The Hubble rate in averaged cosmology
  The calculation of the averaged Hubble expansion rate in an averaged
perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small
corrections to the background value of the expansion rate, which could be
important for measuring the Hubble constant from local observations. It also
predicts an intrinsic variance associated with the finite scale of any
measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its
variance depend on both the definition of the Hubble rate and the spatial
surface on which the average is performed. We quantitatively study different
definitions of the averaged Hubble rate encountered in the literature by
consistently calculating the backreaction effect at second order in
perturbation theory, and compare the results. We employ for the first time a
recently developed gauge-invariant definition of an averaged scalar. We also
discuss the variance of the Hubble rate for the different definitions.
