The Large Number Limit of Multifield Inflation

TL;DR

This paper analyzes multifield slow-roll inflation models with monomial potentials, revealing how spectral indices and ratios scale with the number of fields, and deriving bounds that can be tested observationally.

Contribution

It introduces a novel relation showing spectral parameters scale with the logarithm of the number of fields and provides bounds on observable quantities in multifield inflation.

Findings

Spectral indices and ratios scale with log of the number of fields.

An upper bound on the number of fields is derived based on slow variation parameters.

The tensor-to-scalar ratio and spectral index bounds are testable in near-future observations.

Abstract

We compute the tensor and scalar spectral index $n_t$, $n_s$, the tensor-to-scalar ratio $r$, the consistency relation $n_t/r$ in the general monomial multifield slow-roll inflation models with potentials $V \sim\sum_i\lambda_i \left|\phi_i\right|^{p_i}$. The general models give a novel relation that $n_t$, $n_s$ and $n_t/r$ are all proportional to the logarithm of the number of fields $N_f$ when $N_f$ is getting extremely large with the order of magnitude around $\mathcal{O}(10^{40})$. An upper bound $N_f\lesssim N_*e^{ZN_*}$ is given by requiring the slow variation parameter small enough where $N_*$ is the e-folding number and $Z$ is a function of distributions of $\lambda_i$ and $p_i$. Besides, $n_t/r$ differs from the single-field result $-1/8$ with substantial probability except for a few very special cases. Finally, we derive theoretical bounds $r>2/N_*$ ($r\gtrsim0.03$) and for $n_t$ which can be tested by observation in the near future.