Using BBN in cosmological parameter extraction from CMB: a forecast for Planck

Data from future high-precision Cosmic Microwave Background (CMB) measurements will be sensitive to the primordial Helium abundance $Y_p$. At the same time, this parameter can be predicted from Big Bang Nucleosynthesis (BBN) as a function of the baryon and radiation densities, as well as a neutrino chemical potential. We suggest to use this information to impose a self-consistent BBN prior on $Y_p$ and determine its impact on parameter inference from simulated Planck data. We find that this approach can significantly improve bounds on cosmological parameters compared to an analysis which treats $Y_p$ as a free parameter, if the neutrino chemical potential is taken to vanish. We demonstrate that fixing the Helium fraction to an arbitrary value can seriously bias parameter estimates. Under the assumption of degenerate BBN (i.e., letting the neutrino chemical potential $\xi$ vary), the BBN prior's constraining power is somewhat weakened, but nevertheless allows us to constrain $\xi$ with an accuracy that rivals bounds inferred from present data on light element abundances.