Supersymmetric massive gravity and dark matter -

Abstract

This dissertation is composed of two parts. The first is constructing the supersymmetric form of the Higgs Massive Gravity. The second part is forming the Hamiltonian formulation of the recently proposed Mimetic Dark Matter. When four scalar fields with global Lorentz symmetry take a vacuum expectation value, diffeomorphism invariance is broken spontaneously and then the graviton acquires mass. To supersymmetrize this model, four chiral superfields with global Lorentz symmetry are considered and the matter action is formed out of these superfields. Then, using the rules of tensor calculus, supergravity Lagrangian is coupled to the four chiral multiplets. Similar to the bosonic case, when the scalar components of the chiral multiplets acquire a vacuum expectation value, both diffeomorphism invariance and local supersymmetry are broken spontaneously. This will make the scalar fields vectors and the chiral spinors Rarita-Schwinger fields since the global Lorentz index A is then identified with the space-time Lorentz index. At the end, we show that in the broken phase the spectrum of the model consists of a massive graviton, two massive gravitinos and a massive vector. For the second part, we construct the Hamiltonian of Mimetic Gravity. The equations of motion in this formalism are those of general relativity plus two more equations. However, these two equations are proved to be the constraint equation and the conservation of the energy-momentum tensor. Poisson brackets are computed and closure is proved. At the end, comparison with the Hamiltonian dust is done.