Photon mass as a probe to extra dimensions

TL;DR

This paper proposes that the photon acquires a tiny mass due to a geometrical localization mechanism in extra dimensions, linking it to the Ricci scalar and cosmological constant, with potential observable implications.

Contribution

It introduces a model where photon mass arises from extra-dimensional geometry, providing a specific mass formula related to the Ricci scalar and cosmological constant.

Findings

Photon mass estimated at ~2×10^{-69} kg, below current experimental bounds.

Photon mass depends on the Ricci scalar, linking it to cosmological and astrophysical environments.

Potential for future experimental detection of photon mass as evidence for extra dimensions.

Abstract

In this manuscript we show that the geometrical localization mechanism implies a four dimensional mass for the photon. The consistence of the model provides a mass given exactly by $m_{\gamma}=\sqrt{R}/4$ where $R$ is the Ricci scalar. As a consequence, the cosmological photon has a mass related to the vacuum solution of the Einstein equation. At the present age of the universe we have a dS vacuum with $R=4\Lambda$, where Lambda is a positive cosmological constant. With this we find that $m_{\gamma}\approx 2\times 10^{-69}$ kg, which is below the present experimental upper bounds, and such correction may be observed in the next years with more precise measurements. By considering the value of $R$ inside some astrophysical sources and environments we find that the bound is also satisfied. The experimental verification of this mass, beyond pointing to the existence of extra dimensions, would imply in a fundamental change in cosmology, astrophysics and in particle physics since the same mechanism is valid for non-abelian gauge fields.