COBE LIMITS ON EXPLOSIVE STRUCTURE FORMATION SCENARIOS

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 greater-than-or-similar-to 10(-3)[R(b0)/(5 Mpc)]2h0(3)f0-OMEGA(B), where R(b0) is the average radius of the bubbles today, h0 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 f0 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) < 10(-3). This limit rules out explosive models as an explanation for structure on scales approximately 15 Mpc or greater in a universe with OMEGA(B)h0(3)f0 greater-than-or-similar-to 0.1. If COBE can achieve sensitivities of y almost-equal-to 10(-4), then either a distortion will be detected, or this scenario will be ruled out for structure formation (a) on scales approximately 14 Mpc or greater for values of OMEGA(B)h0(3)f0 greater-than-or-similar-to 0.01, and (b) for galactic scales (a few megaparsecs) with OMEGA(B)h0(3)f0 greater-than-or-similar-to 0.1. We also briefly discuss the (large-angle) anisotropy in the microwave background generated by explosive scenarios to compare with COBE anisotropy measurements.