Solar system relativity tests, formulas for light deflection by a central mass, and modification of the lens equation, for a Weyl scaling invariant dark energy

TL;DR

This paper investigates how dark energy modeled by a Weyl invariant action affects solar system tests of general relativity, showing modifications are negligible locally but could influence cosmological gravitational lensing.

Contribution

It derives formulas for light deflection and lensing corrections due to dark energy in a Weyl invariant framework, extending standard general relativity results.

Findings

Standard solar system tests remain unaffected within current experimental errors.

A new light deflection contribution proportional to the cosmological constant is identified.

Formulas for lensing corrections including the effect of dark energy are provided.

Abstract

We estimate the changes in solar system tests of general relativity when "dark energy" arises from a Weyl scaling invariant action, using the modified Schwarzschild-like spherically symmetric solution obtained in this case by Adler and Ramazano\vglu. We show that the standard results of general relativity are modified by amounts that are far below current experimental errors. However, because the metric is not conformally flat when the central mass $M$ vanishes, there is a contribution to light deflection proportional to the cosmological constant $\Lambda$, with opposite sign to the one proportional to $M$. This could have implications for gravitational lensing in cosmological contexts, so we have calculated the corresponding correction to the "lens equation" for gravitational lensing. We also give formulas for the light deflection angle through order $\Lambda M$, assuming a parameterized spherically symmetric metric for the external region of the central mass.