Measuring Hubble' constant in our inhomogeneous Universe

Recent observations of Cepheids in the Virgo cluster have bolstered theevidence that supports a Hubble constant in 70-90 km/s/Mpc range. Thisevidence, by and large, probes the expansion of the Universe within 100 Mpc. Weinvestigate the possibility that the expansion rate within this region issystematically higher than the true expansion rate due to the presence of alocal, large underdense region or void. We begin by calculating the expecteddeviations between the locally measured Hubble constant and the true Hubbleconstant for a variety of models. We also discuss the expected correlationsbetween these deviations and mass fluctuation for the sample volume. We findthat the fluctuations are small for the standard cold dark matter as well asmixed dark matter models but can be substantial in a number of interesting andviable nonstandard scenarios. However, deviations in the Hubble flow for aregion of radius 200 Mpc are small for virtually all reasonable models.Therefore, methods based on supernovae or the Sunyaev-Zel'dovich effect, whichcan probe 200 Mpc scales, will be essential in determining the true Hubbleconstant. We discuss, in detail, the fluctuations induced in the cosmicbackground radiation by voids at the last scattering surface. In addition, wediscuss the dipole and quadrupole fluctuations one would expect if the voidenclosing us is aspherical or if we lie off-center.