The LBT $Y_{\rm p}$ Project V: Cosmological Implications of a New Determination of Primordial $^4$He

Technical Summary: The LBT Yp Project V: Cosmological Implications of a New Determination of Primordial 4He

Problem and Motivation
The primordial abundance of helium-4 ($Y_p$) serves as a critical probe of Big Bang Nucleosynthesis (BBN) and the early Universe ($z \sim 10^{10}$), complementing Cosmic Microwave Background (CMB) observations ($z \sim 1100$). While the abundance of deuterium (D/H) is well-measured in high-redshift quasar absorption systems, the determination of $Y_p$ has historically been limited by systematic uncertainties in low-metallicity H II region observations and the necessity of linear regression extrapolations to zero metallicity. Previous measurements, such as those by Aver et al. (2021a), yielded $Y_p = 0.2448 \pm 0.0033$. The LBT $Y_p$ Project aims to reduce these uncertainties by observing a large sample of extremely metal-poor H II regions to determine $Y_p$ directly from the mean of the lowest metallicity objects, thereby minimizing reliance on regression models and stellar contamination corrections. This precision is essential for testing the Standard Model of particle physics (specifically the number of relativistic degrees of freedom, $N_\nu$) and the concordance between BBN and CMB cosmologies.

Methodology
The authors combine new observational data with updated theoretical calculations:

1. Observations: The study utilizes data from the Large Binocular Telescope (LBT) covering 54 extragalactic H II regions with oxygen abundances $O/H < 15 \times 10^{-5}$. Spectra were analyzed using a $\chi^2$ likelihood function fitting 24 emission lines (H and He) to determine physical parameters (electron temperature, density, reddening, etc.). Objects failing a 95% confidence level cut or showing unusual spectral features were excluded, leaving a robust sample of 41 objects. The final determination of $Y_p$ focuses on the 15 objects with the lowest metallicity ($O/H \le 4 \times 10^{-5}$), where the correlation between helium abundance and metallicity is negligible.
2. Theoretical Framework: The BBN calculations utilize the code from previous works (Fields et al. 2020; Yeh et al. 2022) but incorporate the latest Particle Data Group value for the neutron lifetime ($\tau_n = 878.3 \pm 0.4$ s). The analysis employs a likelihood-based approach, convolving BBN theoretical predictions with observational likelihoods for $Y_p$ and D/H, and CMB likelihoods from Planck data.
3. Statistical Analysis: The authors perform marginalization over parameters to derive constraints on the baryon-to-photon ratio ($\eta$) and the effective number of neutrino species ($N_\nu$). They analyze cases where $N_\nu$ is fixed at 3 (Standard BBN) and where $N_\nu$ is a free parameter.

Key Contributions

• New Primordial Helium Abundance: The project reports a new, highly precise determination of the primordial helium mass fraction:
  $$Y_p = 0.2458 \pm 0.0013$$
  This corresponds to a helium-to-hydrogen ratio of $y_p = 0.08146 \pm 0.00058$. This result is derived from the mean of 15 extremely metal-poor objects, reducing the uncertainty by a factor of $\sim 2.5$ compared to the previous best regression-based result.
• Updated Neutron Lifetime: The analysis incorporates the updated neutron lifetime, though the authors note its impact on $Y_p$ is small compared to other reaction uncertainties.
• Concordance Testing: The paper provides a rigorous comparison of BBN predictions against the new $Y_p$ measurement, the latest D/H measurement ($D/H = (2.513 \pm 0.028) \times 10^{-5}$), and Planck CMB data.

Results

1. Standard BBN ($N_\nu = 3$): When $N_\nu$ is fixed at 3, the combination of CMB, BBN, and observational data yields a baryon-to-photon ratio of $\eta = (6.120 \pm 0.038) \times 10^{-10}$, corresponding to a baryon density parameter $\Omega_B h^2 = 0.02236 \pm 0.00014$. The results show excellent agreement between the CMB-determined baryon density and the BBN-predicted abundances.
2. Varying $N_\nu$: When $N_\nu$ is allowed to vary, the combined analysis yields:
   • $\eta = (6.101 \pm 0.044) \times 10^{-10}$
   • $N_\nu = 2.925 \pm 0.082$
   • For $N_\nu \ge 3$, the 95% confidence limit is $\Delta N_\nu = N_\nu - 3 \le 0.125$.
3. Comparison with Previous Work: The new $Y_p$ value shifts the best-fit $N_\nu$ closer to the Standard Model value of 3 and significantly reduces the uncertainty compared to the previous result ($N_\nu = 2.898 \pm 0.141$). The uncertainty in $N_\nu$ is now dominated by the observational uncertainty in $Y_p$, which is smaller than the theoretical uncertainty in the CMB+BBN prediction.

Significance and Claims
The paper claims that the new determination of $Y_p$ demonstrates strong consistency with the Standard Model of particle physics and the standard cosmological model ($\Lambda$CDM).

• Validation of Standard Cosmology: The concordance between BBN (at $\sim 1$ sec) and the CMB (at $\sim 400,000$ yr) is maintained, with no evidence for new physics altering the expansion rate or particle content between these epochs.
• Constraints on New Physics: The tight constraint on $\Delta N_\nu \le 0.125$ places stringent limits on physics beyond the Standard Model. Specifically, it rules out the existence of scalar particles in equilibrium (which would contribute $\Delta N_\nu \approx 0.57$) and constrains right-handed neutrino interactions, requiring a decoupling temperature $T_{d\nu_R} > m_t$ and a gauge boson mass $M_{Z'} \gtrsim 350$ TeV.
• Future Outlook: The authors note that while the current uncertainty in $Y_p$ ($\sigma \approx 0.0013$) is a significant improvement, further reduction (to $\sigma(Y_p) < 0.0006$) would be required to test the subtle effects of neutrino heating ($N_{eff} \approx 3.044$) against the standard neutrino count ($N_\nu = 3$). They suggest that future CMB experiments like the Simons Observatory may eventually provide competitive constraints on $N_{eff}$.

The paper concludes that the LBT $Y_p$ Project has successfully achieved a precision in helium abundance determination that is now competitive with, and in some aspects superior to, theoretical predictions, enabling a new era of precision cosmology tests.