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

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.