Cosmic backgrounds from primeval dust

Energy released by pregalactic sources and absorbed by dust should appear as a cosmic submillimeter background, and should be observable by COBE as a distortion of the cosmic microwave background. We develop a general formalism which describes the spectrum and anisotropy of the radiation as a nearly isotropic background with fluctuations. Our theory incorporates spatial and temporal variations in the density of both luminosity and dust, and is sufficiently robust to treat emission by point sources as well as smoother emission in high and low optical depth situations. The fluctuations are calculated using linear perturbation theory for arbitrary dust and luminosity clumping, and are calculated nonperturbatively for compact infrared sources using shot-noise models. We present a catalog of numerical models which cover a wide range of high- and low-redshift galaxy formation scenarios and galaxy clustering assumptions to illustrate explicitly spectral shapes and amplitudes and the viability of anisotropy detection by ground-based submillimeter telescopes, balloon experiments, COBE's FIRAS and DIRBE, and SIRTF. Large detectable anisotropies are predicted in the far-infrared on subarcminute scales. For many realistic models a large accompanying near-infrared background is predicted. We show that although spectral information alone can determine the total energy release, it provides only coarse information about the dust abundance and type, the redshift, and other parameters. However, in combination with the anisotropy signal, which depends on the evolution of both cosmic structures and energy release, these submillimeter studies promise to provide a powerful probe of pregalactic history. Limits on the density and clustering length of emitting galaxies are already significant.