Prospects and limitations for constraining light relics with primordial abundance measurements

The light relic density affects the thermal and expansion history of the early Universe, leaving a number of observable imprints. We focus on the primordial abundances of light elements produced during the process of big bang nucleosynthesis that are influenced by the light relic density. Primordial abundances can be used to infer the density of light relics and thereby serve as a probe of physics beyond the standard model. We calculate the observational uncertainty on primordial light element abundances and associated quantities that would be required in order for these measurements to achieve sensitivity to the light relic density comparable to that anticipated from upcoming cosmic microwave background surveys. We identify the nuclear reaction rates that need to be better measured to maximize the utility of future observations. We show that improved measurements of the primordial helium-4 abundance can improve constraints on light relics, while more precise measurements of the primordial deuterium abundance are unlikely to be competitive with cosmic microwave background measurements of the light relic density.

Figure 1

Forecasted $1\text{−}\sigma$ error on $N_{\mathrm{eff}}$ as a function of the observational uncertainty of the primordial deuterium abundance, the primordial ${}^4\mathrm{He}$ abundance ($Y_{\mathrm{p}}$), and the neutron lifetime using current constraints on $\eta$ and $N_{\mathrm{eff}}$ from Planck [4], and current primordial abundance measurements listed in Table 1, marginalized over all nuclear rates with uncertainties listed in Table 3. The red crosses indicate the current uncertainties.

Figure 2

Same as Fig. 1 but with forecasted constraints on $\eta$ and $N_{\mathrm{eff}}$ from CMB-S4 [9, 20].

Figure 3

Forecasted $1\text{−}\sigma$ errors for $N_{\mathrm{eff}}$ as a function of $\sigma (Y_{\mathrm{p}})/Y_{\mathrm{p}}$ and $\sigma (\mathrm{D})/\mathrm{D}$ marginalizing over $\eta$ and a specified nuclear rate (with all other parameters held fixed). The red cross denotes the current uncertainties.

Figure 4

Forecasted $1\text{−}\sigma$ errors on $N_{\mathrm{eff}}$ from joint constraints on primordial deuterium and ${}^4\mathrm{He}$ abundances with all nuclear reaction rates held fixed for three choices of CMB priors on $\eta$: no CMB prior (left), the current uncertainty from Planck measurements (center), and the projected precision from CMB-S4 (right). The dotted, dot-dashed, and dashed lines represent the $\sigma (N_{\mathrm{eff}})=0.03$, 0.06, and 0.09 contours, respectively, while the white dots denote the current uncertainties on the primordial abundances.