Massive Higher Derivative Gravity Theories

TL;DR

This thesis investigates massive higher derivative gravity theories, deriving scattering amplitudes, Newtonian potentials, and analyzing unitarity and spectra in various spacetime backgrounds, including Anti-de Sitter, de Sitter, and flat spacetime.

Contribution

It provides a comprehensive analysis of massive higher derivative gravity theories, including the derivation of scattering amplitudes, potential energies, and the identification of a three-dimensional unitary theory.

Findings

Derived tree-level scattering amplitudes in D-dimensional (A)dS and flat spacetimes.

Calculated Newtonian potential energies for various cases.

Identified a three-dimensional unitary gravity theory and analyzed its spectrum.

Abstract

In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in $D$ dimensional (Anti)-de Sitter and flat spacetimes for the most general quadratic curvature theory augmented with the Pauli-Fierz mass term. From the amplitude expression, the Newtonian potential energies are calculated for various cases. Also, from this amplitude and the propagator structure, a three dimensional unitary theory is identified. In the second part of the thesis, the found three dimensional unitary theory is studied in more detail from a canonical point of view. The general higher order action is written in terms of gauge-invariant functions both in flat and de Sitter backgrounds. The analysis is extended by adding static sources, spinning masses and the gravitational Chern-Simons term separately to the theory in the case of flat spacetime. For all cases the microscopic spectrum and the masses are found. In the discussion of curved spacetime, the masses are found in the relativistic and non-relativistic limits. In the Appendix, some useful calculations that are frequently used in the bulk of the thesis are given.