Energy-momentum tensor of cosmological fluctuations during inflation

Abstract

We study the renormalized energy-momentum tensor (EMT) of cosmological scalar fluctuations during the slow-rollover regime for chaotic inflation with a quadratic potential and find that it is characterized by a negative energy density which grows during slow-rollover. We also approach the back-reaction problem as a second-order calculation in perturbation theory finding no evidence that the back-reaction of cosmological fluctuations is a gauge artifact. In agreement with the results for the EMT, the average expansion rate is decreased by the back-reaction of cosmological fluctuations.

Gauge invariant averages for the cosmological backreaction

“…In such a context we cannot covariantly define the spatial boundaries as done for the temporal ones, for lack of appropriate fields at our disposal. Using for B(x) a function of the coordinates, which does not change under a GT, the integral (2.10) fails to be gauge invariant: repeating the same procedure as before we find that the final result (2.12), is replaced in this case by: 14) where 15) We see that the breaking of gauge invariance is given by an integral over a ring-shaped region lying near the space boundary, B = r 0 , and having a "thickness" ∆r controlled by the magnitude of the GT. We shall now argue that this breaking term tends to be subdominant for large enough spatial volumes.…”

Backreaction in the Lemaître–Tolman–Bondi model

“…where δ(t − t 0 (r) − τ c ) is the delta function, τ c is the constant value of proper time which labels the hypersurface, and on the second line we have plugged in (5) and (11). To keep the analogy with the FRW case as close as possible, we will consider only spacetimes where the coordinate r ranges from 0 to ∞.…”

“…First, naive perturbative results break down when perturbations have an effect on the background, in other words when backreaction is important. In addition to the usual issues of cosmological perturbation theory such as gauge-invariance [8,11,22], one has to worry about new problems such as convergence and consistency of the perturbative expansion. These make consistent backreaction calculations in the perturbative framework an involved task.…”

“…Fully relativistic quantitative studies of backreaction have usually been done in the context of perturbative solutions around a FRW background [8,9,10,11,12,13,14,15,16,17] (see [13] for a more extensive list of references). Of particular interest has been the possibility that backreaction of long wavelength perturbations could lead to a dynamical relaxation of vacuum energy, at the same stroke providing an elegant inflationary mechanism and explaining why the vacuum energy is so much smaller than theoretically expected [14,17,18,19,20].…”

“…This feature is obviously not present in an exact inhomogeneous solution, but the difference between the average behaviour and the behaviour of the corresponding smooth spacetime can be studied unambiguously. With an exact solution one can also study the choice of the hypersurface of averaging in isolation of the different issue of the choice of gauge [8,10,11,12,13,22].…”