Imprints of primordial voids on the cosmic microwave background

We generalize in several ways the results existing in the literature: a) wemake use of an exact general relativistic solution for a spherical, nearlyempty cavity in the matter dominated era to evaluate the null geodesics and theSachs-Wolfe effect; b) we evaluate the magnitude of the adiabatic fluctuationsof the photon-baryon plasma; c) we study the influence of the shell profile;and d) we take into account the finite thickness of the last scattering surface(LSS) and the influence of its position with respect to the void center. Wefind empirically an analytic approximation to the Sachs-Wolfe effect for allcrossing geometries and we derive an upper limit of $\approx$ 25 $h^{-1}$ Mpcfor the comoving radii of voids sitting on the LSS in order to achievecompatibility with COBE's data. As a nearly empty void has an overcomovingexpansion of a factor of $\approx$ 4 between decoupling and the present, themaximum allowed size at present is $\approx$ 100 $h^{-1}$ Mpc. On the otherhand, the smallness of the comoving size relative to the sound horizon reducesstrongly the adiabatic effect by Silk damping and makes it negligible. Most ofthe signature of primordial voids comes therefore from metric effects andconsists of subdegree spots blue or red depending on whether the center liesbeyond or within the LSS. In conclusion we refine and confirm earlierconstraints on a power law void spectrum originated in an inflationary phasetransition and capable of generating the observed large scale structure.Comment: 14 pages, 5 figures, submitted to Montly Notice