Observational constraints on dark radiation in brane cosmology

We analyze the observational constraints on brane-world cosmology whereby the universe is described as a three-brane embedded in a five-dimensional anti–de Sitter space. In this brane-universe cosmology, the Friedmann equation is modified by the appearance of extra terms which derive from the existence of the extra dimensions. In the present work we concentrate on the “dark radiation” term which diminishes with the cosmic scale factor as $a^{-4}.$ We show that, although the observational constraints from primordial abundances allow only a small contribution when this term is positive, a much wider range of negative values is allowed. Furthermore, such a negative contribution can reconcile the tension between the observed primordial ${}^4\mathrm{He}$ and D abundances. We also discuss the possible constraints on this term from the power spectrum of CMB anisotropies in the limit of negligible cosmological perturbation on the brane world. We show that BBN limits the possible contribution from dark radiation just before the $e^{+}{e}^{-}$ annihilation epoch to lie between -123% and +11% of the background photon energy density. Combining this with the CMB constraint reduces this range to between -41% and +10.5% at the $2\sigma$ confidence level.