Loop cosmological implications of a non-minimally coupled scalar field

TL;DR

This paper explores how a non-minimally coupled scalar field influences inflation in loop cosmology, finding that negative coupling constants and larger absolute values favor successful inflation with more e-folds.

Contribution

It demonstrates that negative non-minimal coupling enhances inflationary success in loop cosmology, using conformal transformation and both analytical and numerical methods.

Findings

Negative coupling constant favors successful inflation.

Larger |ξ| leads to more e-folds.

Inflation viability depends on initial conditions and coupling range.

Abstract

Non-minimal actions with matter represented by a scalar field coupled to gravity are considered in the context of a homogeneous and isotropic universe. The coupling is of the form $-\xi/2 \phi^2 R$. The possibility of successful inflation is investigated taking into account features of loop cosmology. For that end a conformal transformation is performed. That brings the theory into the standard minimally coupled form (Einstein frame) with some effective field and its potential. Both analytical and numerical estimates show that a negative coupling constant is preferable for successful inflation. Moreover, provided fixed initial conditions, larger $|\xi|$ leads to a greater number of {\em e}-folds. The latter is obtained for a reasonable range of initial conditions and the coupling parameter and indicates a possibility for successful inflation.