Gravitational wave consistency relations for multifield inflation

Understand

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 $V \sim \sum_i \lambda_i |\phi_i|^p$ have different predictions for $n_t/r$ than single-field models, even when all the couplings are equal $\lambda_i=\lambda_j$, due to the probabilistic nature of the fields' initial values.
• We analyze well-motivated prior probabilities for the $\lambda_i$ 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$\sigma$ level.