Anisotropic singularities in chiral modified gravity

Abstract

In four space-time dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. All these theories describe just two propagating polarizations of the graviton. General Relativity with an arbitrary cosmological constant is the only parity-invariant member of this family. We review how these modified gravity theories arise within the framework of pure-connection formulation. We introduce a new convenient parametrisation of this family of theories by using certain set of auxiliary fields. Modifications of General Relativity can be arranged so as to become important in regions with large Weyl curvature, while the behaviour is indistinguishable from GR where Weyl curvature is small. We show how the Kasner singularity of General Relativity is resolved in a particular class of modified gravity theories of this type, leading to solutions in which the fundamental connection field is regular all through the space-time. There arises a new asymptotically De Sitter region 'behind' the would-be singularity, the complete solution thus being of a bounce type.

Induced gravity and minimally and conformally coupled scalar fields in Bianchi-I cosmological models

“…It is shown that in the Kasner universe, this connection is always finite even when the metric is singular. While the authors of [59] and other papers, developing this idea work with the modified gravity in contrast to our more conservative approach, we find their idea of the finite quantities, existing in all the spacetime attractive and interesting.…”

Spin connection formulations of real Lorentzian general relativity

“…With the SL(2, C) forms at hand, we can now recover the SD Lagrangians in their pure-connection and BF forms. We start with the former, which is given by [10,11] 6) and is supplemented by the reality constraints [38]…”

“…is the one satisfying the Einstein equations when A i is a solution [38], and the ten reality constraints (6.7) are equivalent to the statement that this metric is real Lorentzian. Since this property is preserved under evolution, these constraints are compatible with the dynamics from the canonical viewpoint.…”

“…where f is homogeneous of degree one, thus generalizing (6.6). As for the reality constraints, a natural generalization of (6.7) would be [38] F i ∧F j = 0 , Im f (X) = 0 ,…”

Pure-Connection Gravity and Anisotropic Singularities

“…Therefore, to solve for the gauge-field dynamics, one has to resort to formalism with auxiliary matrix field Ψ ij together with the connection A i -the formalism which is obtained by excluding only the B-field from (10). This procedure was followed by in our paper [15], where a general solution for the Bianchi I case was obtained in the form…”