Backreaction in trans-Planckian cosmology: renormalization, trace anomaly and selfconsistent solutions

TL;DR

This paper investigates the effects of modified dispersion relations on quantum scalar fields in cosmology, focusing on renormalization, trace anomaly, and self-consistent solutions within the semiclassical Einstein framework.

Contribution

It provides a detailed renormalization procedure for modified dispersion relations and demonstrates the existence of self-consistent de Sitter solutions in this context.

Findings

Renormalization involves up to fourth adiabatic order in 3+1 dimensions.

The trace anomaly is recovered in the appropriate limit.

Self-consistent de Sitter solutions are found for higher-order dispersion relations.

Abstract

We analyze the semiclassical Einstein equations for quantum scalar fields satisfying modified dispersion relations. We first discuss in detail the renormalization procedure based on adiabatic subtraction and dimensional regularization. We show that, contrary to what expected from power counting arguments, in 3+1 dimensions the subtraction involves up to the fourth adiabatic order even for dispersion relations containing higher powers of the momentum. Then we analyze the dependence of the trace of the renormalized energy momentum tensor with the scale of new physics, and we recover the usual trace anomaly in the appropriate limit. We also find selfconsistent de Sitter solutions for dispersion relations that contain up to the fourth power of the momentum. Using this particular example, we also discuss the possibility that the modified dispersion relation can be mimicked at lower energies by an effective initial state in a theory with the usual dispersion relation.