Primordial Abundance Calculator

Big Bang Nucleosynthesis (BBN) occurred between 10 seconds and 20 minutes after the Big Bang, when the universe cooled to ~0.1 MeV. At this temperature, protons and neutrons combined to form deuterium, which then fused into helium and trace amounts of lithium and beryllium. The Primordial Abundance Calculator uses the **standard BBN reaction network** with 12 key nuclear reactions, including:

• p(n,γ)D
• D(p,γ)³He
• D(D,n)³He
• ³He(n,p)T
• T(D,n)⁴He
• ³He(D,p)⁴He
• ⁷Be(n,p)⁷Li

The deuterium bottleneck is critical: fusion into ⁴He only proceeds efficiently once deuterium exceeds its photodissociation threshold. This calculator solves the full rate equations using the **Wagoner-Cowan-Fowler** framework, updated with modern cross-sections from NACRE II and JINA REACLIB databases.

The Primordial Abundance Calculator is indispensable in modern cosmology. It provides the only direct probe of the universe at 1 second old, testing the ΛCDM model and constraining new physics. The predicted ⁴He mass fraction (Y_p ≈ 0.247) is observed in metal-poor galaxies, while D/H ≈ 2.5 × 10⁻⁵ is measured in high-redshift quasar absorption systems. Discrepancies in ⁷Li (the "lithium problem") drive research into stellar depletion, non-standard neutrinos, or axions. This tool enables real-time sensitivity analysis, showing how η variations affect each isotope.

Used in university courses, research papers, and public outreach, it bridges theory and observation. The calculator’s accuracy matches professional codes like PRIMAT and PArthENoPE, but with an intuitive interface suitable for students and experts alike.

To ensure precision with the Primordial Abundance Calculator:

1. Baryon-to-Photon Ratio (η × 10¹⁰): Use 6.1 ± 0.1 from Planck 2018. Values outside 5–7 deviate from CMB.
2. Neutron Lifetime: Enter 879.4 s (PDG 2024). Older values (e.g., 880.3 s) slightly increase ⁴He.
3. Hubble Parameter (h): Use 0.674. Higher h accelerates freeze-out, reducing D and ³He.
4. Deuterium Bottleneck: Keep "Yes" for standard BBN. "No" is for pedagogical use only.
5. Results are mass fractions (Y for ⁴He) or number ratios (D/H, ³He/H, ⁷Li/H).

For advanced users, vary η to explore non-standard models (e.g., sterile neutrinos, lepton asymmetry). Compare outputs with observations from HST, Keck, or JWST.

Use the Primordial Abundance Calculator when:

• Teaching Cosmology: Demonstrate how η determines light element yields in undergraduate or graduate courses.
• Research & Publications: Test BBN sensitivity to new physics (e.g., extra neutrino species, varying constants).
• Public Outreach: Explain "Why is the universe 75% hydrogen and 25% helium?" using interactive results.
• Model Validation: Cross-check custom BBN codes against standard predictions.
• Conference Posters: Generate plots of Y_p vs. η for visual impact.

It’s especially valuable when new CMB data (e.g., from CMB-S4 or Simons Observatory) updates η constraints, allowing instant recalculation of predicted abundances.

The core purpose of the Primordial Abundance Calculator is to democratize access to Big Bang Nucleosynthesis predictions. While professional codes require Fortran or Python expertise, this web tool delivers publication-quality results in seconds. It serves:

• Students: Learning the physics of the early universe.
• Researchers: Rapid prototyping of BBN modifications.
• Educators: Interactive classroom demonstrations.
• Science Communicators: Accurate data for articles and videos.

Built on the **Standard Model of Cosmology**, it uses the freeze-out temperature T_f ≈ 0.8 MeV, neutron-to-proton ratio n/p ≈ e⁻Δm/T_f ≈ 1/6, and solves the reaction network via implicit integration. The ⁴He yield is robust (ΔY_p/Δη ≈ 0.01), while D and ³He are η-sensitive tracers. ⁷Li shows tension with observations, motivating beyond-Standard-Model research.

This calculator supports the scientific method by enabling hypothesis testing. For example, increasing neutrino species (N_ν > 3) raises Y_p — a testable prediction. Similarly, a shorter neutron lifetime reduces ⁴He by ~0.001 per 10 s decrease.

Long-term, as JWST measures D/H in z > 10 systems and refines H_0, this tool will evolve with updated parameters. Its open design ensures transparency and reproducibility — hallmarks of credible science. For deeper study, visit Primordial Abundance on ScienceDirect or explore cosmology tools at Agri Care Hub.