Gauge Formulation for Higher Order Gravity

TL;DR

This paper develops a gauge-theoretic formulation of higher order gravity incorporating derivatives of curvature, analyzing Lagrangians and solutions that recover Newtonian gravity and predict modifications at larger scales.

Contribution

It introduces a second order gauge theory approach to gravity, including derivatives of curvature, and explores quadratic Lagrangians with novel solutions.

Findings

Static isotropic solution exhibits Newtonian behavior at short distances.

Derived equations of motion for a generalized Lagrangian similar to Podolsky's electrodynamics.

Found modifications to gravity at meso-large distances.

Abstract

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature. We analyze the form of the second field strenght, $G=\partial F +fAF$, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of $F$ and quadratic contractions of $G$ are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his Generalized Electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behaviour at short distances as well as a meso-large distance modification.