Constraining the helium abundance with CMB

TL;DR

The paper investigates whether the primordial helium fraction $Y_p$ can be constrained from CMB data alone, using a 7-parameter MCMC analysis that includes $Y_p$ alongside standard cosmological variables. It finds a present-day CMB constraint of $0.160<Y_p<0.501$ (68% c.l.) and reveals correlations with the reionization redshift $z_r$ and the spectral index $n_s$, highlighting degeneracies that limit precision on $Y_p$ from current data. Forecasts with Planck suggest a ~5% measurement of $Y_p$, but the strong $Y_p$–$\\\omega_b$ degeneracy requires a Gaussian prior on $Y_p$ to accurately infer the baryon density; a cosmic-variance-limited experiment could reach $\\Delta Y_p \\\sim 0.0036$, enabling discrimination between BBN-predicted and astrophysical helium values. Overall, the work provides a CMB-based cross-check of BBN helium predictions, clarifies how $Y_p$ uncertainties propagate into baryon density estimates, and guides analysis strategies for Planck-era data.

Abstract

We consider for the first time the ability of present-day cosmic microwave background (CMB) anisotropies data to determine the primordial helium mass fraction, Y_p. We find that CMB data alone gives the confidence interval 0.160 < Y_p < 0.501 (at 68% c.l.). We analyse the impact on the baryon abundance as measured by CMB and discuss the implications for big bang nucleosynthesis. We identify and discuss correlations between the helium mass fraction and both the redshift of reionization and the spectral index. We forecast the precision of future CMB observations, and find that Planck alone will measure Y_p with error-bars of 5%. We point out that the uncertainty in the determination of the helium fraction will have to be taken into account in order to correctly estimate the baryon density from Planck-quality CMB data.

Figures (8)

• Figure 1: On the left (blue) we plot a few current direct astrophysical measurements of the helium mass fraction $Y_p$ with their $1-\sigma$ statistical errors, and the value inferred from deuterium measurements combined with SBBN (red) (see text for references). On the right (green), a direct comparison with CMB present-day accuracy (actual data, this work; the errorbar extends in the range $0.16 < Y_p < 0.50$) and with its future potential (Fisher matrix forecast for Planck and a Cosmic Variance Limited experiment).
• Figure 2: Evolution of the number density of electrons normalized to the number density of baryons, $f_e=n_e/n_b$, as a function of redshift for different values of the helium fraction $Y_p$. The black-solid curve corresponds to the standard value $Y_p = 0.24$, the red-dashed (blue-dot-dashed) to $Y_p=0.36$ ($Y_p=0.12$). The labels (a) to (d) indicate the four different phases discussed in the text.
• Figure 3: CMB temperature (top panel) and polarization (bottom panel) power spectra and percentage difference with two different values of the helium fraction for a standard $\Lambda$CDM model. The solid-black (dashed-blue) line corresponds to a 10% larger (smaller) value of $Y_p$ wrt to the standard value, $Y_p = 0.24$. All other parameters are fixed to the value of our fiducial model (Table \ref{['t:fiducial']}), in particular, we have $\tau_{\textrm{r}}=0.166$.
• Figure 4: One-dimensional posterior likelihood distribution for the helium mass fraction, $Y_p$, using CMB data only. The solid-black line is for all other parameters marginalized, the dashed-red line gives the mean likelihood.
• Figure 5: Joint 68% and 99% confidence contours in the ($\omega_b, Y_p$)-plane from CMB data alone. The solid-blue line gives the SBBN prediction burlesNT01, which on this figure almost looks like a straight line.