Revisiting the Constraint on the Helium Abundance from CMB

TL;DR

The paper addresses whether the primordial helium abundance $Y_p$ can be constrained from CMB observations alone. It adopts a χ^2 minimization over six cosmological parameters within a flat ΛCDM framework, contrasting with prior MCMC approaches, and assesses current and future constraints including BBN priors. The findings show that current CMB data yield only weak bounds on $Y_p$, and Planck would also struggle to constrain $Y_p$ tightly unless a standard BBN relation $Y_p(\omega_b,\Delta N)$ is imposed, in which case constraints on other parameters (especially $n_s$) improve due to reduced degeneracies. The work highlights that BBN theory can serve as a practical prior in CMB analyses, while independent $Y_p$ measurements provide a consistency test for the standard BBN paradigm in the era of precision cosmology.

Abstract

We revisit the constraint on the primordial helium mass fraction Yp from observations of cosmic microwave background (CMB) alone. By minimizing chi square of recent CMB experiments over 6 other cosmological parameters, we obtained rather weak constraints as 0.17 < Yp < 0.52 at 1 sigma C.L. for a particular data set. We also study the future constraint on cosmological parameters when we take account of the prediction of the standard big bang nucleosynthesis (BBN) theory as a prior on the helium mass fraction where Yp can be fixed for a given energy density of baryon. We discuss the implications of the prediction of the standard BBN on the analysis of CMB.

Figures (5)

• Figure 1: The CMB power spectra for the cases with $Y_p=0.1$ (green dashed line), $0.24$ (red solid line) and $0.5$ (blue dotted line). Other cosmological parameters are taken to be the WMAP mean values for the power-law $\Lambda$CDM model.
• Figure 2: The values of $\Delta \chi^2$ are shown as a function of $Y_p$. Other cosmological parameters are taken to minimize $\chi^2$. The red solid line is for the data of WMAP, CBI and ACBAR. The green dashed line includes BOOMERANG data in addition.
• Figure 3: The CMB power spectra for the case with $Y_p=0.24, \omega_m=0.135,\omega_b=0.023, h=0.72, \tau=0.117, n_s=0.96$ (red solid line), $Y_p=0.1, \omega_m=0.130, \omega_b=0.023, h=0.72, \tau=0.101, n_s=0.95$ (green dashed line) and $Y_p=0.5,\omega_m=0.148, \omega_b=0.023, h=0.72, \tau = 0.117, n_s=0.99$ (blue dotted line). Notice that these power spectra are almost indistinguishable up to multipole region $l \sim 1000$.
• Figure 4: Expected contour of the 1$\sigma$ constraint from Planck experiment. We take $Y_p$ as an independent free parameter. Other cosmological parameters are marginalized over in this figure. The thin and nearly horizontal band is the theoretical BBN calculation of $Y_p$ as a function of $\omega_b$ with its width representing 1$\sigma$ error from reaction rates. Here we assumed $\Delta N=0$.
• Figure 5: Expected contours of 1$\sigma$ constraints from Planck experiment for the cases without the BBN relation (solid red line) and with it (dashed green line). We marginalized over other cosmological parameters in this figure. $Y_p$ is determined by the BBN relation.