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 n t and the amplitude A t of the tensor power spectrum are both suppressed by the factor (1 + 2 H 2 * / m 2 gh ) -1 , where H * is the Hubble rate at horizon exit and m gh 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 -8 n t 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.