Dark Energy and Extending the Geodesic Equations of Motion: Its Construction and Experimental Constraints

TL;DR

This paper explores extensions to the geodesic equations motivated by dark energy, demonstrating they are not ruled out by current experiments and do not affect light-based phenomena like gravitational lensing.

Contribution

It introduces a specific class of geodesic extensions linked to dark energy and shows they are consistent with existing experimental constraints and the equivalence principle.

Findings

Extensions do not alter massless particle trajectories

Gravitational lensing remains unaffected

Extensions are compatible with current experimental bounds

Abstract

With the discovery of Dark Energy, $\Lambda_{DE}$, there is now a universal length scale, $\ell_{DE}=c/(\Lambda_{DE} G)^{1/2}$, associated with the universe that allows for an extension of the geodesic equations of motion. In this paper, we will study a specific class of such extensions, and show that contrary to expectations, they are not automatically ruled out by either theoretical considerations or experimental constraints. In particular, we show that while these extensions affect the motion of massive particles, the motion of massless particles are not changed; such phenomena as gravitational lensing remain unchanged. We also show that these extensions do not violate the equivalence principal, and that because $\ell_{DE}=14010^{800}_{820}$ Mpc, a specific choice of this extension can be made so that effects of this extension are not be measurable either from terrestrial experiments, or through observations of the motion of solar system bodies. A lower bound for the only parameter used in this extension is set.