BBN Solver for BFP Theory

This repository contains the Python script used to solve for the primordial helium-4 abundance within the Base Field Pressure (BFP) theoretical framework.

## Physics

The BFP light-speed evolution \(c(z) = c_0(1+z)^{-\beta}\) (with \(\beta = 0.7360\), calibrated by Pantheon+) modifies the Hubble expansion rate in the radiation-dominated epoch through \(H(T) \propto T^{2-\beta/2}\). This altered expansion history changes the freeze-out temperature of weak interactions, which determines the neutron-to-proton ratio and consequently the primordial helium-4 abundance.

## Key Results

- **Helium-4 abundance**: \(Y_p^{\text{BFP}} = 0.2482\), in excellent agreement with the observational constraint \(Y_p = 0.245 \pm 0.003\) (Aver et al. 2021), deviating by only \(1.1\sigma\)
- **Freeze-out temperature**: The BFP freeze-out occurs at \(T_f = 0.54\) MeV (vs. \(0.80\) MeV in \(\Lambda\)CDM)
- **No parameter tuning**: The \(\beta = 0.736\) value that passes BBN is exactly the same value independently determined from the Pantheon+ supernova fit
- **Falsifiable prediction**: BFP predicts \(Y_p = 0.2482\); future BBN observations with precision approaching \(\pm 0.001\) could distinguish between the two models

## Usage

```bash
python bfp_bbn_solver.py

The script outputs:

Freeze-out temperature

Neutron-to-proton ratio

Primordial helium-4 abundance

Related Papers

BFP flagship paper v15: 10.5281/zenodo.20673914

BBN paper: 10.5281/zenodo.20540178

Dependencies

Python 3.8+

NumPy

SciPy

License

CC BY 4.0