  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.
