Quadratic curvature theories formulated as Covariant Canonical Gauge theories of Gravity

Abstract

The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation framework are applied to derive a Palatini type gauge theory of gravity. The metric $g_{\mu \nu }$, the affine connection $γ\indices{^λ_{μν}}$ and their respective conjugate momenta, $k^{\mu \nu \sigma }$ and $q\indices{_η^{αξβ}}$ tensors, are the independent field components describing the gravity. The metric is the basic dynamical field, and the connection is the gauge field. The torsion-free and metricity-compatible version of the space-time Hamiltonian is built from all possible invariants of the $q\indices{_η^{αξβ}}$ tensor components up to second order. These correspond in the Lagrangian picture to Riemann tensor invariants of the same order. We show that the quadratic tensor invariant is necessary for constructing the canonical momentum field from the gauge field derivatives, and hence for transforming between Hamiltonian and Lagrangian pictures. Moreover, the theory is extended by dropping metric compatibility and enforcing conformal invariance. This approach could be used for the quantization of the quadratic curvature theories, as for example in the case of conformal gravity.

arXiv comment6 pages, 1 figure, last version before publishing in Phys Rev D

References in corpus (13)

• Alternatives to Dark Matter and Dark Energy
• Modified teleparallel theories of gravity
• Making the Case for Conformal Gravity
• Scale invariance, new inflation and decaying Lambda terms
• Inflation from M-Theory with Fourth-order Corrections and Large Extra Dimensions
• General Relativity and Weyl Geometry
• Palatini versus metric formulation in higher curvature gravity
• Inflationary universe from higher-derivative quantum gravity
• Gravitational Theory without the Cosmological Constant Problem
• Canonical Transformation Path to Gauge Theories of Gravity
• A correspondence between $1^{st}$ and $2^{nd}$ order formalism by a metricity constraint
• Gauge Theory by canonical Transformations
• On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation

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• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Covariant canonical gauge theory of gravitation for fermions
• Covariant Canonical Gauge Gravitation and Cosmology
• Low-Redshift Constraints on Covariant Canonical Gauge Theory of Gravity
• On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation
• 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
• Rigorous derivation of dark energy and inflation as geometry effects in Covariant Canonical Gauge Gravity
• On CCGG, the De Donder-Weyl Hamiltonian formulation of canonical gauge gravity