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

TL;DR

The paper addresses how to incorporate primordial helium constraints into CMB parameter inference by using a BBN-consistent prior on $Y_p$ via $Y_p^{BBN}(\Omega_b h^2, DeltaN, xi)$ for Planck forecasts. It performs a Bayesian Planck forecast comparing fixed, free, and BBN-prior treatments of $Y_p$ across standard and degenerate BBN scenarios, using Planck-like data and PArthENoPE for the $Y_p^{BBN}$ relation. In the standard BBN case, the BBN prior tightens $Y_p$ to about $\sigma(Y_p) \approx 6.2\times10^{-4}$ and reduces errors on key parameters, while fixing $Y_p$ to 0.24 biases several estimates. In the degenerate BBN case, the prior dramatically improves constraints on the neutrino chemical potential $\xi$ to $\sigma(\xi) \approx 0.061$, enabling a Planck-level probe of lepton asymmetry comparable to light-element data, and showing the method’s potential as an independent consistency check.

Abstract

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 $ξ$ vary), the BBN prior's constraining power is somewhat weakened, but nevertheless allows us to constrain $ξ$ with an accuracy that rivals bounds inferred from present data on light element abundances.

Figures (4)

• Figure 1: Marginalised posterior probabilities for the parameters of the minimal model. The dashed purple curves correspond to the case where $Y_p$ is fixed to an "incorrect" value of 0.24, the red curves have $Y_p$ as a free parameter and the thick black curves correspond to the case with a standard BBN prior.
• Figure 2: Two-dimensional marginalised joint posterior 68%- and 95%-credible contours for the minimal model. The thick red contours correspond to results with free $Y_p$, the thin black contours represent the result when standard BBN is imposed. This plot illustrates the degeneracies of $Y_p$ with other cosmological parameters and shows how they can be broken by imposing the BBN prior.
• Figure 3: Marginalised posterior probabilities for the parameters of the extended model, still with zero neutrino chemical potential. The dashed purple curves correspond to the case where $Y_p$ is fixed to a value of 0.24, the red curves have $Y_p$ as a free parameter and the thick black curves correspond to the case with a standard BBN prior.
• Figure 4: Two-dimensional marginalised joint posterior 68%- and 95%-credible contours for $\xi$ and $f_\nu$ in the extended model with free neutrino chemical potential. Red lines correspond to "free $Y_p$", the thin black lines are the results of imposing the BBN prior.