Inflation, black holes with primary hair, and regular planar black holes from an infinite tower of regularized Lovelock-Proca corrections

Abstract: Infinite towers of higher-order corrections to General Relativity have been proposed as a mechanism to resolve singularities in early-universe cosmology and black holes, in a variety of settings. In this work, we consider an infinite tower of higher-order Proca corrections inspired by dimensional regularizations of Lovelock invariants. We find that the Big Bang singularity present in General Relativity is replaced by an inflationary epoch. Furthermore, the Lovelock-Proca tower allows for regular planar black hole solutions and spherically symmetric black holes with primary hair.