Light bending and gravitational lensing in energy-momentum-squared gravity

TL;DR

This paper investigates how energy-momentum-squared gravity (EMSG) modifies light bending and gravitational lensing, deriving new potentials, testing solar system constraints, and exploring observable effects on microlensing images.

Contribution

It introduces the post-Newtonian expansion of EMSG, derives photon trajectories, and assesses observational signatures, providing constraints and potential detectability of EMSG effects.

Findings

EMSG introduces a new potential affecting photon trajectories.

The free parameter of EMSG is tightly constrained by solar system tests.

EMSG can cause detectable micro-arcsecond shifts in lensed images.

Abstract

In the present work, we derive the motion of light in the weak-field limit of energy-momentum-squared gravity (EMSG). To do so, we introduce the post-Newtonian (PN) expansion of this modified theory of gravity. It is shown that in addition to the Newtonian potential, a new EMSG potential affects the trajectory of photons. As a result, in this theory, photons do not behave as predicted by general relativity (GR). To evaluate the EMSG theory by the solar system tests, we study light deflection and Shapiro time delay. Regarding the results obtained in \cite{bertotti2003test,shapiro2004measurement}, we restrict the free parameter of the theory and show that it lies within the range $-4.0\times 10^{-27}\, \text{m}\,\text{s}^2\,\text{kg}^{-1} < f_0' < 8.7\times 10^{-26}\,\text{m}\,\text{s}^2\,\text{kg}^{-1}$. This interval is in agreement with those derived in \cite{nazari2020Constraining,akarsu2018constraint}. This consistency manifests that this theory passes these solar system tests with flying colors. Interestingly, it turns out that the magnitude of the EMSG correction strongly depends on the density of the deflector. So, we investigate the possible effects of EMSG on images of a light source microlensed by a compact dense object such as neutron stars. It is estimated that the EMSG correction to the position of lensed images could be as large as $(1-0.1)$ micro-arcseconds which may be detected by future high-resolution missions. Moreover, the total magnification and the shape of light curves are obtained in the EMSG theory. It is revealed that except for a small deviation, the overall behavior of the EMSG light curves is similar to that in GR.