Gravitational wave consistency relations for multifield inflation

TL;DR

This paper investigates how multifield inflation models predict different tensor spectral index and tensor-to-scalar ratio relations compared to single-field models, providing a testable signature for such theories.

Contribution

It demonstrates that multifield inflation models with specific potentials produce distinct $n_t/r$ predictions, especially with many fields and certain potential powers, differing significantly from single-field results.

Findings

Multifield models with $V \,\sim\, \sum_i \lambda_i |\phi_i|^p$ predict different $n_t/r$ ratios.

For models with ~100 fields and $p>3/4$, $n_t/r$ differs from -1/8 at 5σ significance.

Provides a probabilistic framework for predicting $n_t/r$ in 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 $V \sim \sum_i \lambda_i |\phi_i|^p$ 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. This gives a novel and testable prediction for the simplest multifield inflation models.