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 $(1+2{\mathbf{H}}_{\ast }^2/m_{\text{gh}}^2{)}^{-1}$, where ${\mathbf{H}}_{\ast }$ is the Hubble rate at horizon exit and $m_{\text{gh}}$ 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 $-8n_t$ 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.

19+4 pages, v3: matches published version

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Cited by in corpus (3)

• Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections
• Ultraviolet Completion of the Big Bang in Quadratic Gravity
• Strict renormalizability as a paradigm for fundamental physics