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

Abstract

In the present work, we derive the motion of light in the weak-field limit of energy-momentumsquared 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 [1, 2], we restrict the free parameter of the theory and show that it lies within the range −4.0 × 10 −27 m s 2 kg −1 < f 0 < 8.7 × 10 −26 m s 2 kg −1 . This interval is in agreement with those derived in [3,4]. 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 highresolution 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. We also show that as long as the light source and the dense lens are aligned, the EMSG correction is effective, and the combined light of the lensed images is different from the GR case. This issue makes it possible to observe signatures of this theory in the microlensing regime.

A survey of strong cosmic censorship conjecture beyond Einstein’s gravity

“…Although the EMSG with η > 0 is prone to exposing a well-behaved cosmology in the late time [98] as well as the early universe [99] 7 , however, the possibility of η < 0 does not rule out by constraints obtained from astrophysics objects with a high density such as neutron stars [105]. This was also recently confirmed by studying the motion of light in the weak-field limit of EMSG [106]. Therefore, by focusing on PS-QMs we will survey the possibility of revival of the SCCC for both cases η > 0 and η < 0.…”