Conflict between some higher-order curvature invariant terms

TL;DR

This paper demonstrates a fundamental conflict between certain higher-order curvature terms in quantum gravity, specifically between curvature squared and Gauss-Bonnet squared terms, affecting early universe models.

Contribution

It reveals a hermiticity conflict that restricts the simultaneous inclusion of these curvature terms in gravitational actions.

Findings

Hermiticity conflict between curvature squared and Gauss-Bonnet squared terms

Implication that only one of these terms can be included alongside Einstein-Hilbert

Exploration of early cosmic evolution with Gauss-Bonnet squared term

Abstract

A viable quantum theory does not allow curvature invariant terms of different higher orders to be accommodated in the gravitational action. We show that there is indeed a conflict between the curvature squared and Gauss-Bonnet squared terms from the point of view of hermiticity. This means one should choose either, in addition to the Einstein-Hilbert term, but never the two together. We explore early cosmic evolution with Gauss-Bonnet squared term.