Evaluation of the cosmological constant in inflation with a massive non-minimal scalar field

TL;DR

This paper investigates how trans-Planckian physics and nonlinear dispersion relations influence the vacuum energy density during inflation, revealing finite values and parameter-dependent effects on the cosmological constant.

Contribution

It provides a detailed analysis of the vacuum energy evolution with nonlinear dispersion relations in de Sitter space, including constraints on parameters from backreaction effects.

Findings

Vacuum energy density remains finite under nonlinear dispersion relations.

Quartic correction yields larger vacuum energy than sextic correction for certain parameters.

Backreaction constrains the parameters of nonlinear dispersion relations.

Abstract

In Schroedinger picture we study the possible effects of trans-Planckian physics on the quantum evolution of massive non-minimally coupled scalar field in de Sitter space. For the nonlinear Corley-Jacobson type dispersion relations with quartic or sextic correction, we obtain the time evolution of the vacuum state wave functional during slow-roll inflation, and calculate explicitly the corresponding expectation value of vacuum energy density. We find that the vacuum energy density is finite. For the usual dispersion parameter choice, the vacuum energy density for quartic correction to the dispersion relation is larger than for sextic correction, while for some other parameter choices, the vacuum energy density for quartic correction is smaller than for sextic correction. We also use the backreaction to constrain the magnitude of parameters in nonlinear dispersion relation, and show how the cosmological constant depends on the parameters and the energy scale during the inflation at the grand unification phase transition.