On the measurement of the Hubble constant in a local low-density universe

Abstract

Astrophysical observations indicate that the ``Local Universe" has a relatively lower matter density ($Ω_0$) than the predictions of the standard inflation cosmology and the large-scale motions of galaxies which provide a mean mass density to be very close to unity. In such a local underdense region the Hubble expansion may not be representative of the global behaviour. Utilizing an underdense sphere embedded in a flat universe as the model of our ``Local Universe", we show that the local Hubble constant would be 1.2 -- 1.4 times larger than the global value on scale of $\sim80$ Mpc, depending on the variation of $Ω_0$. This may account for the recent measurements of the unpleasantly large Hubble constant of $\sim$80 km/s/Mpc using the Cepheid variables in the Virgo cluster and the relative distance between Virgo and Coma cluster and removes the resulted apparent paradox of the age of our universe.