Parameter space for range of bare graviton mass in an FLRW universe based on dRGT massive gravity theory

We discuss the existence of graviton in a Friedmann-Lemaitre-Robertson-Walker (FLRW) metric of isotropic and homogeneous universe based on de Rham-Gabadadze-Tolley (dRGT) nonlinear massive gravity theory. We consider a similar FLRW fiducial metric in the formulation that lead to a Friedmann-Lemaitre equation similar to the case of cosmological constant based dark energy model. We show that these equations can be constructed by considering a constraint equation found from varying the corresponding action with respect to the fiducial metric. Under a specific choice of fiducial metric lapse function, we determine the range of present cosmological time bare graviton mass in a parameter space by considering the observed cosmological constant density parameter and the related Higuchi bound for the lower dressed graviton mass value. The existence of an indefinite condition in the corresponding parameter space is also discussed and analyzed, as well as the characteristics of the related bare graviton mass and the strong-coupling scale quantity.