Coordinate-time lapse function of FLRW accelerated expanding universe in dRGT massive gravity theory

Abstract

In this paper, 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. Physically, this function is considered to connect a general observer coordinate-time to the related proper-time and also to another normal observer under specific condition. We find that in the standard dRGT formalism, the corresponding lapse function can exhibit unphysical behavior in the parameter space region with a negative cosmological-constant-like term. To solve this problem, we reconsider the cosmological constant energy density 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.