Light deflection in unified gravity and measurable deviation from general relativity in the second post-Newtonian order

TL;DR

This paper compares predictions of unified gravity and general relativity for light deflection, revealing measurable differences at the second post-Newtonian order that could be tested in future experiments.

Contribution

It introduces a gauge theory of unified gravity extending the Standard Model and calculates light deflection, showing potential observable deviations from general relativity at higher PN orders.

Findings

First PN order predictions agree with experiments.

Second PN order shows ~23-27% differences in polarization-dependent deflections.

Future experiments could distinguish between the two theories.

Abstract

Light does not travel in a perfectly straight line when it passes near massive objects. In this work, we calculate the gravitational deflection of light using the gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)], formulated as an extension of the Standard Model. The nonlinear graviton-graviton interaction is accounted for in the lowest order. The dynamical equations of light in external gravitational field in unified gravity are essentially different from the dynamical equations obtained using the curved metric of general relativity. The goal of the present work is to compare the predictions of unified gravity and general relativity for the gravitational deflection of light. Since the calculation of the gravitational deflection of light in unified gravity is fundamentally different from the pertinent calculation in general relativity, we devote ample space for approximations used. The deflection angles obtained from unified gravity and general relativity are equal in the first post-Newtonian (PN) order, and agree with previous experiments available for the Sun. However, the second PN order terms of unified gravity reveal measurable relative differences of $7/30\approx23.3\%$ and $4/15\approx26.7\%$ for the out-of-plane and in-plane polarizations, respectively, in comparison with the polarization-independent value of general relativity. Therefore, we expect that experimentally differentiating between the two theories will become possible in the near future. For future experiments, we also make calculations for other astrophysical objects, such as for a neutron star, which is in the limit of the PN approximation. The application of unified gravity to black holes, for which the PN approximation is not valid, is left as a topic of further work.