Narrow Results

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources.

Stochastic gravity extends semiclassical gravity by allowing for a systematic and self-consistent description of the metric fluctuations produced by the quantum fluctuations of the stress tensor. The effect of minimally coupled scalar fields with arbitrary mass in de Sitter spacetime is discussed, assuming that these fields are in the Bunch–Davies de Sitter invariant vacuum. The matter field fluctuations are described by the noise kernel which is obtained from the symmetrized two-point correlation of the stress tensor operator. The noise kernel is computed in terms of de Sitter invariant bi-tensors. It turns out that in a de Sitter background the two-point function of the linearized Einstein tensor, which is gauge invariant, is directly related to the noise kernel.

In this paper, we consider a quantum mechanical system to model the effect of quantum fields on the evolution of the early universe. The system consists of an inverted oscillator bilinearly coupled to a set of harmonic oscillators. We point out that the role of noise may be crucial in the dynamics of the oscillator, which is analyzed using the theory of harmonic oscillators with random frequency. Using this analogy, we argue that due to the fluctuations around its mean value, a positive vacuum energy density would not produce an exponentially expanding but an oscillating universe, in the same fashion that an inverted pendulum is stabilized by random oscillations of the suspension point (stochastic Kapitza pendulum). The results emphasize the relevance of noise in the evolution of the scale factor.

Validity of the results of semiclassical analysis relies upon the assumption that the 2nd order or higher order corrections are negligible compared to 1st order semiclassical results which are based only on expectation values of operators. However, if the quantum fluctuations are large, then one may need to supplement semiclassical analysis with corrections coming from second order calculations. In the stochastic gravity paradigm, these fluctuations are quantified by noise kernel which are then supposed to act as a source of geometric fluctuations. In this work, we study the behaviour of noise kernel for a scalar field in de Sitter spacetime. We also carry out a similar analysis for some other FRW spacetimes invoking an equivalence that exists between scalar fields in de Sitter and FRW spacetimes.

Based on the stochastic gravity, we study the loop corrections to the scalar and tensor perturbations during inflation. Since the loop corrections to scalar perturbations suffer the infrared(IR) divergence, we consider the IR regularization to obtain the finite value. We find that the loop correction is amplified by the e-folding, in other words there appears the logarithmic corrections, just as discussed by M.Sloth et.al. On the other hand, we find that the tensor perturbations do not suffer from the infrared divergence.