Inflation in large N limit of supersymmetric gauge theories

TL;DR

This work shows that inflation can be driven by gauge-invariant multi-flat directions in SU($N$) or SO($N$) SUSY gauge theories, avoiding gauge-singlet inflatons. By constructing a large-$N$ flat-direction sector with a non-minimal kinetic term, the authors derive an effective radial slow-roll dynamics with $\epsilon_{eff}=\epsilon/N$ and $\eta_{eff}=\eta/N$, enabling sub-Planckian inflation provided $N$ is large (around $600$). The curvature perturbation spectrum retains the single-field form with ${\cal P}_{\mathcal{R}}(k) \simeq \frac{V}{24\pi^2 M_p^4 \epsilon_{eff}}$ and a spectral index $n-1 = -(6\epsilon - 2\eta)/N$, approaching scale invariance as $N$ grows. The results highlight a possible embedding of inflation in gauge dynamics via many flat directions, but rely on a substantial increase in the gauge group rank and matter content, presenting significant model-building challenges.

Abstract

Within supersymmetry we provide an example where the inflaton sector is derived from a gauge invariant polynomial of SU(N) or SO(N) gauge theory. Inflation in our model is driven by multi-flat directions, which assist accelerated expansion. We show that multi-flat directions can flatten the individual non-renormalizable potentials such that inflation can occur at sub-Planckian scales. We calculate the density perturbations and the spectral index, we find that the spectral index is closer to scale invariance for large N. In order to realize a successful cosmology we require large N of order, N~600.