Flattening the Inflaton's Potential with Quantum Corrections II

TL;DR

This work presents a low-scale slow-roll inflation model where quantum corrections flatten the inflaton potential via renormalisation-group running of the inflaton mass. Implemented as a hybrid inflation scheme with $V^{1/4}\sim 10^{10}$–$10^{11}$ GeV, the model fixes the RG-driven function $f(\epsilon\ln\phi)$ and an associated parameter $\epsilon$, yielding a viable spectral index while predicting a distinctive bend in the power spectrum, $P(k)=Q k^{-2\nu} e^{\sigma k^{\nu}}$. The spectrum can accommodate $n\lesssim 1$ and provides a concrete, testable alternative to other low-scale inflation scenarios, with a potentially observable imprint distinguishing it from models like Randall–Soljacic–Guth. Overall, the paper demonstrates a natural, non-tuned path to slow-roll inflation tied to SUSY/string-inspired dynamics and RG effects, with clear phenomenological consequences for the shape of $P(k)$ and the scale dependence of $n(k)$.

Abstract

In a previous paper I showed that a classical scalar potential with $V''/V \sim 1$ can be sufficiently flattened by quantum corrections to give rise to slow-roll inflation. In this paper I give a hybrid inflation implementation of that idea which can naturally produce a spectral index in the observationally viable range even for $V^{1/4} \sim 10^{10}$ to $10^{11}$ GeV. Although any observationally viable spectral index can be obtained, the model does predict a distinctive spectral shape.

Figures (3)

• Figure 1: The potential Eq. (4), with $f$ given by Eqs. (16) and (18), for $f(0) = 1$ and $A = 0.5$. The potential energy at $\phi=0$ is subtracted and the normalisation is arbitrary. The number of $e$-folds of inflation until the inflaton starts to fast roll towards $\phi=0$ is plotted on the same graph. The smallest and largest observable scales might be expected to correspond to $N - N_{\rm fr} \sim 10$ and 20, respectively, though there is considerable uncertainty in this estimate.
• Figure 2: The spectra for $f(0)=1$ and the displayed values of $A$.
• Figure 3: The spectral indices for $f(0)=1$ and the displayed values of $A$.