Cosmological Parameter Estimation with a Joint-Likelihood Analysis of the Cosmic Microwave Background and Big Bang Nucleosynthesis

Abstract

We present the first joint-likelihood analysis of Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) data. Bayesian inference is performed on the baryon abundance and the effective number of neutrino species, $N_{\rm eff}$, using a CMB Boltzmann solver in combination with LINX, a new flexible and efficient BBN code. We marginalize over Planck nuisance parameters and nuclear rates to find $N_{\rm{eff}} = 3.08_{-0.13}^{+0.13},\,2.94 _{-0.16}^{+0.16},$ or $2.98_{-0.13}^{+0.14}$, for three separate reaction networks. This framework enables robust testing of the Lambda Cold Dark Matter paradigm and its variants with CMB and BBN data.

Figures (5)

• Figure 1: Parameter medians and 68% credible limits with the inclusion of Planck data only, BBN data only, and both BBN and Planck data, as labeled at the bottom of the figure. Values from individual analyses line up top-to-bottom. Square markers in the left set of columns indicate $N_{\rm{eff}}$ is held fixed, while circular markers in the right set of columns indicate analyses where $N_{\rm{eff}}$ is allowed to float. The $\Lambda$CDM value of $N_{\rm{eff}}=3.045$ is indicated with the black dashed line. Purple, red, and green points use the PRIMAT, PArthENoPE, and YOF networks, respectively. Pink points indicate that a constant uncertainty is added to the deuterium part of the BBN likelihood. Otherwise, all available nuisance parameters are marginalized over. This figure summarizes the parameter values from analyses in this work and their sensitivity to different data sets and BBN reaction networks; illustrating e.g. shrinking error bars relative to BBN when CMB data is included and systematics from using different BBN reaction networks.
• Figure 2: A schematic illustrating the joint likelihood used for the CMB+BBN analyses. Note that each likelihood is computed at the same values of the input parameters $\Omega_b h^2$ and $N_{\rm{eff}}$, and the Y$_\mathrm{P}^\mathrm{pred}$ output of the BBN solver is used as input to the Boltzmann solver to ensure consistency.
• Figure 3: Variation in the standard deviation for the prediction of D/H in the PRIMAT network as a function of model parameters $N_{\rm{eff}}$ and $\Omega_b h^2$, obtained by sampling 200 different sets of values for the BBN nuisance parameters at each point in the grid.
• Figure 4: 68% and 95% contours in the $\Omega_bh^2-N_{\rm{eff}}$ plane for YOF (left), PArthENoPE (center), and PRIMAT (right) nuclear reaction networks. In each panel, the light-blue dotted contours correspond to the BBN-only analysis, the black-dashed to the CMB-only analysis, and the orange-solid to the joint CMB+BBN analysis. All CMB and BBN nuisance parameters are marginalized over. When using the PRIMAT network, the resulting value of $N_{\rm{eff}}$ in the joint analysis is pushed high. When using the YOF network, the constraining power of BBN is minimal.
• Figure 5: 68% and 95% posterior contours for the nuisance parameters $q_i$ that determine the scaling of three key deuterium burning rates in the PRIMAT network. The BBN-only analysis (blue, dashed) is compared to a joint CMB+BBN analysis (orange, solid), allowing $\Omega_b h^2$ to float and fixing $N_{\rm{eff}}= 3.045$. In the joint analysis, these rates are pushed away from their central values to attain a better joint fit with the CMB.