Limits on Brane-World and Particle Dark Radiation from Big Bang Nucleosynthesis and the CMB

The term dark radiation is used both to describe a noninteracting neutrino species and as a correction to the Friedmann Equation in the simplest five-dimensional RS-II brane-world cosmology. In this paper we consider the constraints on both meanings of dark radiation based upon the newest results for light-element nuclear reaction rates, observed light-element abundances and the power spectrum of the Cosmic Microwave Background (CMB). Adding dark radiation during big bang nucleosynthesis (BBN) alters the Friedmann expansion rate causing the nuclear reactions to freeze out at a different temperature. This changes the final light element abundances at the end of BBN. Its influence on the CMB is to change the effective expansion rate at the surface of last scattering. We find that the BBN constraint reduces the allowed range for both types of dark radiation at 10 Mev to between $-12.1\%$ and $+6.2\%$ of the {\bf total} background energy density at 10 Mev. Combining this result with fits to the CMB power spectrum, produces different results for particle vs. brane-world dark radiation. In the brane-world, the range decreases to $-6.0\%$ to $+6.2\%$. Thus, we find, that the ratio of dark radiation to the background total relativistic mass energy density $ρ_{\rm DR}/ρ$ is consistent with zero although there remains a very slight preference for a positive (rather than negative) contribution.