Primordial nucleosynthesis with varying fundamental constants: Improved constraints and a possible solution to the Lithium problem

Abstract: Primordial nucleosynthesis is an observational cornerstone of the Hot Big Bang model and a sensitive probe of physics beyond the standard model. Its success has been limited by the so-called Lithium problem, for which many solutions have been proposed. We report on a self-consistent perturbative analysis of the effects of variations in nature's fundamental constants, which are unavoidable in most extensions of the standard model, on primordial nucleosynthesis, focusing on a broad class of Grand Unified Theory models. A statistical comparison between theoretical predictions and observational measurements of ${}^4$He, D, ${}^3$He and, ${}^7$Li consistently yields a preferred value of the fine-structure constant $\alpha$ at the nucleosynthesis epoch that is larger than the current laboratory one. The level of statistical significance and the preferred extent of variation depend on model assumptions but the former can be more than four standard deviations, while the latter is always compatible with constraints at lower redshifts. If Lithium is not included in the analysis, the preference for a variation of $\alpha$ is not statistically significant. The abundance of ${}^3$He is relatively insensitive to such variations. Our analysis highlights a viable and physically motivated solution to the Lithium problem, which warrants further study.

• The paper presents a perturbative analysis showing that a positive variation in the fine-structure constant may resolve the Lithium discrepancy in primordial nucleosynthesis.
• It uses Unification and Dilaton models along with sensitivity coefficients to quantitatively assess the impact on light element abundances.
• The study reinforces the link between Grand Unified Theories and cosmological observations, offering statistically significant insights for future cross-verification.

Primordial Nucleosynthesis with Varying Fundamental Constants: An Evaluation

The paper "Primordial nucleosynthesis with varying fundamental constants" by M. T. Clara and C. J. A. P. Martins offers a comprehensive assessment of how variations in fundamental constants influence primordial nucleosynthesis, and proposes a potential resolution to the longstanding Lithium problem. This research underscores the interplay between cosmology and particle physics, utilizing observations of Big Bang Nucleosynthesis (BBN) to probe the stability of fundamental constants.

Primordial nucleosynthesis is pivotal for understanding the early universe, as it predicts the abundances of light elements based on known physics, mainly characterized by the baryon-to-photon ratio. However, discrepancies between observed and theoretical ${}^7$Li abundances have raised questions, often referred to as the "Lithium problem."

Analytical Approach

The research leverages a perturbative approach, focusing on variations of the fine-structure constant $\alpha$. Most extensions of the standard model, like string theory, suggest that fundamental constants could vary with spacetime, making this approach timely and relevant. The study takes a detailed, model-dependent stance, systematically analyzing how grand unified theories (GUTs) could lead to different predictions for $\alpha$ during the nucleosynthesis epoch.

The analysis employs two representative models: the Unification model and the Dilaton model. Both models introduce parameters $R$ and $S$, which relate variations in nucleon masses and other coupling constants to $\alpha$. Sensitivity coefficients from prior works are utilized to quantify how variations in these parameters affect abundances of ${}^4$He, D, ${}^3$He, and ${}^7$Li.

Observational and Theoretical Synthesis

The observational data and theoretical predictions are compared, with primordial element abundances from sources like the Particle Data Group and recent observational studies. The study also examines the impact of excluding ${}^7$Li and ${}^3$He from the analysis to assess the robustness of constraints on $\alpha$.

Key findings include:

• Persistent preference for a positive variation in $\alpha$, with statistical significance magnified when including ${}^7$Li in the dataset.
• Helium-3's abundance exerts minimal influence, indicating robustness primarily driven by other nuclides.
• Specific models yield preferred values of $\Delta\alpha/\alpha$ at more than four standard deviations above zero, supporting compatibility with constraints at lower redshifts.

Implications and Prospects

This paper's implications stretch across theoretical and observational cosmology. The research supports the notion that varying constants could feasibly address the Lithium problem, reinforcing the validity of GUTs in explaining early universe conditions. The analysis also calls attention to the necessity of critical examination of cosmological parameters, such as the effective number of neutrinos, which might mask or mimic variations in fundamental constants.

Future work will likely explore the dependency of nucleosynthesis predictions on particle masses and potential energy scales of new physics. Cross-verifying these results with independent constraints from quasar absorption lines or other astrophysical phenomena might offer a broader perspective on the cosmological implications of this research.

In conclusion, this paper provides a compelling analysis situated in advanced theoretical models, offering a feasible path towards resolving perennial discrepancies in cosmological observations while simultaneously probing the boundaries of established physics.