Pure-Connection Gravity and Anisotropic Singularities

Abstract

Abstract:In four space-time dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. They are most properly described by a connection field, with space-time metric being a secondary and derived concept. All these theories have the same number of degrees of freedom as general relativity, which is the only parity-invariant member of this family. Modifications of general relativity can be arranged so as to become important in regions with large curvature. In this paper, we review how a certain simple modification of this sort can resolve the Schwarzschild black-hole and Kasner anisotropic singularities of general relativity. In the corresponding solutions, the fundamental connection field is regular in space-time.

Scattering amplitudes in affine gravity

“…Originally discussed by Eddington and Schrödinger [25][26][27], most investigations involving the connection as a fundamental degree of freedom are carried out in a formulations where the relevant connection lives in a related gauge bundle, e.g. SO(3) [28][29][30][31][32][33], or SO(1, 3) [34]. On paper, the purely affine theory has many interesting properties.…”

Quantum cosmology of pure connection general relativity

“…This action has some similarities with the action (4) for a relativistic particle; in particular we have a lapse-like variable ρ similar to the 'einbein' λ used there. However, (35) is already in Hamiltonian form, with C i and P i analogous to position and momentum variables for a relativistic particle, in contrast with (4) defined in terms of position variables only.…”

“…A somewhat simpler anisotropic model is obtained by assuming that the homogeneous submanifolds S in the decomposition M = R × S are diffeomorphic to flat R 3 ; the group of isometries acting on each of these leaves is then an Abelian group of translations. This is the Bianchi I model, which was studied for a generalised class of pure connection theories of gravity in [35].…”