The Robustness of n_s < 0.95 in Racetrack Inflation

TL;DR

The paper addresses why racetrack inflation generically predicts a red-tilted spectrum with $n_s \lesssim 0.95$. It reduces the multi-field racetrack potential to an effective single-field model near a saddle, deriving an analytic expression for $n_s$ in terms of the saddle value $\eta_0$ and the number of e-folds $N$. The key finding is that $n_s$ is largely determined by $\eta_0$ and remains below ~0.95 for typical parameters, with higher values accessible only under extra fine-tuning or multi-field dynamics. This work clarifies the robustness of the bound and delineates the experimental and model-building implications for scenarios seeking larger $n_s$.

Abstract

A spectral index n_s < 0.95 appears to be a generic prediction of racetrack inflation models. Reducing a general racetrack model to a single-field inflation model with a simple potential, we obtain an analytic expression for the spectral index, which explains this result. By considering the limits of validity of the derivation, possible ways to achieve higher values of the spectral index are described, although these require further fine-tuning of the potential.

Figures (2)

• Figure 1: Plot of $n_s(\eta_0)$ for Taylor expanded, approximate cosine, and full racetrack potentials (curves from top to bottom).
• Figure 2: Plot of $n_s(\eta_0)$ given in (\ref{['nsp']}) for $2p = 4,6,8,10,20,30,40,50,100$ (increasing $p$ corresponds to larger spectral index).