Gravitational fluctuations in de Sitter cosmology

Abstract

De Sitter spacetime plays an important role in cosmology: the geometry of most inflationary models is close to de Sitter spacetime and so will be the late-time behavior of the present universe with accelerated expansion. In linearized perturbation theory the metric fluctuations in a de Sitter cosmology describe very well the anisotropies of the microwave background and the observed large scale structure. Recently there has been some interest in the need to go beyond the linear approximation to include the effect of matter loops. This will allow testing perturbation theory in a de Sitter background, checking possible large back-reaction effects on the de Sitter geometry, and also eventually to discriminate between inflationary models that lead to similar results at tree level. Working in the framework of stochastic gravity, or equivalently in the large N expansion, one may derive the two-point correlations for the gravitational fluctuations incorporating the effects of matter loops. One may characterize the quantum gravitational fluctuations in a gauge invariant way by the two-point functions of the linearized Riemann tensor. This can be given in terms of the two-point linearized Einstein and Weyl tensors. Assuming minimally coupled scalar fields in a de Sitter invariant state, the two-point functions of the linearized Einstein tensor over the de Sitter background have been computed in terms of de Sitter invariant bi-tensors.