Renormallizable gravity and Lorentz violation with spin-2 fields

Abstract

The aim of the present resarch plan is to investigate the viability of a potentially renormalizable gravitational theory in D = 2 + 1 dimensions and the possibility of Lorentz violation in the real world in D = 3 + 1 dimensions. Regarding the first subject, we will suggest a new 3D quantum gravity model, a kind of higher derivative topologically massive gravity in order to produce a renormalizable self-interacting spin-2 theory. An essential ingredient is unimodular constraint, which fixes the absolute value of the metric determinant to one. This procedure expands a linearized Weyl symmetry beyond the linearized approximation, which will certainly contribute to its renormalizability. Since we have a higher derivative model, free of ghosts (at tree level) we believe that we will end up with a unitary and renormalizable gravitational theory in D = 2 + 1 dimensions. There is no such theory in D = 2 + 1 dimensions to the best we know. Regarding the second part of this work, we investigate the effect of Lorentz breaking terms in the propagation of massless spin-2 particles. Besides the gravitational Chern-Simons Lorentz violating term suggested by Jackiw and Pi e include also the Cotton term and quadratic terms in the curvature which are (the last ones) parity invariant. The influence of those terms on the usual gravitational theory (Einstein-Hilbert) have already been investigated in the literature. However, here in order to drawn model independent conclusions we study those breaking terms in the only viable alternative candidate to the EH model, known as WTDIFF, which has a nonlinear version known as unimodular gravity. Different features will be investigated including analytic propperties of the propagator and the interaction between sources. Such investigations may be relevant from both theoretical and experimental point of view when we search for Lorentz violations signals at low energy. (AU)