Quantum induced metric fluctuations in de Sitter cosmology

Enric Verdaguer

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 and 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 being able 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 metric fluctuations incorporating the effects of matter loops. One may distinguish two types of fluctuations, called intrinsic and induced. The induced metric fluctuations are described in a de Sitter background in a gauge independent way in terms of the two-point correlations of the linearized Einstein tensor. Assuming minimally coupled scalar fields in a de Sitter invariant state, the induced two-point metric correlations can be given in terms of de Sitter invariant bi-tensors. We will discuss these issues and the main conclusions.