Affine theory of gravitation

Abstract

We propose a new theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct the simplest dynamical Lagrangian density that is entirely composed from the connection, via its curvature and torsion, and is an algebraic function of its derivatives. It is given by the contraction of the Ricci tensor with a tensor which is inverse to the symmetric, contracted square of the torsion tensor, $k_{\mu \nu }=S_{\lambda \mu }^{\rho }{S}_{\rho \nu }^{\lambda }$. We vary the total action for the gravitational field and matter with respect to the affine connection, assuming that the matter fields couple to the connection only through $k_{\mu \nu }$. We derive the resulting field equations and show that they are identical with the Einstein equations of general relativity with a nonzero cosmological constant, if the tensor $k_{\mu \nu }$ is regarded as the metric tensor. The cosmological constant is simply a constant of proportionality between the two tensors, which together with $c$ and $G$ provides a natural system of units in gravitational physics. This theory therefore provides a physically valid construction of the metric as an algebraic function of the connection, and naturally explains dark energy as an intrinsic property of spacetime. The observed accelerating expansion of the Universe may be the strongest evidence for torsion.

8 pages; revised version

References in corpus (5)

• Extended Theories of Gravity
• Cosmology with torsion: An alternative to cosmic inflation
• Nonsingular, big-bounce cosmology from spinor-torsion coupling
• Gravitation, electromagnetism and cosmological constant in purely affine gravity
• The Maxwell Lagrangian in purely affine gravity

Cited by in corpus (24)

• Reconstructing wormhole solutions in curvature based Extended Theories of Gravity
• Testing Generalized Einstein-Cartan-Kibble-Sciama Gravity using Weak Deflection Angle and Shadow Cast
• Big bounce and closed universe from spin and torsion
• Analysis of big bounce in Einstein--Cartan cosmology
• The simplest origin of the big bounce and inflation
• Quintessential Inflation with Dynamical Higgs Generation as an Affine Gravity
• A nonsingular, anisotropic universe in a black hole with torsion and particle production
• Entropy Production in Affine Inflation
• Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) Polynomial Affine Gravity
• Separate Einstein-Eddington Spaces and the Cosmological Constant
• Non-particle dark matter from Hubble parameter
• Beyond Einstein: A Polynomial Affine Model of Gravity
• Cosmological Dark sector from a Mimetic-Metric-Torsion perspective
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Phantom dark energy from scalar$-$torsion coupling
• Aspects of the polynomial affine model of gravity in three dimensions
• A polynomial affine model of gravity: after ten years
• Precession shift in curvature based Extended Theories of Gravity and Quintessence fields
• Affine Dynamics with Torsion
• Emergent Planck mass and dark energy from affine gravity
• Pure gauge theory for the gravitational spin connection
• Polynomial affine model of gravity in three-dimensions
• Does the metric play a fundamental role in the building of gravitational models?
• Affine connections on singular warped products