Cosmological Horizon Modes and Linear Response in de Sitter Spacetime

TL;DR

This paper investigates the linear response of quantum fields and spacetime geometry in de Sitter space, highlighting the conditions under which semi-classical gravity is valid and identifying horizon-scale scalar degrees of freedom that may cause significant backreaction.

Contribution

It introduces a framework for analyzing quantum backreaction in de Sitter space, emphasizing the role of horizon-scale scalar modes from the trace anomaly.

Findings

Semi-classical approximation holds for sub-Planckian fluctuations.

Horizon-scale scalar degrees of freedom can induce large backreaction effects.

Quantum backreaction is significant on cosmological horizon scales.

Abstract

Linearized fluctuations of quantized matter fields and the spacetime geometry around de Sitter space are considered in the case that the matter fields are conformally invariant. Taking the unperturbed state of the matter to be the de Sitter invariant Bunch-Davies state, the linear variation of the stress tensor about its self-consistent mean value serves as a source for fluctuations in the geometry through the semi-classical Einstein equations. This linear response framework is used to investigate both the importance of quantum backreaction and the validity of the semi-classical approximation in cosmology. The full variation of the stress tensor, delta T^a_b contains two kinds of terms: (1) those that depend explicitly upon the linearized metric variation delta g_{cd} through the [T^a_b, T^{cd}] causal response function; and (2) state dependent variations, independent of delta g_{cd}. For perturbations of the first kind, the criterion for the validity of the semi-classical approximation in de Sitter space is satisfied for fluctuations on all scales well below the Planck scale. The perturbations of the second kind contain additional massless scalar degrees of freedom associated with changes of state of the fields on the cosmological horizon scale. These scalar degrees of freedom arise necessarily from the local auxiliary field form of the effective action associated with the trace anomaly, are potentially large on the horizon scale, and therefore can lead to substantial non-linear quantum backreaction effects in cosmology.