Chaotic Inflation with a Fractional Power-Law Potential in Strongly Coupled Gauge Theories

TL;DR

This work shows that chaotic inflation with a fractional power-law potential can be realized in simple strongly coupled SUSY gauge theories, where dimensional transmutation dynamically sets the inflationary energy scale and explains why it is far below the Planck scale. The core mechanism uses an SP($N$) gauge theory with multiple fundamentals and gauge-singlet couplings, leading to a deformed moduli constraint that generates a potential $V(S) \propto |S|^{p}$ with $p=2/(N+1)$. Supergravity corrections are controlled by a shift symmetry in the inflaton direction, ensuring the fractional-power potential remains viable, while the model yields concrete predictions for the CMB observables: $n_s = 1 - \frac{p+2}{2N_e}$ and $r = \frac{4p}{N_e}$, with a normalisation to $Λ \approx 10^{15}$ GeV; upcoming experiments (e.g., Planck, CMBPol, LiteBIRD) can test the tensor-to-scalar ratio $r$ in this framework. The approach provides a compelling link between high-scale gauge dynamics and observable inflationary physics, though it notes caveats related to the conformal window and potential post-inflation SUSY-breaking effects.

Abstract

Models of chaotic inflation with a fractional power-law potential are not only viable but also testable in the foreseeable future. We show that such models can be realized in simple strongly coupled supersymmetric gauge theories. In these models, the energy scale during inflation is dynamically generated by the dimensional transmutation due to the strong gauge dynamics. Therefore, such models not only explain the origin of the fractional power in the inflationary potential but also provide a reason why the energy scale of inflation is much smaller than the Planck scale.