Gauge Formulation for Higher Order Gravity

Abstract

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature. We analyze the form of the second field strenght, $G=\partial F+fAF$, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of $F$ and quadratic contractions of $G$ are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his Generalized Electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behaviour at short distances as well as a meso-large distance modification.

Published version

References in corpus (4)

• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• AdS and stabilized extra dimensions in multidimensional gravitational models with nonlinear scalar curvature terms 1/R and R^4
• Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress-energy tensor
• Electromagnetic Field in Lyra Manifold: A First Order Approach

Cited by in corpus (14)

• Higher-order modified Starobinsky inflation
• Hamilton-Jacobi formalism for Podolsky's electromagnetic theory on the null-plane
• f(Lovelock) theories of gravity
• Scalar-multi-tensorial equivalence for higher order $f\left(R,{\nabla }_{\mu }R,{\nabla }_{{\mu }_1}{\nabla }_{{\mu }_2}R,...,{\nabla }_{{\mu }_1}...{\nabla }_{{\mu }_n}R\right)$ theories of gravity
• Plasma-like Vacuum in Podolsky Regularized Classical Electrodynamics
• The canonical structure of Podolsky's generalized electrodynamics on the Null-Plane
• $f\left(R,{\nabla }_{{\mu }_1}R,\dots ,{\nabla }_{{\mu }_1}\dots {\nabla }_{{\mu }_n}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach
• Observational constraints to a phenomenological $f\left(R,\nabla R\right)$-model
• Observational constraints on varying fundamental constants in a minimal CPC model
• Transition amplitude, partition function and the role of physical degrees of freedom in gauge theories
• Cosmic acceleration from second order gauge gravity
• Spherically Symmetric Solutions in Higher-Derivative Theories of Gravity
• Gravitational Waves Emission in Quadratic Gravity: longitudinal modes, angular momentum emission, and positivity of the radiated power
• Higher-order gravity models: corrections up to cubic curvature invariants and inflation