Merging matter and geometry in the same Lagrangian

TL;DR

This paper introduces a novel Lagrangian density that unifies matter and geometry, leading to a gravity theory consistent with General Relativity in dust conditions and inherently satisfying Mach's Principle.

Contribution

It proposes a new Lagrangian formulation combining matter and geometry, resulting in a pressuron gravity theory that aligns with GR in specific limits.

Findings

Reduces to a pressuron theory indistinguishable from GR in dust limit

Intrinsic satisfaction of Mach's Principle through combined matter-geometry Lagrangian

Potential to describe realistic gravitational phenomena

Abstract

We show that a Lagrangian density proportional to $\sqrt{-g} \L_m^2/R$ reduces to a pressuron theory of gravity that is indistinguishable from General Relativity in the dust limit. The combination of matter and geometry in the same Lagrangian density intrinsically satisfies Mach's Principle --- since matter cannot exist without curvature and vice versa --- while it may have the correct phenomenology in order to describe actual gravity.