Investigation of the fundamental constants stability based on the reactor Oklo burn-up analysis

TL;DR

This paper uses Oklo reactor data to place stringent limits on the BSBM model parameters for varying fine structure constant, indicating the model's characteristic length must be much smaller than the Planck length.

Contribution

It provides new constraints on the BSBM model parameters by integrating equations from the Big Bang to present, based on Oklo analysis, refining the understanding of fundamental constant variations.

Findings

Constraints on BSBM model parameters derived from Oklo data.

The characteristic length of BSBM must be much smaller than the Planck length.

Limits on electromagnetic energy fraction in matter from the analysis.

Abstract

New severe constraints on the variation of the fine structure constant have been obtained from reactor Oklo analysis in our previous work. We investigate here how these constraints confine the parameter of BSBM model of varying $\alpha$. Integrating the coupled system of equations from the Big Bang up to the present time and taking into account the Oklo limits we have obtained the following margin on the combination of the parameters of BSBM model: $$ |\zeta_m (\frac{l}{l_{pl}})^2|<6\cdot 10^{-7}, $$ where $l_{pl}=(\frac{G\hbar}{c^3})^{\frac{1}{2}} \approx 1.6 \cdot 10^{-33}$ cm is a Plank length and $l$ is the characteristic length of the BSBM model. The natural value of the parameter $\zeta_m$ - the fraction of electromagnetic energy in matter - is about $10^{-4}$. As a result it is followed from our analysis that the characteristic length $l$ of BSBM theory should be considerably smaller than the Plank length to fulfill the Oklo constraints on $\alpha$ variation.