Non-Gravitating Scalar Field in the FRW Background

TL;DR

This paper investigates a scalar field in the FRW universe that can be made non-gravitating through specific interactions, analyzing the conditions under which it does not contribute to spacetime curvature, especially in inflation scenarios.

Contribution

It identifies conditions for a scalar field to be non-gravitating in FRW backgrounds and clarifies the role of singular solutions and energy-momentum tensor contributions.

Findings

Certain interaction terms lead to a vanishing energy-momentum tensor.

Singular solutions contribute subtly to the energy-momentum tensor.

Non-gravitating solutions are not valid when singularities are considered.

Abstract

We study interacting scalar field theory non-minimally coupled to gravity in the FRW background. We show that for a specific choice of interaction terms, the energy-momentum tensor of the scalar field vanishes, and as a result the scalar field does not gravitate. The naive space dependent solution to equations of motion gives rise to singular field profile. We carefully analyze the energy-momentum tensor for such a solution and show that the singularity of the solution gives a subtle contribution to the energy-momentum tensor. The space dependent solution therefore is not non-gravitating. Our conclusion is applicable to other space-time dependent non-gravitating solutions as well. We study hybrid inflation scenario in this model when purely time dependent non-gravitating field is coupled to another scalar field.