IA/U.Lisboa Seminar - Minimal Quasidilaton - 27 março 2017

I will introduce a quasidilaton scalar field to the minimal theory of massive gravity with the Minkowski fiducial metric, in such a way that the quasidilaton global symmetry is maintained and that the theory admits a stable self-accelerating de Sitter solution. I will start with a precursor theory that contains three propagating gravitational degrees of freedom without a quasidilaton scalar and introduce Stuckelberg fields to covariantize its action. This makes it possible for us to formulate the quasidilaton global symmetry that mixes the Stuckelberg fields and the quasidilaton scalar field. By the Hamiltonian analysis we confirm that the precursor theory with the quasidilaton scalar contains four degrees of freedom, three from the precursor massive gravity and one from the quasidilaton scalar. I will further remove one propagating degree of freedom to construct the minimal quasidilaton theory with three propagating degrees of freedom, corresponding to two polarizations of gravitational waves from the minimal theory of massive gravity and one scalar from the quasidilaton field, by carefully introducing two additional constraints to the system in the Hamiltonian language. Switching to the Lagrangian language, I will find self-accelerating de Sitter solutions in the minimal quasidilaton theory and analyze their stability. We will see that the self-accelerating de Sitter solution is stable in a wide range of parameters.