Non-Metric Gravity I: Field Equations

TL;DR

This paper introduces a class of modified gravity theories based on Plebanski formulation, where the connection no longer matches the usual spin-connection, leading to new second-order field equations involving derivatives of a scalar function of auxiliary fields.

Contribution

It generalizes Plebanski gravity by adding a scalar-dependent term, resulting in novel second-order field equations with distinct geometric and dynamical properties.

Findings

Connection differs from self-dual spin-connection in GR.

Field equations relate metric derivatives to auxiliary field components.

Energy conservation and Bianchi identities are preserved.

Abstract

We describe and study a certain class of modified gravity theories. Our starting point is Plebanski formulation of gravity in terms of a triple B^i of 2-forms, a connection A^i and a ``Lagrange multiplier'' field Psi^ij. The generalization we consider stems from presence in the action of an extra term proportional to a scalar function of Psi^ij. As in the usual Plebanski general relativity (GR) case, a certain metric can be constructed from B^i. However, unlike in GR, the connection A^i no longer coincides with the self-dual part of the metric-compatible spin-connection. Field equations of the theory are shown to be relations between derivatives of the metric and components of field Psi, as well as its derivatives, the later being in contrast to the GR case. The equations are of second order in derivatives. An analog of the Bianchi identity is still present in the theory, as well as its contracted version tantamount to energy conservation equation.