An analysis of constraints on relativistic species from primordial nucleosynthesis and the cosmic microwave background

TL;DR

The study investigates constraints on the effective number of relativistic species, $N_ ext{eff}$, by jointly analyzing CMB data and primordial abundances, with updated BBN nuclear inputs and a BBN likelihood embedded in CosmoMC. It demonstrates good concordance between BBN and CMB in constraining $N_ ext{eff}$, though results depend on the adopted helium abundance priors. A key result is that incorporating D/H with BBN theory and CMB data yields a tight constraint around $N_ ext{eff} \approx 3.9\pm0.4$, highlighting the complementarity of light-element observations and the CMB. The work also shows that updates to the $d(p,\gamma)^3\mathrm{He}$ cross section shift inferred baryon density and lithium yields, and it underscores the potential of improved D/H measurements as a powerful cosmological probe of the expansion rate in the early universe.

Abstract

We present constraints on the number of relativistic species from a joint analysis of cosmic microwave background (CMB) fluctuations and light element abundances (helium and deuterium) compared to big bang nucleosynthesis (BBN) predictions. Our BBN calculations include updates of nuclear rates in light of recent experimental and theoretical information, with the most significant change occuring for the d(p,gamma)^3He cross section. We calculate a likelihood function for BBN theory and observations that accounts for both observational errors and nuclear rate uncertainties and can be easily embedded in cosmological parameter fitting. We then demonstrate that CMB and BBN are in good agreement, suggesting that the number of relativistic species did not change between the time of BBN and the time of recombination. The level of agreement between BBN and CMB, as well as the agreement with the standard model of particle physics, depends somewhat on systematic differences among determinations of the primordial helium abundance. We demonstrate that interesting constraints can be derived combining only CMB and D/H observations with BBN theory, suggesting that an improved D/H constraint would be an extremely valuable probe of cosmology.

Figures (3)

• Figure 1: (Color online) Upper Panel: $S$-factor data for the reaction $d(p,\gamma)^3\mathrm{He}$ are shown, along with the best-fit curve and $2\sigma$ intervals based purely on those data nollett00 (dash-dot and dash-dot-dot-dot curves) and on the ab initio calculation viviani00marcucci05 (solid). All errors are shown as $2\sigma$ intervals for comparability with Fig. 3 of Ref. nollett00. Lower Panels: Sensitivity functions nollett00 showing the relative importance of this reaction at varying energy for D/H ($g_2$) and Li/H ($g_7$) yields, evaluated at $\Omega_bh^2=0.019$. Convolving the $S$-factor error band with the sensitivity function gives the total uncertainty arising from this reaction. The strongest sensitivity to the $d(p,\gamma)^3\mathrm{He}$ rate occurs at the largest $|g_i|$, in the 50--500 keV range.
• Figure 2: (Color online) Left panels: Yields of light nuclides as functions of the baryon density, $\Omega_bh^2$. Each band indicates yields for a single value (integer plus 0.046) of $N_\mathrm{eff}$ and its thickness the $1\sigma$ nuclear uncertainty on those yields. Bands are shaded lighter for smaller values of $N_\mathrm{eff}$ and darker for larger $N_\mathrm{eff}$. Also shown are horizontal bands indicating observational constraints on abundances peimbert07bonifacio07pettini08izotov10aver11 and a vertical band indicating the WMAP7 $1\sigma$ interval for $\Omega_bh^2$. Right panels: The same yields shown as functions of $N_\mathrm{eff}$ at the CMB-inferred value of $\Omega_bh^2$, essentially slices along the band labeled "WMAP" in the left panels. Salmon-colored bands indicate yields with our adopted rates, and their widths indicate a quadrature sum of nuclear errors and the error on $\Omega_bh^2$. In the $Y_\mathrm{p}$ graph, blue $1\sigma$ and $2\sigma$ contours indicate constraints from WMAP7+SPT alone, while black curves paralleling the adopted yields indicate the effects of using the old Particle Data Group pdg02 (upper) and Serebrov serebrov08 (lower) values of $\tau_n$ (no errors shown). In the D/H and $^7$Li/H graphs, the thin solid curves indicate the result of using the empirical rate for $d(p,\gamma)^3\mathrm{He}$, again without showing the errors. Horizontal bands indicate observational constraints as discussed in the text.
• Figure 3: (Color online) Constraints on $N_\mathrm{eff}$ from just CMB and $D/H$ measurements, shown as marginalized likelihoods. The black solid curve is CMB alone, the black dotted curve shows CMB with BBN constraints on the relation between $Y_\mathrm{p}$ and $N_\mathrm{eff}$, and the red dashed curve also adds the observed abundance of $D/H$.