Inflation at Low Scales: General Analysis and a Detailed Model

TL;DR

The paper shows that inflation driven by potentials dominated near the maximum by terms $\phi^m$ with $m>2$ can occur at symmetry-breaking scales well below the Planck scale, avoiding the typical fine-tuning problem of quadratic potentials. It reveals that the scalar spectral index satisfies $0.93 < n_s < 0.97$ for all $m>2$, depending only on the order $m$ of the first non-vanishing derivative, and presents a detailed SO(3) PNGB model where gauge-loop corrections realize a quartic-dominated potential with $n_s=0.95$ and negligible tensor modes. The analysis illustrates that low-scale inflation is viable for a broad class of potentials and that cosmological observables may not tightly constrain the precise potential form. It also discusses fermionic couplings, which can impose lower bounds on the symmetry-breaking scale in explicit symmetry-breaking scenarios.

Abstract

Models of inflationary cosmology based on spontaneous symmetry breaking typically suffer from the shortcoming that the symmetry breaking scale is driven to nearly the Planck scale by observational constraints. In this paper we investigate inflationary potentials in a general context, and show that this difficulty is characteristic only of potentials $V(φ)$ dominated near their maxima by terms of order $φ^2$. We find that potentials dominated by terms of order $φ^m$ with \hbox{$m > 2$} can satisfy observational constraints at an arbitrary symmetry breaking scale. Of particular interest, the spectral index of density fluctuations is shown to depend only on the order of the lowest non-vanishing derivative of $V(φ)$ near the maximum. This result is illustrated in the context of a specific model, with a broken ${\rm SO(3)}$ symmetry, in which the potential is generated by gauge boson loops.