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The Hubble tension cast a blight on the standard cosmology. As a possibleattitude to the problem, the local variation of the expansion rate in aninhomogeneous cosmology has been proposed where the spatial averaging over afinite domain was introduced in order to construct local Friedmann spacetime.However, it is not clear that the concept of the spatial averaging itself isgauge invariant or not. Namely the conclusion obtained by the averaging in aparticular gauge is physically meaningful or not. In this paper we address thisquestion, namely the gauge invariance of the spatial averaging in cosmology .We show that the answer is positive by studying the spatial average in thegauge-invariant cosmological perturbation theory.

On the gauge invariance of the locally averaged Friedmann Universe and the Hubble tension