Formation of voids in the Universe within the Lemaître–Tolman model

We develop models of void formation starting from a small initial fluctuation at recombination and growing to a realistic present-day density profile in agreement with observations of voids. The model construction is an extension of previously developed algorithms for finding a Lemaître–Tolman metric that evolves between two profiles of either density or velocity specified at two times. Of the four profiles of concern (those of density and velocity at recombination and at the present day), two can be specified and the other two follow from the derived model.
We find that, in order to reproduce the present-day void density profiles, the initial velocity profile is more important than the initial density profile.
Extrapolation of current cosmic microwave background (CMB) observations to the scales relevant to protovoids is very uncertain. Even so, we find that it is very difficult to make both the initial density and velocity fluctuation amplitudes small enough and still obtain a realistic void by today.