Palatini's cousin: A New Variational Principle

TL;DR

This paper introduces a new variational principle in Riemannian geometry that independently varies an auxiliary metric and the Levi Civita connection, leading to simpler second-order field equations and different cosmological implications compared to the Palatini method.

Contribution

It proposes a novel variational approach with an auxiliary metric that simplifies equations and alters cosmological models relative to the Palatini method.

Findings

Field equations are second order PDEs.

No gradients of matter variables appear.

Cosmological physics differs from Palatini-based models.

Abstract

A variational principle is suggested within Riemannnian geometry, in which an auxiliary metric and the Levi Civita connection are varied independently. The auxiliary metric plays the role of a Lagrange multiplier and introduces non-minimal coupling of matter to the curvature scalar. The field equations are 2nd order PDEs and easier to handle than those following from the so-called Palatini method. Moreover, in contrast to the latter method. no gradients of the matter variables appear. In cosmological modeling, the physics resulting from the new variational principle will differ from the modeling using the Palatini method.