COBE limits on explosive structure formation scenarios

Abstract

We calculate the distortions to the spectrum of the cosmic background radiation (CBR) that would be produced by explosive models for the formation of large-Scale structure; we then compare these predictions to the recent measurements of the spectrum made by the Cosmic Background Explorer (COBE) satellite. These models invoke high-energy explosions at redshifts of 7 or greater to catalyze the collapse of material on large mass scales. In our calculations, we take the injection of energy to be instantaneous, we include the effects of inverse Compton cooling and cosmological expansion on the evolution of the resultant bubbles, and we consider both an early noncosmological phase and a late-time cosmological phase (the largest contribution to the spectral distortion is generated in the first phase). Our primary result is the predicted amplitude of the Compton y-distortion we find roughly y &gt;~ 10^-3^[R_b0_/(5 Mpc)]^2^2 h^3^_0_f_0<SUB>OMEGA</SUB>_B_ where R_b0_ is the average radius of the bubbles today, h_0_ is the Hubble constant in units of 100 km s^-1^ Mpc^-1^, {OMEGA}_B_ is the ratio of the density in baryons to the critical density required to just close the universe, and finally f_0_ is the filling factor of bubbles in the universe. (This approximate expression ignores the complicated redshift dependence, which can increase the predicted distortion by as much as a factor of 10 and is discussed in the paper). Recent COBE observations of the cosmic background radiation find y_obs_ &lt; 10^-3^. This limit rules out explosive models as an explanation for structure on scales ~15 Mpc or greater in a universe with {OMEGA}_B_h^3^_0_f_0_ &gt;~ 0.1. If COBE can achieve sensitivities of y ~ 10^-4^, then either a distortion will be detected, or this scenario will be ruled out for structure formation (a) on scales ~14 Mpc or greater for values of {OMEGA}_B_h^3^_0_ f_0_ &gt;~ 0.01, and (b) for galactic scales (a few megaparsecs) with {OMEGA}_B_h^3^_0_ f_0_ &gt;~ 0.1. We also briefly discuss the (large-angle) anisotropy in the microwave background generated by explosive scenarios to compare with COBE anisotropy measurements.