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Measurements of the Type Ia supernovae Hubble diagram which suggest that the Universe is accelerating due to the effect of dark energy may be biased because we are located in a 200–300 Mpc underdense ‘void’ which is expanding 20–30 per cent faster than the average rate. With the smaller global Hubble parameter, the  Wilkinson Microwave Anisotropy Probe  5 data on cosmic microwave background (CMB) anisotropies can be fitted without requiring dark energy if there is some excess power in the spectrum of primordial perturbations on 100 Mpc scales. The Sloan Digital Sky Survey (SDSS) data on galaxy clustering can also be fitted if there is a small component of hot dark matter in the form of 0.5 eV mass neutrinos. We show however that if the primordial fluctuations are Gaussian, the expected variance of the Hubble parameter and the matter density are far too small to allow such a large local void. Nevertheless, many such large voids have been identified in the SDSS Luminous Red Galaxy survey in a search for the late integrated Sachs–Wolfe effect due to dark energy. The observed CMB temperature decrements imply that they are nearly empty, thus these real voids too are in gross conflict with the concordance Λ cold dark matter model. The recently observed high peculiar velocity flow presents another challenge for the model. Therefore, whether a large local void actually exists must be tested through observations and cannot be dismissed a priori.

Constraints on large‐scale inhomogeneities from WMAP 5 and SDSS: confrontation with recent observations