Backreaction from non-conformal quantum fields in de Sitter spacetime

We study the backreaction on the mean field geometry due to a non-conformal quantum field in a Robertson-Walker background. In the regime of small mass and small deviation from conformal coupling, we compute perturbatively the expectation value of the stress tensor of the field for a variety of vacuum states, and use it to obtain explicitly the semiclassical gravity solutions for isotropic perturbations around de Sitter spacetime, which is found to be stable. Our results show clearly the crucial role of the non-local terms that appear in the effective action: they cancel the contribution from local terms proportional to the logarithm of the scale factor which would otherwise become dominant at late times and prevent the existence of a stable self-consistent de Sitter solution. Finally, the opposite regime of a strongly non-conformal field with a large mass is also considered.Comment: 31 page

Stress tensor fluctuations in de Sitter spacetime

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m^2/H^2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.Comment: 35 pages, 4 figure