Constraints on the scalar-field potential in warm inflation

TL;DR

This paper investigates the fine-tuning of the scalar potential in warm inflation, finding that certain dissipation regimes require flatter potentials than cold inflation, while others allow for steeper potentials.

Contribution

It quantifies the fine-tuning parameter in warm inflation and compares bounds across different dissipation regimes, highlighting conditions that relax or tighten potential flatness requirements.

Findings

Warm inflation with dissipation rate $\Gamma \propto T^c$, $c extgreater 0$ requires flatter potentials than cold inflation.

For $c extless 0$, the potential flatness bounds can be significantly relaxed.

Models with negative temperature dependence can accommodate steeper potentials.

Abstract

We quantify the degree of fine tuning required to achieve an observationally viable period of inflation in the strongly dissipative regime of warm inflation. The ``fine-tuning'' parameter $\lambda$ is taken to be the ratio of the change in the height of the potential $\Delta V$ to the change in the scalar field $(\Delta \phi)^{4}$, i.e. the width of the potential, and therefore measures the requisite degree of flatness in the potential. The best motivated warm inflationary scenarios involve a dissipation rate of the kind $\Gamma\propto T^c$ with $c\geq 0$, and for all such cases, the bounds on $\lambda$ are tighter than those for standard cold inflation by at least 3 orders of magnitude. In other words, these models require an even flatter potential than standard inflation. On the other hand for the case of warm inflation with $c< 0$, we find that in a strongly dissipative regime the bound on $\lambda$ can significantly weaken with respect to cold inflation. Thus, if a warm inflation model can be constructed in a strongly dissipative, negatively temperature-dependent regime, it accommodates steeper potentials otherwise ruled out in standard inflation.