Theories of Massive Gravity in 2+1 Dimensions

Abstract

This thesis is dedicated to the study of theories of massive gravity. The formulation of higher spin gauge field theories, along with a Chern-Simons (CS) like term for fields of higher spins is presented. Through this setup, general features of theories describing massless/massive fields of higher spin in arbitrary dimensions is discussed. In 2+1 dimensions, the existence of multiple mass-generating mechanisms i.e. metric-based masses and topological masses, offers the possibility for gauge bosons to acquire mixed masses. This scenario is first introduced in a theory of photons where both Proca mass term and CS mass term is simultaneously present. The mass-mixing which occurs in this theory is further analysed through the Stückelberg formalism. Motivated by these results, a theory of massive gravity where gravitons obtain masses from both Fierz-Pauli mass term and CS mass term is studied. This theory allows for 3 propagating massive graviton modes, and their masses have undergone considerable mixing. This mass-mixing is made explicit through a Stückelberg analysis. The bimetric theory of gravity is a non-trivial generalization of the theory of General Relativity. This theory provides a consistent non-linear theory of massive gravity which is studied in detail. In this thesis, the bimetric theory of gravity is extended in 2+1 dimensiosn to the theory of Topologically Massive Bimetric Gravity (TMBG). In the theory of TMBG, the mass-mixing which arises from the interaction of the two metrics and their corresponding CS terms occurs at the nonlinear stage itself. For the version of TMBG studied in this thesis, the linearized theory shows that there are 3 massive graviton modes, which corresponds to the same 3 modes found earlier. Finally, quantum loop corrections to the graviton propagator from massive photons (which acquire mass from both CS and Proca mechanism) is calculated.

arXiv commentMScThesis (154 pages, University of Freiburg) (v2 same as v1; removed obsolete tex pakages)

References in corpus (25)

• The Confrontation between General Relativity and Experiment
• The Black Hole in Three Dimensional Space Time
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• Cosmic strings
• Generalization of the Fierz-Pauli Action
• Massive Gravity
• Theoretical Aspects of Massive Gravity
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
• Photon and Graviton Mass Limits
• Three-Dimensional Gravity Revisited
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• xPerm: fast index canonicalization for tensor computer algebra
• Introduction to the Classical Theory of Higher Spins
• Cosmic Strings and Superstrings
• New limits on cosmic strings from gravitational wave observation
• Lectures on the Quantum Hall Effect
• Elements of Vasiliev theory
• Massive, Topologically Massive, Models
• Topological Mass Generation in Four Dimensions
• From Higher Spins to Strings: A Primer
• The Status of Cosmic Topology after Planck Data
• A cosmotopological relation for a unified field theory
• Gravitational anomaly and fundamental forces
• Unavoidable Conflict Between Massive Gravity Models and Massive Topological Terms