In recent cosmology, the Hubble constant problem has attracted much attention. As a possible solution to the problem, the local variation of the expansion rate in an inhomogeneous cosmology has been proposed where the spatial averaging over a finite domain was introduced in order to construct local Friedmann spacetime. However the treatment was restricted in comoving synchronous gauge ad there is some confusion on the gauge ambiguity of the results. In this letter we study the spatial averaging in the Newtonian gauge in order to clarify the gauge ambiguity and obtain the same results as before.
The Hubble tension casts a blight on the standard cosmology. As a possible solution to the problem, the local variation of the expansion rate has been proposed where the spatial averaging over a finite domain was introduced in order to restore the local Friedmannian behavior in an inhomogeneous cosmology. So far, however, the approaches are limited to the particular choices of the gauges, and it has been unclear whether the results are gauge-invariant. In this paper, we present the gauge-invariant formulation of the local expansion rate which is driven by the spatial average of the gauge-invariant inhomogeneous density. We show that the local cosmological parameters in the finite domain may change from the global parameters, and the relations between them are expressed by the gauge-invariant averaged density.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.