Extending unified gravity to account for graviton-graviton interaction

TL;DR

This paper extends a gauge theory of unified gravity to include graviton-graviton interactions, crucial for understanding gravitational wave propagation in external fields, while maintaining gauge invariance.

Contribution

It introduces an extension of the unified gravity theory to incorporate graviton self-interactions within the Standard Model framework.

Findings

Preserves 4xU(1) gauge invariance in the extended theory

Enables analysis of gravitational wave interactions in external potentials

Provides a framework for future gravitational field interaction studies

Abstract

Recently, a gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)] has been developed to extend the Standard Model to include gravity. Here we present unified gravity using the ordinary four-vector and tensor field notation of the Standard Model. The main goal of the present work is to extend the original Minkowski spacetime formulation of the theory to account for graviton-graviton interaction. This is a necessary extension for problems involving interactions between gravitational fields, for example, in the propagation of gravitational waves in external gravitational potentials. The 4xU(1) gauge invariance of unified gravity is preserved in this extension.