The multi-measure cosmological model and its peculiar effective potential

TL;DR

This paper investigates the effective potential in a multi-measure cosmological model, revealing its limitations during early universe evolution and emphasizing the importance of numerical analysis for accurate scalar field behavior.

Contribution

It provides a detailed analysis of the effective potential's applicability in a multi-measure cosmological model, highlighting deviations in early universe dynamics and the need for numerical methods.

Findings

Effective potential closely approximates the actual potential during most of the universe's evolution.

Significant deviations occur in the earliest moments, affecting inflaton behavior.

Numerical potential shapes differ markedly from the effective potential early on.

Abstract

The multi-measures model applied to cosmology has been recently shown to reproduce qualitatively the expected stages of the Universe evolution, along with some unexpected features. In this article, we continue its exploration with a detailed study of the effective potential of the model. An analysis of the limits of applicability of the effective potential show that during most of the Universe evolution, the effective potential is a very good approximation of the actual potential term. There is, however, a deviation between the two occurring in the earliest moments of the evolution, which has an important role on the behavior of the inflaton scalar field. In the studied cases, during this initial time, the inflaton is increasing in absolute value, which seems consistent with "climbing up" the effective potential. To investigate this behavior, we use numerical integration to find the numerical potential and we show that during the early stage of the evolution, the shape of the numerical potential is very different from that of the effective one and instead of a left plateau followed by steep slope, one observes only a slope with additional local maximum and minimum. This result demonstrates that for complicated equations of motion of the inflaton, one should not rely only on the notion of kinetic and effective potential terms to describe the problem as they may not be accurate in the entire numerical domain.