Paths to gravitation via the gauging of parametrized field theories

This is the authors' abstract. We don't add key points for this paper.

In special-relativistic physics, spacetime is imbued with a fixed, nondynamical metric tensor. A path to gravitational theory is to promote this tensor to a genuine dynamical field. An alternative description of special-relativistic physics involves no fixed spacetime geometry but instead the inclusion of scalar fields XI(x^μ) which dynamically may take the form of inertial coordinates in spacetime. This suggests an alternative approach to gravity where the invariance of actions under global Poincar\'e transformations of XI is promoted to either a local Poincar\'e, local translational, or local Lorentz symmetry via the introduction of gauge fields. Points of commonality and departure of the resulting gravitational theories as compared to general relativity are discussed. It is shown that the model based on local Lorentz symmetry is an extension of general relativity that can introduce a standard of time into the dynamics of the gravitational field and allows for spacetimes described by a Minkowski metric or flat Euclidean signature metric despite the gravitational gauge field possessing nonzero curvature.