Variation of $\alpha$ from a Dark Matter Force

TL;DR

This paper explores how a long-range scalar force coupled to dark matter and certain Standard Model particles could cause variations in the fine structure constant, detectable through cosmological observations and potentially testable by future experiments.

Contribution

It introduces a mechanism linking dark matter-induced scalar fields to observable variations in the fine structure constant, offering a novel way to probe dark sector interactions.

Findings

The proposed mechanism can explain the mild deviation in the fine structure constant suggested by Planck data.

Violations of the Equivalence Principle might be detectable with future experiments.

The model's parameters are consistent with current cosmological and astrophysical constraints.

Abstract

We consider a long range scalar force that mainly couples to dark matter and unstable Standard Model states, like the muon, with tiny strength. Probing this type of force would present a challenge to observations. We point out that the dependence of the induced background scalar field on dark matter number density can cause the mass of the unstable particles to have spatial and temporal variations. These variations, in turn, leave an imprint on the value of the fine structure constant $\alpha$, through threshold corrections, that could be detected in astronomical and cosmological measurements. Our mechanism can accommodate the mild preference of the Planck data for such a deviation, $(\alpha_{_{\rm CMB}}-\alpha_{\rm present})/\alpha_{\rm present} = (-3.6\pm 3.7)\times 10^{-3}$. In this case, the requisite parameters typically imply that violations of Equivalence Principle may be within reach of future experiments.