IMPRINTS OF PRIMORDIAL VOIDS ON THE COSMIC MICROWAVE BACKGROUND

We generalize in several ways the results existing in the literature r egarding the interaction between primordial voids and the cosmic micro wave background: (a) we make use of an exact general relativistic solu tion for a spherical, nearly empty cavity in the matter-dominated era to evaluate the null geodesics and the Sachs-Wolfe effect; (b) we eval uate the magnitude of the adiabatic fluctuations of the photon-baryon plasma; (c) we study the influence of the shell profile; and (d) we ta ke into account the finite thickness of the last scattering surface (L SS) and the influence of its position with respect to the void centre. We find empirically an analytic approximation to the Sachs-Wolfe effe ct for all crossing geometries and we derive an upper limit of approxi mate to 25 h(-1) Mpc for the comoving radii of voids sitting on the LS S in order to achieve compatibility with COBE data. As a nearly empty void has an overcomoving expansion of a factor of approximate to 4 bet ween decoupling and the present, the maximum allowed size at present i s approximate to 100h(-1)Mpc. On the other hand, the smallness of the comoving size relative to the sound horizon reduces strongly the adiab atic effect by Silk damping and makes it negligible. Most of the signa ture of primordial voids comes therefore from metric effects and consi sts of subdegree spots that are blue or red depending on whether their centre lies beyond or within the LSS. In conclusion we refine and con firm earlier constraints on a power-law void spectrum originating in a n inflationary phase transition and capable of generating the observed large-scale structure.