# Light Bending in the Infinite Derivative Theories of Gravity

## TL;DR

This paper calculates how light bending differs in infinite derivative gravity theories from general relativity, showing dependence on energy scales and suggesting potential observational tests with X-ray astronomy.

## Contribution

It introduces a semiclassical method to compute photon deflection in ghost-free infinite derivative gravity, revealing energy-dependent deviations from GR predictions.

## Key findings

- Deflection angle depends on the ratio Λ/E.
- Transition from GR-like to zero deflection occurs at specific energy ratios.
- Potential for observational testing with X-ray telescopes like Chandra.

## Abstract

Light bending is one of the significant predictions of general relativity (GR) and it has been confirmed with great accuracy during the last one hundred years. In this paper, we semiclassically calculate the deflection angle for the photons that just grazing the Sun in the infinite derivative theories of gravity (IDG) which is a ghost and singularity free theory of gravity. From our calculations, we find that the deflection angle $\theta$ only depends on $\Lambda/E$. $\theta \rightarrow \theta_E$ when $\Lambda/E \rightarrow \infty$ and decrease to zero when $\Lambda/E \rightarrow 0$. The transition interval occurs at $10^{4}< E/\Lambda < 10^{7}$. It should be pointed out that this model can be tested by the Chandra X-ray Observatory if $0.01 eV < \Lambda < 0.1 eV$.