Quadratic Gravity

Abstract

An extension of general relativity (GR) obtained by adding local quadratic terms to the action will be considered. Such theory can be a viable UV completion of GR. The additional terms soften gravity above a certain energy scale and render gravity renormalizable. The presence of 4 derivatives implies via the Ostrogradsky theorem that the classical Hamiltonian is unbounded from below. Nevertheless, I will argue that the relevant solutions are not unstable, but metastable: when the energies are much below a threshold (that is high enough to describe the whole cosmology) runaways are avoided. Remarkably, the chaotic inflation theory of initial conditions ensures that such bound is satisfied and testable implications for the early universe will be discussed. I will also argue that the basic unitarity condition is satisfied when the theory is correctly formulated at the quantum level. Moreover, thanks to the UV softening of gravity, sufficiently light objects must be horizonless and I will discuss explicit analytic examples of horizonless ultracompact objects, which have interesting physical implications.