Cosmology and gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity

TL;DR

This paper explores the cosmological implications of a consistent 4D Einstein-Gauss-Bonnet gravity theory, analyzing tensor perturbations, their unique dispersion relation, and deriving observational bounds on the coupling parameter.

Contribution

It provides the first observational constraint on the coupling parameter in a consistent 4D Einstein-Gauss-Bonnet gravity theory, clarifying its perturbative degrees of freedom and differences from naive limits.

Findings

The theory has only tensorial gravitational degrees of freedom besides matter.

Perturbations are free of pathologies for certain parameter conditions.

A unique $k^4$ term in tensor mode dispersion relations affects small-scale behavior.

Abstract

In a very recent paper [1], we have proposed a novel $4$-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of $D\to4$ Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant $\tilde{\alpha}$. This has been made possible by breaking a part of diffeomorphism invariance, and thus is consistent with the Lovelock theorem. In the present paper, we study cosmological implications of the theory in the presence of a perfect fluid and clarify the similarities and differences between the results obtained from the consistent $4$-dimensional theory and those from the previously considered, naive (and inconsistent) $D\rightarrow 4$ limit. Studying the linear perturbations, we explicitly show that the theory only has tensorial gravitational degrees of freedom (besides the matter degree) and that for $\tilde{\alpha}>0$ and $\dot{H}<0$, perturbations are free of any pathologies so that we can implement the setup to construct early and/or late time cosmological models. Interestingly, a $k^4$ term appears in the dispersion relation of tensor modes which plays significant roles at small scales and makes the theory different than not only general relativity but also many other modified gravity theories as well as the naive (and inconsistent) $D\to 4$ limit. Taking into account the $k^4$ term, the observational constraint on the propagation of gravitational waves yields the bound $\tilde{\alpha} \lesssim (10\,{\rm meV})^{-2}$. This is the first bound on the only parameter (besides the Newton's constant and the choice of a constraint that stems from a temporal gauge fixing) in the consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity.