Curvature fluctuations on asymptotically de Sitter spacetimes via the semiclassical Einstein's equations

TL;DR

This paper extends the semiclassical Einstein's equations by treating the Einstein tensor as a stochastic variable, analyzing curvature fluctuations in asymptotically de Sitter spacetimes, and demonstrating the robustness of the almost scale-invariant power spectrum.

Contribution

It applies a stochastic extension of semiclassical Einstein's equations to more realistic cosmological models, showing the persistence of the nearly scale-invariant power spectrum.

Findings

Power spectrum remains almost scale-invariant in asymptotically de Sitter spacetimes.

Framework is robust without relying on renormalization freedom.

Applicable to physically motivated cosmological scenarios.

Abstract

It has been proposed recently to consider in the framework of cosmology an extension of the semiclassical Einstein's equations in which the Einstein tensor is considered as a random function. This paradigm yields a hierarchy of equations between the $n$-point functions of the quantum, normal ordered, stress energy-tensor and those associated to the stochastic Einstein tensor. Assuming that the matter content is a conformally coupled massive scalar field on de Sitter spacetime, this framework has been applied to compute the power spectrum of the quantum fluctuations and to show that it is almost scale-invariant. We test the robustness and the range of applicability of this proposal by applying it to a less idealized, but physically motivated, scenario, namely we consider Friedmann-Robertson-Walker spacetimes which behave only asymptotically in the past as a de Sitter spacetime. We show in particular that, under this new assumption and independently from any renormalization freedom, the power spectrum associated to scalar perturbations of the metric behaves consistently with an almost scale-invariant power spectrum.