On the analogue of Einstein-Gauss-Bonnet theory in 3+1 dimensions

TL;DR

This paper explores how the trace anomaly effective action in four dimensions can resemble Einstein-Gauss-Bonnet gravity, providing a new framework for studying higher curvature corrections in strong gravity regimes.

Contribution

It demonstrates that the trace anomaly effective action can mimic Einstein-Gauss-Bonnet theory in 4D on specific backgrounds, linking quantum anomalies to classical modified gravity.

Findings

Trace anomaly effective action matches Einstein-Gauss-Bonnet equations on certain backgrounds.

Friedmann-like equations coincide in both frameworks on FRW spacetime.

Correspondence extends to quadratic and cubic perturbations.

Abstract

Higher curvature corrections to the Einstein-Hilbert term may play an important role in probing the strong-field regime of gravity. In this letter, we demonstrate that the local effective action reproducing the trace anomaly can resemble the Einstein-Gauss-Bonnet theory in four dimensions on specific backgrounds. The two key observations support this claim: 1) the covariant equation of the trace anomaly coincides with the trace of the metric variation in Einstein-Gauss-Bonnet theory, and 2) on the FRW space-time, the Friedmann-like equations in both frameworks coincide, with this correspondence extending to the quadratic and cubic perturbations. As an intrinsically four-dimensional construct, the trace anomaly effective action emerges as a promising framework for exploring higher curvature corrections to Einstein's General Relativity in a self-consistent manner.