuations on the perturbations themselves is investigated for a large class of inflationary models. Specifically, the equations describing the evolution of long wavelength cosmological metric and matter perturbations in an inflationary universe are solved to second order in both the amplitude of the perturbations and in the slow roll expansion parameter. Assuming that the linear fluctuations have random phases, we show that the fractional correction to the power spectrum due to the leading infrared back-reaction terms does not change the shape of the spectrum. The amplitude of the effect is suppressed by the product of the inflationary slow-roll parameter and the amplitude of the linear power spectrum. The non-gaussianity of the spectrum induced by back-reaction is commented upon.Comment: 9 page

The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I

The dynamics of solutions of the Einstein-Vlasov system with Bianchi I symmetry is discussed in the case of massive or massless particles. It is shown that in the case of massive particles the solutions are asymptotic to isotropic dust solutions at late times. The initial singularity is more difficult to analyse. It is shown that the asymptotic behaviour there must be one of a small set of possibilities but it is not clear whether all of these possibilities are realized. One solution is exhibited in the case of massless particles which behaves quite differently near the singularity from any Bianchi I solution with perfect fluid as matter model. In particular the matter is not dynamically negligeable near the singularity for this solution.Comment: 16 page

Absence of a Periodic Component in Quasar z-Distribution

Since the discovery of quasars in papers often appeared and appear the assertions that the redshift quasar distribution includes a periodic component with the period $\Delta z = 0.063$ or 0.11. A statement of such kind, if it is correct, may manifest the existence of a far order in quasar distribution in cosmological time, that might lead to a fundamental revision all the cosmological paradigm. In the present time there is a unique opportunity to check this statement with a high precision, using the rich statictics of 2dF and SDSS catalogues (about 85000 quasars). Our analysis indicates that the periodic component in distribution of quasar redshifts is absent at high confidence level