Basics of massive spin-2 theories

Kürekçi, Şahin
In this thesis, basics of massive spin-2 theories are studied. The theory of general relativity cannot explain some problems in very small and in very large scales and it needs a modification. The way of modifying general relativity by giving mass to the propagating particle graviton is called massive gravity. The first correct massive gravity theory is the linear theory written by Fierz and Pauli. However, later on it has been found that this theory does not match up with the physical predictions of general relativity in the zero mass limit. This discontinuity in the mass parameter of the theory is called the van Dam-Veltman-Zakharov (vDVZ) discontinuity. When the method of Stueckelberg providing to preserve the gauge symmetry of the massless theory to take a smooth limit is applied to the theory of massive gravity it was seen that the reason of this dis continuity was a scalar field which does not decouple from the source even in the massless limit. Later, it was proposed by Vainshtein that the vDVZ discontinuity may disappear by studying the non-linear theory. However, when the Hamiltonian analysis of the non-linear massive gravity theory was done it was understood that theory consists of an extra unphysical degree of freedom which is called the Boulware-Deser ghost.