The largest possible voids

Observational constraints on the isotropy of the microwave background on angular scales greater than 1^deg^ seriously limit the possible fluctuations in the gravitational potential in the universe because of the Sachs-Wolfe effect. Consequently, they also provide a limit on the initial density inhomogeneities in the universe. We use these limits to show that the typical voids in the mass distribution in an {OMEGA} = 1 universe have limiting diameter D < 80 h^-1^ Mpc and that, for Gaussian initial fluctuations, there should be at most one void in the whole Hubble volume with a diameter D > 130 h^-1^ Mpc. Consequently, the observation of voids in the galaxy distribution larger than the above limit would imply that either (1) gravitational instabilities do not produce the observed structure on large scales, (2) variations in the galaxy distribution can be much more extreme than in the mass distribution (that is, light does not trace mass), or (3) the universe has a density parameter {OMEGA} not equal to 1. If the current upper limits on the cosmic microwave background isotropy were reduced by a factor of 4, our upper limit would come into conflict with the currently observed sizes of voids, and one would have to invoke one of the above alternatives.