Bound on the variation in the fine structure constant implied by Oklo data

TL;DR

This paper refines bounds on the variation of the fine structure constant over 1.8 billion years using Oklo reactor data, accounting for theoretical uncertainties, and discusses implications for dark energy models.

Contribution

It provides a detailed analysis of uncertainties in estimating the change in alpha from Oklo data, improving the robustness of bounds on fundamental constant variation.

Findings

The change in alpha since Oklo operation is less than 10 parts per billion.

Uncertainties in nuclear modeling are within a factor of 2-3, affecting the correction estimates.

The bounds constrain certain dark energy and string theory models.

Abstract

Dynamical models of dark energy can imply that the fine structure constant $\alpha$ varies over cosmological time scales. Data on shifts in resonance energies $E_r$ from the Oklo natural fission reactor have been used to place restrictive bounds on the change in $\alpha$ over the last 1.8 billion years. We review the uncertainties in these analyses, focussing on corrections to the standard estimate of $k_\alpha\!=\!\alpha\,dE_r/d\alpha$ due to Damour and Dyson. Guided, in part, by the best practice for assessing systematic errors in theoretical estimates spelt out by Dobaczewski et al. [in J. Phys. G: Nucl. Part. Phys. 41, 074001 (2014)], we compute these corrections in a variety of models tuned to reproduce existing nuclear data. Although the net correction is uncertain to within a factor of 2 or 3, it constitutes at most no more than 25% of the Damour-Dyson estimate of $k_\alpha$. Making similar allowances for the uncertainties in the modeling of the operation of the Oklo reactors, we conclude that the relative change in $\alpha$ since the Oklo reactors were last active (redshift $z\simeq 0.14$) is less than $\sim 10$ parts per billion. To illustrate the utility of this bound at low-$z$, we consider its implications for the string theory-inspired runaway dilaton model of Damour, Piazza and Veneziano.