Remarks on Higgs Mechanism for Gravitons

TL;DR

This paper develops models demonstrating the Higgs mechanism for gravitons via scalar field potentials, ensuring massive gravitons in flat spacetime without non-unitary modes, and provides a general solution for such potentials.

Contribution

It introduces two classes of scalar potentials that enable Higgs mechanism for gravitons, with conditions ensuring massive gravitons in Minkowski space without non-unitary modes.

Findings

Derived conditions for scalar potentials to give mass to gravitons

Found a general solution for the scalar potential

Presented a specific potential valid for any cosmological constant

Abstract

We construct two kinds of model exhibiting Higgs mechanism for gravitons in potentials of scalar fields. One class of the model is based on a potential which is a generic function of the induced internal metric $H^{AB}$, and the other involves a potential which is a generic function of the usual metric tensor $g_{\mu\nu}$ and the induced curved metric $Y_{\mu\nu}$. In the both models, we derive conditions on the scalar potential in such a way that gravitons acquire mass in a flat Minkowski space-time without non-unitary propagating modes in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. We solve the conditions and find a general solution for the potential. As an interesting specific solution, we present a simple potential for which the Higgs mechanism for gravitons holds in any value of cosmological constant.