The local sub-mm luminosity functions and predictions from ASTRO-F/SIRTF to Herschel

We present new determinations of the local sub-mm luminosity functions. We find the local sub-mm luminosity density converging to 7.3+/-0.2 x 10^19 W/Hz/Mpc^3 /h_65 at 850um solving the ``sub-mm Olbers' Paradox.'' Using the sub-mm colour temperature relations from the SCUBA Local Universe Galaxy Survey, and the discovery of excess 450um excess emission in these galaxies, we interpolate and extrapolate the IRAS detections to make predictions of the SEDs of all 15411 PSC-z galaxies from 50-3000um. Despite the long extrapolations we find excellent agreement with (a) the 90um luminosity function of Serjeant et al. (2001), (b) the 850um luminosity function of Dunne et al. (2000), (c) the mm-wave photometry of Andreani & Franceschini (1996); (d) the asymptotic differential and integral source count predictions at 50-3000um by Rowan-Robinson (2001). Remarkably, the local luminosity density and the extragalactic background light together strongly constrain the cosmic star formation history for a wide class of evolutionary assumptions. We find that the extragalactic background light, the 850um 8mJy source counts, and the Omega_* constraints all independently point to a decline in the comoving star formation rate at z>1