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

TL;DR

This work introduces a four-dimensional gravity theory built from an infinite tower of regularized Lovelock-Proca corrections, using Weyl geometry to regulate higher-curvature invariants. The main result is that the tower converts the initial cosmological singularity into an inflationary phase with a graceful exit and produces regular planar black holes, as well as spherically symmetric black holes endowed with primary hair, distinct from the scalar-tensor Horndeski counterpart. The dynamics are encoded in a generalized Friedmann equation $F(H^2)=rac{8\

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.