Einstein-Gauss-Bonnet gravity in 4-dimensional space-time

Abstract

In this Letter we present a general covariant modified theory of gravity in $D\!=\!4$ space-time dimensions which propagates only the massless graviton and bypasses the Lovelock's theorem. The theory we present is formulated in $D\!>\!4$ dimensions and its action consists of the Einstein-Hilbert term with a cosmological constant, and the Gauss-Bonnet term multiplied by a factor $1/(D\!-\!4)$. The four-dimensional theory is defined as the limit $D\!\to\!4$. In this singular limit the Gauss-Bonnet invariant gives rise to non-trivial contributions to gravitational dynamics, while preserving the number of graviton degrees of freedom and being free from Ostrogradsky instability. We report several appealing new predictions of this theory, including the corrections to the dispersion relation of cosmological tensor and scalar modes, singularity resolution for spherically symmetric solutions, and others.Comment: 6 pages, 1 figure; v3 accepted manuscrip