Gravitational wave consistency relations for multifield inflation

Abstract

We study the tensor spectral index n(t) and the tensor-to-scalar ratio r in the simplest multifield extension to single-field, slow-roll inflation models. We show that multifield models with potentials V∼[under ∑]iλ_{i}|ϕ_{i}|^{p} have different predictions for n(t)/r than single-field models, even when all the couplings are equal λ_{i}=λ_{j}, due to the probabilistic nature of the fields' initial values. We analyze well-motivated prior probabilities for the λ_{i} and initial conditions to make detailed predictions for the marginalized probability distribution of n(t)/r. With O(100) fields and p>3/4, we find that n(t)/r differs from the single-field result of n(t)/r=-1/8 at the 5σ level. This gives a novel and testable prediction for the simplest multifield inflation models.