Conformal Backreaction, Chiral and Conformal Anomalies in the Early Universe

TL;DR

This paper explores how conformal anomalies and backreaction effects influence gravity in the early universe, especially during inflation, using the anomaly effective action formalism and analyzing their non-local structures.

Contribution

It provides a systematic analysis of the anomaly effective action in flat spacetime, revealing the non-local mixings and scheme-dependent variations relevant for early universe cosmology.

Findings

Anomaly contributions arise from specific bilinear mixings like $R oxminus E$ and $R oxminus C^2$.

The effective action's form depends on the regularization scheme used.

Anomalies impact the evolution of chiral asymmetries during the early universe.

Abstract

The backreaction of a conformal matter sector and its associated conformal anomaly on gravity can be systematically studied using the formalism of the anomaly effective action. This action, defined precisely in flat spacetime within ordinary quantum field theory, can be analyzed perturbatively in terms of external graviton insertions. The expansion coefficients correspond to correlation functions of the stress-energy tensor, which are renormalized through two key counterterms: the square of the Weyl tensor $(C^2)$ and the Gauss-Bonnet term $(E)$. Anomalous conformal Ward identities impose hierarchical constraints on this expansion, revealing that the anomaly's contribution arises from bilinear mixings of the form $R \Box^{-1} E$ and $R \Box^{-1} C^2$, supplemented by local Weyl-invariant terms. These mixings reflect the non-local structure of the anomaly. The precise form of the effective action, however, may vary depending on the regularization scheme used, with potential differences manifesting through additional Weyl-invariant terms. These actions encapsulate the breaking of Weyl invariance in the early universe, with implications that are particularly relevant during the inflationary epoch. For chiral and gravitational anomalies, we demonstrate that the corresponding effective actions exhibit similar structures, influencing the evolution of chiral asymmetries in the early universe plasma.