Primordial gravitational waves in quadratic gravity

Abstract

Quadratic gravity is a fourth-order (in derivatives) theory that can serve as an attractive upgrade to the standard description of gravity provided by General Relativity, thanks to its renormalizability and its built-in description of primordial inflation. We bring quadratic gravity into a second-order form by introducing an auxiliary tensor field and we consider the primordial tensor fluctuations (gravitational waves) in the theory around a Friedmann-Lemaître-Robertson-Walker background. After a canonical quantization of the perturbations, we calculate the tensor power spectrum in quasi de Sitter spacetime. We find that the spectral index nt and the amplitude At of the tensor power spectrum are both suppressed by the factor (1 + 2H2*/m2gh)-1, where H* is the Hubble rate at horizon exit and mgh is the mass of the spin-two ghost. This restores the slow-roll consistency condition familiar from single-field inflation models, where the tensor-to-scalar ratio r is equal to -8nt in the lowest nontrivial order in the slow-roll approximation. We also discuss the well-known issue of the ghost problem in fourth-order theories and how it pertains to the results at hand.