On the Lapse Function of FLRW Accelerated Expanding Universe in dRGT Massive Gravity Theory

TL;DR

This paper investigates the lapse function behavior in FLRW cosmology within dRGT massive gravity, identifying issues with unphysical solutions and proposing a modified model with a cosmological background density to ensure consistent accelerated expansion.

Contribution

It introduces a cosmological background density parameter into dRGT massive gravity to eliminate unphysical lapse functions and maintain accelerated universe expansion.

Findings

Unphysical lapse functions occur in standard dRGT formalism.

Adding a background density parameter resolves singularities.

The modified model supports only accelerated expansion.

Abstract

In this report, we discuss the behavior of coordinate-time dependent lapse function of FLRW metric of an accelerated expanding universe in the de Rham-Gabadadze-Tolley massive gravity theory. We find for the conventional dRGT formalism the corresponding lapse function can exhibit unphysical behaviors in the associated parameter space with a negative cosmological-constant-like term that leads to the decelerated universe model. To solve this problem, we introduce the so-called cosmological background density parameter to the perfect fluid stress-energy tensor which induces negative pressure. It turns out that this setup could overcome the existence of singular and negative square lapse function in the related parameter space and restore all the parameter space to admit only the accelerated expanding universe model.