A correspondence between $1^{st}$ and $2^{nd}$ order formalism by a metricity constraint

Abstract

A way to obtain a correspondence between the first order and second order formalism is studied. By introducing a Lagrange multiplier coupled to the covariant derivative of the metric, a metricity constraint is implemented. The new contributions which comes from the variation of the Lagrange multiplier transforms the field equations from the first order to the second order formalism, yet the action is formulated in the first order. In this way all the higher derivatives terms in the second order formalism appear as derivatives of the Lagrange multiplier. Using the same method for breaking metricity condition and building conformal invariant theory is briefly discussed, so the method goes beyond just the study of first order or second formulations of gravity, in fact vast new possible theories of gravity are envisioned this way.

5 pages. Accepted for publication in Phys Rev D

References in corpus (5)

• Cosmological inflation in $F(R,\mathcal{G})$ gravity
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Palatini versus metric formulation in higher curvature gravity
• Metric-affine f(R,T) theories of gravity and their applications
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• Dynamically Generated Inflationary Lambda-CDM
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Gauge theory of Gravity based on the correspondence between the $1^{st}$ and the $2^{nd}$ order formalisms
• Unified Dark Energy and Dark Matter from Dynamical Spacetime Cosmology
• Equivalence of first and second order formulations of the Einstein-Hilbert theory