Matter scattering in $R_{\mu \nu}^2$ gravity and unitarity

TL;DR

This paper examines how matter scattering in $R_{}$ gravity maintains unitarity at high energies, unlike Einstein gravity, due to differences in propagator UV behavior, highlighting implications for quantum gravity theories.

Contribution

It demonstrates that $R_{}$ gravity coupled to matter preserves unitarity in high-energy matter scattering, contrasting with Einstein gravity, and links this to UV propagator behavior and renormalizability.

Findings

Matter scattering in $R_{}$ gravity satisfies unitarity bounds at high energy.

Einstein gravity does not satisfy unitarity at high energy in matter scattering.

Differences are attributed to UV behavior of propagators and renormalizability properties.

Abstract

We investigate the ultraviolet (UV) behavior of two-scalar elastic scattering with graviton exchanges in higher curvature gravity theory. In the Einstein gravity, matter scattering is shown not to satisfy tree unitarity at high energy. Among a few possible directions to cure unitarity (i.e. UV completion of Einstein gravity), string theory, modified gravity, inclusion of high-mass/high-spin states, we take $R_{\mu\nu}^2$ gravity coupled to matter. We show that the matter scattering with graviton interactions satisfies the unitarity bound at high energy, in contrast with the Einstein gravity. The difference in unitarity property of the two gravity theories is due to that in the UV behavior of the propagator and is probably connected to that in another UV property, namely renormalizability property of the two.