Effect of ξRϕ2 non-minimal coupling on gravitational light bending
Abstract
We investigate the bending of massless fields by a massive object in the presence of a curvature-scalar √(−g)ξR ϕ2 non-minimal coupling up to one loop, using the perturbative quantum gravity computations. It is well known that without such coupling a self interacting scalar field theory cannot be renormalised in the presence of gravity. The massive object is modelled by a massive scalar ϕ, and it is assumed to be non-relativistic, e.g., a star. We compute the 2-2 scattering of massless scalar and photons off this object via graviton exchanges. Assuming both ξ and the bending angle to be small, we use the eikonal approximation to compute the angle up to cal O(ξG2). At tree level (cal O(ξG)) we find no bending, and hence the cal O(ξG2) result happens to be leading in this case. The non-minimal vertices are qualitatively different from that of the standard minimal ones, e.g. $ \sqrt{G} h_{μν} T^{μν}$, as the former contains explicit momenta of the gravitons instead of the scalar, complementing the second. The bending angle is found to behave like ∼ b−7, where b is the impact parameter. We have emphasised the qualitative differences of our results from that of the well studied minimal case.
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BibTeX
@misc{naskar2026effect,
title = {{Effect of $ξRϕ^2$ non-minimal coupling on gravitational light bending}},
author = {Ayan Kumar Naskar and Avijit Sen Majumder and Sourav Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.16406},
eprint = {2606.16406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16406},
}
RIS
TY - UNPB
TI - Effect of ξRϕ^2 non-minimal coupling on gravitational light bending
AU - Ayan Kumar Naskar
AU - Avijit Sen Majumder
AU - Sourav Bhattacharya
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2606.16406
UR - https://arxiv.org/abs/2606.16406
AB - We investigate the bending of massless fields by a massive object in the presence of a curvature-scalar √(−g)ξR ϕ^2 non-minimal coupling up to one loop, using the perturbative quantum gravity computations. It is well known that without such coupling a self interacting scalar field theory cannot be renormalised in the presence of gravity. The massive object is modelled by a massive scalar ϕ, and it is assumed to be non-relativistic, e.g., a star. We compute the 2-2 scattering of massless scalar and photons off this object via graviton exchanges. Assuming both ξ and the bending angle to be small, we use the eikonal approximation to compute the angle up to cal O(ξG^2). At tree level (cal O(ξG)) we find no bending, and hence the cal O(ξG^2) result happens to be leading in this case. The non-minimal vertices are qualitatively different from that of the standard minimal ones, e.g. $ \sqrt{G} h_{μν} T^{μν}$, as the former contains explicit momenta of the gravitons instead of the scalar, complementing the second. The bending angle is found to behave like ∼ b^−7, where b is the impact parameter. We have emphasised the qualitative differences of our results from that of the well studied minimal case.
ER -