Constraining The Early-Universe Baryon Density And Expansion Rate

TL;DR

This work tests the consistency of standard cosmology by jointly constraining the early-Universe expansion rate and baryon density through BBN and CMB/LSS observations. Using BBN abundances as baryometers and chronometers, alongside CMB/LSS constraints on $\eta_{10}$ and the effective neutrino number $N_\nu$, the authors find strong, compatible bounds: $N_\nu$ favors around the standard value with 95% limits $1.8 < N_\nu < 3.2$ and $\eta_{10}$ is tightly constrained to $5.9 < \eta_{10} < 6.4$; the results indicate no significant post-BBN entropy production. The analysis also notes a lithium problem and discusses potential Ly-$\alpha$ forest tensions, underscoring the robustness of the BBN-CMB/LSS concordance while highlighting avenues for future precision, such as Planck-era measurements of neutrino anisotropic stress. Overall, the paper demonstrates a coherent cross-epoch picture where early-Universe physics, including possible non-standard radiation content, remains tightly bounded by observations.

Abstract

We explore constraints on extensions to the standard models of cosmology and particle physics which modify the early-Universe expansion rate S = H'/H (parametrized by the effective number of neutrinos N_nu). The constraints on N_nu and the baryon density parameter (eta_B = n_B/n_gamma = 10^(-10)*eta_10) from BBN at 20 minutes are compared with those from the CMB at 400 kyr and LSS at 14 Gyr. BBN provides the strongest constraint on N_nu (1.6 < N_nu < 3.3 at 95% confidence), but a weaker constraint on eta_B. The CMB/LSS best constrain the baryon density (5.9 < eta_10 < 6.4 at 95% confidence), independent of N_nu, but provide a relatively weak N_nu constraint, consistent with N_nu = 3. Using the best fit values and the allowed ranges of the CMB/LSS-derived parameters to calculate the BBN-predicted primordial abundances yields excellent agreement with the observationally inferred abundance of deuterium and good agreement with 4He, confirming the consistency between the BBN and CMB/LSS results. However, the BBN-predicted abundance of 7Li is high, by a factor of 3 or more. We comment on the value of N_nu and a possible anomaly in the matter power spectrum inferred from observations of the Ly-alpha forest. The good agreement between our BBN and CMB/LSS results permit us to constrain any post-BBN entropy production as well as to limit the production of any non-thermalized relativistic particles and, allow us to combine them finding 95% ranges, 1.8 < N_nu < 3.2 and 5.9 < eta_10 < 6.4.

Figures (9)

• Figure 1: The probability distribution of the baryon density parameter, $_{10}$. The dashed line shows the probability distribution inferred from SBBN (N$_{ } = 3$) and the adopted primordial abundance of deuterium (see §3). The solid line is the probability distribution of $_{10}$ inferred for N$_{ } = 3$ from the combination of the WMAP-5yr data, small scale CMB data, matter power spectrum data from 2dFGRS and SDSS LRG, SNIa, and the HST Key Project (see §4).
• Figure 2: The 68% and 95% contours in the N$_{ }$ - $_{10}$ plane derived from a comparison of the observationally-inferred and the BBN-predicted primordial abundances of D and $^4$He. The shaded region is excluded by the 95% upper bound to the helium abundance in eq. 15 (see, eq. 20).
• Figure 3: The top panel shows the CMB power spectrum for the best fit models with N$_{ }$ fixed at N$_{ }$ = 1 (solid black), N$_{ }$ = 3 (dashed red), and N$_{ }$ = 5 (dot-dashed blue) illustrating its insensitivity to N$_{ }$ in the absence of an independent constraint on $\Omega_{\rm M}h^{2}$. The bottom panel shows the matter power spectra for the same set of parameter values, illustrating its sensitivity to N$_{ }$.
• Figure 4: The 68% and 95% contours in the N$_{ }$ - $\Omega_{\rm M}h^2$ plane inferred from the combination of the WMAP-5yr data, small scale CMB data, luminosity distances of SNIa and the HST Key Project prior on $H_0$. The dashed line shows the locus of points corresponding to the same value of $z_{eq} (= 3144$), illustrating the degeneracy between these two parameters. As the contours reveal, this degeneracy may be broken if complementary data is used to constrain $\Omega_{\rm M}h^2$.
• Figure 5: The 68% and 95% contours in the N$_{ } - _{10}$ plane inferred from the combination of the WMAP-5yr data, small scale CMB data, SNIa luminosity distances, and the HST Key Project prior on $H_0$ (see the text and Table 1).