4D Einstein-Gauss-Bonnet gravity from non-Einsteinian phase

Abstract

We set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions of vanishing metrical length [1]. In absence of torsion, the effective field equations depend only on the four-metric, reflecting a quadratic curvature nonlinearity but no higher than second order derivatives. In contrast with recent proposals to obtain 4dEGB theories through a singular rescaling of the Gauss-Bonnet coupling, this formalism requires no (classical) regularization of divergences and is inequivalent to Horndeski gravity, while being generally covariant and independent of compactification. Notably, the vacuum field equations admit FLRW cosmologies containing nonsingular bounce and self-accelerating Universe, and spherically symmetric black holes more general than Schwarzschild. The quadratic theory of gravity emerging here is shown to be preserved against the inclusion of higher Lovelock densities in 5+2n dimensions.