Remarks on Higgs mechanism for gravitons

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 HAB, and the other involves a potential which is a generic function of the usual metric tensor gμν and the induced curved metric Yμν. 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.