A note on Harada's Conformal Killing gravity

TL;DR

This paper demonstrates that Harada's conformal Killing gravity is equivalent to Einstein's equations extended by a conformal Killing tensor, simplifying the equations and providing a straightforward solution approach with applications to flat and constant curvature spaces.

Contribution

It shows the equivalence of Harada's third-order gravity to a second-order extension of Einstein's equations using conformal Killing tensors, simplifying the solution process.

Findings

Harada's gravity is equivalent to Einstein's equations with a conformal Killing tensor.

The equations reduce from third order to second order.

Application examples include flat space and constant curvature scenarios.

Abstract

We show that "Gravity at cosmological distances: Explaining the accelerating expansion without dark energy" recently proposed by J. Harada [6] is equivalent to the Einstein equation extended by the presence of an arbitrary conformal Killing tensor. This turns Harada's equations of third order in the derivatives of the metric tensor to second order, and offers a simple strategy of solution that shortcuts Harada's derivation and obtains both modified Friedmann equations. An application is presented for the case of flat space and constant curvature.