Palatini's cousin: A New Variational Principle

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.

12 pages

References in corpus (9)

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Cited by in corpus (10)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• On new variational principles as alternatives to the Palatini method
• From Brans-Dicke gravity to a geometrical scalar-tensor theory
• The bimetric variational principle for General Relativity
• Filtering out the cosmological constant in the Palatini formalism of modified gravity
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Variational principle and boundary terms in gravity à la Palatini
• Variational Problem and Bigravity Nature of Modified Teleparallel Theories
• A modified variational principle for gravity in modified Weyl geometry
• Comparing metric and Palatini approaches to vector Horndeski theory