Temperature definitions and phase transitions within non-minimal large and small inflationary potentials

TL;DR

This paper compares two temperature definitions in inflationary cosmology, linking thermodynamics to phase transitions, and identifies the most consistent models and conditions for inflation, emphasizing the role of non-minimal coupling.

Contribution

It introduces and analyzes two temperature frameworks for inflation, demonstrating the thermodynamic nature of phase transitions and establishing criteria for viable inflationary models with non-minimal coupling.

Findings

T_{RS} is the most self-consistent temperature choice during inflation.

Inflation onset is associated with a thermodynamic phase transition.

Starobinsky and $ ext{alpha}$-attractor models are favored over hilltop potentials.

Abstract

We explore and compare two distinct temperature definitions for scalar field inflation in the context of small- and large-field potentials. The first is based on a real gas, fluid-like temperature, $T_{RG}$, while the second corresponds to a relativistic species-like temperature, $T_{RS}$. We derive the fundamental thermodynamic relations for both and analyze their implications for the most viable inflationary potentials, consistent with Planck constraints. We also investigate non-minimally coupled scenarios, finding that $T_{RS}$ is the most self-consistent choice, as it decreases during inflation, satisfies standard thermodynamic laws, and exhibits frame-independent behavior in both the Jordan and Einstein frames. Remarkably, the $T_{RS}$ approach shows that the inflaton's dynamics is well-described by Van der Waals-like isotherms, linking inflationary evolution to thermodynamic phase transitions. We find that the onset of inflation is associated with a phase transition acting as the ``trigger'' of the inflationary epoch. Our analysis highlights inconsistencies in the hilltop potential and, more generally, in small-field potentials unless a non-minimal coupling is introduced. Conversely, the Starobinsky and $\alpha$-attractor models emerge as the most suitable paradigms. We further show that \emph{frame independence} is achieved only for coupling values $\zeta \leq 1/6$, supporting very small values. Finally, our study of natural inflation with non-minimal coupling reveals a strong dependence on the coupling parameter, where bounds associated with thermodynamic phase transitions coincide with observationally viable ranges, suggesting that thermodynamic considerations may provide an additional criterion to discriminate among inflationary scenarios.