Modified Theories of Gravity

Abstract

This dissertation is composed of three parts. The first presents the model of unification of Chern-Simons gauge theories and Chern-Simons gravity in 3D space-time. The second is constructing Hamiltonian formulation of ghost free mimetic massive gravity theory. The third is studying the surface terms of mimetic Horava gravity theory. By enlarging the tangent group, we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3D space-time. Either we start working with pontryagin densities in 4D space-time or we start directly considering Chern-Simons actions in 3D space-time. Such unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3D spacetime manifold on which they are defined. For the second topic, we construct the Hamiltonian of ghost free mimetic massive gravity. The linearized theory is studied and the Hamitlonian equations of vii motion are analyzed. Poisson brackets are computed also and closure is proved. The second order scalar Hamiltonian is examined proving that the energy density of mimetic term is indeed positive. The third topic is related to mimetic Horava gravity. It is shown that the surface terms resulting from the variation of the mimetic Horava action constructed will cancel out; therefore, there is no need for the addition of Gibbons-Hawking-York boundary term.