Big-Bang Nucleosynthesis and WIMP Dark Matter Freeze-Out as Probes of Yukawa Cosmology

We investigate Big-Bang Nucleosynthesis (BBN) in the context of Yukawa cosmology. We first derive the modified Friedmann equations by starting from the first law of thermodynamics on the apparent horizon. Using observational data on 4 He, deuterium, and 7 Li abundances, we place stringent bounds on the Yukawa coupling α. The 4 He and deuterium constraints are mutually consistent (−0.24. α. 0.12), while 7 Li requires α ∈ [−0.76, −0.72]. This indicate that Yukawa cosmology cannot resolve the Lithium Problem. We then extend our analysis to WIMP freeze-out, and show that the modified Hubble parameter alters the relic abundance, yielding an independent constraint −0.017. α. 0.018 from omegaCDM h2 = 0.120 ± 0.001. We also derive the modified time-temperature relation, and show that the positive α raises the early Universe temperature. Our analysis demonstrates that BBN and dark matter relic abundance serve as complementary probes of modified gravity. Our studies confirm that Yukawa cosmology is a testable framework for early-Universe physics.

Improvements to AI Systems:

1. Physics-Aware Parameter Constraint Engine

• The AI can automatically derive modified Friedmann equations from thermodynamic principles (e.g., first law on apparent horizon) for any given gravitational theory.

• It can then run Bayesian/MCMC inference to place joint bounds on coupling constants (like α) using multi-probe datasets (BBN abundances, CMB, relic density), flagging inconsistencies between probes (e.g., 4He vs. 7Li) and identifying when a model fails to resolve known anomalies (e.g., Lithium Problem).

2. Cross-Domain Consistency Checker for Cosmological Models

• The AI can integrate BBN, dark matter freeze-out, and time-temperature relations into a single pipeline.

• It can automatically test whether a modified gravity model (e.g., Yukawa cosmology) satisfies all early-Universe constraints simultaneously, and output a tension map showing which observable (e.g., 7Li) drives the model’s exclusion.

3. Automated Theory–Observation Mapper

• Given a new gravitational Lagrangian, the AI can generate predictions for:

• Primordial element abundances (4He, D, 7Li)

• Dark matter relic abundance (ΩCDM h2)

• Temperature evolution T(t)

• It then compares these against existing datasets, and if discrepancies arise, it suggests alternative model parameters or identifies the physical mechanism (e.g., positive α raising early temperature) responsible.

4. Anomaly-Driven Model Selection Agent

• The AI can classify whether a proposed cosmology resolves or exacerbates known tensions (e.g., Lithium Problem) by quantifying the shift in predicted abundances relative to observed values.

• It can then recommend whether to pursue the model further or discard it, based on statistical significance (e.g., α bounds from 4He/D vs. 7Li being mutually exclusive).

5. Real-Time Early-Universe Simulator

• The AI can simulate the full thermal history (from BBN to freeze-out) under modified gravity, outputting time-temperature relations and abundance evolutions.

• It can be used to generate synthetic datasets for testing future observatories (e.g., CMB-S4, ELT) and to optimize experimental strategies for constraining α.

What the Improved AI System Can Do:

• Automatically test any modified gravity theory against all early-Universe observables, producing a single, unified constraint report.

• Identify hidden inconsistencies between probes and flag them as model-breaking or as hints of new physics.

• Provide physicists with a fast, reproducible tool to explore parameter space without manual derivation or numerical coding.

• Serve as a decision-support system for choosing which cosmological models warrant further theoretical or observational investment.

We investigate Big-Bang Nucleosynthesis (BBN) in the context of Yukawa cosmology. We first derive the modified Friedmann equations by starting from the first law of thermodynamics on the apparent horizon. Using observational data on 4 He, deuterium, and 7 Li abundances, we place stringent bounds on the Yukawa coupling alpha. The 4 He and deuterium constraints are mutually consistent (-0.24 alpha 0.12), while 7 Li requires alpha in [-0.76,,-0.72]. This indicate that Yukawa cosmology cannot resolve the Lithium Problem. We then extend our analysis to WIMP freeze-out, and show that the modified Hubble parameter alters the relic abundance, yielding an independent constraint-0.017 alpha 0.018 from CDMh squared = 0.120 plus or minus 0.001. We also derive the modified time-temperature relation, and show that the positive alpha raises the early Universe temperature. Our analysis demonstrates that BBN and dark matter relic abundance serve as complementary probes of modified gravity. Our studies confirm that Yukawa cosmology is a testable framework for early-Universe physics.