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

Astrophysical observations indicate that the ``Local Universe" has a relatively lower matter density (\(\Omega_0\)) 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 \(\Omega_0\). 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.