Generalized interaction in multigravity

TL;DR

This paper develops a comprehensive framework for multigravity models in D-dimensional space-time, generalizing invariant volume and interaction potential, and demonstrates that the model is ghost-free and yields a massive graviton in the weak field limit.

Contribution

It introduces a generalized approach to multigravity, extending the interaction potential and invariant volume, and proves the model's ghost-free nature and massive graviton emergence.

Findings

The model coincides with Pauli-Fierz in bigravity.

The model is ghost-free in the weak field limit.

Interaction leads to a nonzero graviton mass.

Abstract

A general approach to description of multigravity models in D-dimensional space-time is presented. Different possibilities of generalization of the invariant volume are given. Then a most general form of the interaction potential is constructed, which for bigravity coincides with the Pauli-Fierz model. A thorough analysis of the model along the 3+1 expansion formalism is done. It is shown that the absence of ghosts the considered bigravity model is equivalent in the weak field limit to the massive gravity (the Pauli-Fierz model). Thus, on the concrete example it is shown, that the interaction between metrics leads to nonvanishing mass of graviton.