Gravitational wave consistency relations for multifield inflation

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 $V \sim \sum_i λ_i |ϕ_i|^p$ 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 $\mathcal O(100)$ 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 5$σ$ level. This gives a novel and testable prediction for the simplest multifield inflation models.

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