In Search Of Consistent Classical Theories of Gravity

Abstract

General Relativity has provided us a successful framework to describe gravity and has passed numerous experimental as well as theoretical consistency conditions. However, general relativity can possibly be modified by a large class of high energy corrections. In this project, we try to constrain the space of all kinematically allowed classical gravitational theories based on certain consistency conditions. We explicitly construct the basis tree-level S-matrices for four graviton and four-photon scattering in all spacetime dimensions. From the space of possible S-matrices, the consistency condition used to rule out possible S-matrices is a conjecture, called as the Classical Regge Growth Conjecture (CRG conjecture). This conjecture puts a restriction on the growth of any classical (tree-level) S-matrix in the Regge limit. Assuming the CRG conjecture to be true, we find that Einstein gravity is the unique classical theory of gravity in spacetime dimensions less than equal to six. In the latter part of the project, we classify all possible 3 point S-matrices quadratic in photons or gravitons