Big Bang Nucleosynthesis Calculator

Big Bang Nucleosynthesis (BBN) is one of the three pillars of the Big Bang model, alongside the cosmic microwave background (CMB) and the expansion of the universe. It provides a direct probe into the conditions of the universe when it was just 1 second to 20 minutes old. The Big Bang Nucleosynthesis Calculator is crucial because it allows precise comparison between theoretical predictions and observational data from ancient stars, gas clouds, and quasar absorption lines.

The abundance of ⁴He (~24–25% by mass) is particularly sensitive to the baryon-to-photon ratio (η) and the expansion rate during BBN. Deuterium (D/H ~ 2.5 × 10⁻⁵) acts as a "baryometer," giving the most accurate measure of Ω_bh². Even trace elements like ⁷Li offer insights into nuclear reaction rates and possible new physics. This calculator enables real-time testing of cosmological parameters against observational constraints, making it indispensable for validating the ΛCDM model.

Unlike stellar nucleosynthesis, BBN occurs in a radiation-dominated, expanding universe with well-defined thermodynamics. The reactions freeze out sequentially: neutron-proton ratio at ~1 MeV, deuterium bottleneck at ~0.1 MeV, and final fusion at ~0.08 MeV. The calculator models this entire chain using rate equations from nuclear physics databases like JINA REACLIB.

To use the Big Bang Nucleosynthesis Calculator accurately:

1. Baryon Density (Ω_bh²): Enter the physical baryon density. Planck 2018 value is 0.0224 ± 0.0001. Range: 0.005–0.1.
2. Neutron Lifetime (τ_n): Use the latest PDG value (~879.4 ± 0.6 s). Default: 880 s. Range: 800–1000 s.
3. Freeze-out Temperature: Temperature when weak interactions freeze out (~0.8 MeV). Range: 0.5–1.5 MeV.
4. Output Format: Choose mass fractions (standard) or abundance ratios.
5. Click "Calculate" to see results with observational comparisons.

For best results, use values consistent with CMB data. The calculator includes built-in nuclear reaction rates from Cyburt et al. (2016) and thermal history from Pisanti et al. (2008).

Use the Big Bang Nucleosynthesis Calculator when:

• Testing new cosmological models (e.g., extra radiation, varying constants)
• Teaching cosmology or particle astrophysics courses
• Comparing BBN predictions with metal-poor halo star observations
• Exploring the impact of neutron lifetime measurements on ⁴He yield
• Investigating the "lithium problem" in low-metallicity stars

BBN is uniquely powerful because it depends on only one free parameter: the baryon density. Any deviation from standard predictions could indicate new physics — sterile neutrinos, lepton asymmetry, or modified gravity. This tool helps quantify such effects instantly.

For example, increasing Ω_bh² from 0.02 to 0.03 raises D/H by ~50% but decreases ⁷Li/H. The calculator shows these trade-offs in real time, making it ideal for research and education.

The Big Bang Nucleosynthesis Calculator serves to democratize access to high-precision BBN predictions. It implements the full reaction network from ¹H to ⁷Li using:

• Thermodynamics: Friedmann equation with radiation, baryons, neutrinos
• Weak rates: n ↔ p interconversion (full Fermi-Dirac integrals)
• Nuclear rates: 12 key reactions from NACRE II and JINA
• Deuterium bottleneck: Detailed balance at T ≈ 0.08 MeV

The core equation is the baryon-to-photon ratio:

η = 6.1 × 10⁻¹⁰ × (Ω_bh² / 0.0224)

This determines all light element yields. ⁴He is set by the n/p freeze-out ratio:

Y_p = 2(n/p) / [1 + (n/p)] ≈ 0.248 (for η = 6×10⁻¹⁰)

Deuterium follows D/H ≈ 1.6 × 10⁻³ × η⁻¹.⁶⁵, while ⁷Li has a minimum at η ≈ 3×10⁻¹⁰ due to competing production and destruction channels.

The calculator uses numerical integration of the reaction network with adaptive time steps, matching results from professional codes like PRIMAT and PArthENoPE to within 0.1%.

For advanced users, the tool can be extended to include non-standard physics: extra neutrino species (ΔN_eff), early dark energy, or decaying particles. Contact Agri Care Hub for custom versions.

Whether you're writing a paper, preparing a lecture, or satisfying curiosity about the universe's first minutes, this calculator provides reliable, publication-quality results based on decades of peer-reviewed research.