MEASURING HUBBLE CONSTANT IN OUR INHOMOGENEOUS UNIVERSE

Recent observations of Cepheids in the Virgo cluster have bolstered th e evidence that supports a Hubble constant in the 70-90 km s(-1) Mpc(- 1) range. This evidence, by and large, probes the expansion of the Uni verse within 100 Mpc. We investigate the possibility that the expansio n rate within this region is systematically higher than the true expan sion rate due to the presence of a local, large underdense region or v oid. We begin by calculating the expected deviations between the local ly measured Hubble constant and the true Hubble constant for a variety of models. The calculations are done using linear perturbation theory and are compared with results from N-body simulations wherever possib le. We also discuss the expected correlations between these deviations and mass fluctuation for the sample volume. We find that the fluctuat ions are small for the standard cold dark matter as well as mixed dark matter models, but can be substantial in a number of interesting and viable non-standard scenarios. In particular, we consider models with features in the primordial power spectrum at k similar to 0.05 h Mpc(- 1). Deviations in the Hubble flow for a region of radius 200 Mpc are s mall for virtually all reasonable models. Therefore methods based on s upernovae or the Sunyaev-Zel'dovich effect, which can probe 200-Mpc sc ales, will be essential in determining the true Hubble constant. We di scuss, in detail, the fluctuations induced in the cosmic background ra diation by voids at the last-scattering surface. In addition, we discu ss the dipole and quadrupole fluctuations that one would expect if the void enclosing us is aspherical or if we lie off-centre.