Λ\Lambda-Inflation and CMBR Anisotropy

We argue that a $\Lambda$-inflation model can ensure large relative contribution of cosmic gravity waves into the $\Delta T/T$ at COBE scale preserving at the same time a near scale-invariant spectrum of cosmological density perturbations favored by observational data ($n_S\simeq 1$). High efficiency of these models to meet observational tests is discussed.Comment: 5pages, to appear in "Cosmology and Particle Physics", eds J.Garcia-Bellido, R.Durrer, and M.Shaposhniko

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

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

Gravity Waves Signatures from Anisotropic pre-Inflation

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a pre-inflationary anisotropic geometry characterized by a Kasner-like expansion, which is driven dynamically towards inflation by a scalar field. We investigate the evolution of linear metric fluctuations around this background, and calculate the amplification of the long-wavelength GW of a certain polarization during the anisotropic expansion (this effect is absent for another GW polarization, and for scalar fluctuations). These GW are superimposed to the usual tensor modes of quantum origin from inflation, and are potentially observable if the total number of inflationary e-folds exceeds the minimum required to homogenize the observable universe only by a small margin. Their contribution to the temperature anisotropy angular power spectrum decreases with the multipole l as l^(-p), where p depends on the slope of the initial GW power-spectrum. Constraints on the long-wavelength GW can be translated into limits on the total duration of inflation and the initial GW amplitude. The instability of classical GW (and zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or contraction) may have other interesting applications. In particular, if GW become non-linear, they can significantly alter the geometry before the onset of inflation