Composite higher derivative theory of gravity

Abstract

We investigate a higher derivative theory that belongs to the class of composite field theories. Starting from the Yang-Mills theory based on the Lorentz group, we express the gauge vector fields in terms of the tetrad decomposition of a space-time metric with a nontrivial coupling constant. The resulting composite gauge theory is a natural candidate for an alternative theory of pure gravity. In the limit of vanishing coupling constant, all classical high-precision tests for theories of gravity are passed. An exact static isotropic solution is found, which is less singular than the Schwarzschild solution of general relativity. Composite field theories come with a natural canonical Hamiltonian formulation and a natural set of constraints, so that they provide an ideal setting for future quantization. Finally, we propose possible couplings of the gravitational field to matter.

Mathematical structure and physical content of composite gravity in weak-field approximation

“…whereg is a dimensionless coupling constant that controls the relative weight of the symmetric and antisymmetric contributions to b κ μ . Only forg ¼ 1 can the four-vector variables (7) be interpreted as a connection field [2]. Such an interpretation would be essential for a closer relation to general relativity.…”

“…A composite higher derivative theory of gravity has recently been proposed in [2]. The general idea of a composite theory is to specify the variables of a "workhorse theory" in terms of more fundamental variables and their time derivatives [3,4].…”

“…The occurrence of time derivatives in the "composition rule" leads to a higher derivative theory, which is naturally tamed by the constraints resulting from the composition rule. For the composite theory of gravity proposed in [2], the underlying workhorse theory is the Yang-Mills theory [5] based on the Lorentz group, and the composition rule expresses the corresponding gauge vector fields in terms of the tetrad or vierbein variables providing a Cholesky-type decomposition of a metric. As a consequence of the composite structure of the proposed theory, it differs significantly from contentious previous attempts [6][7][8] to turn the Yang-Mills theory based on the Lorentz group into a theory of gravity.…”

“…Whereas the original formulation of composite gravity in [2] was based on the Lagrangian framework, we here switch to the Hamiltonian approach. As a Hamiltonian formulation separates time from space, it certainly cannot provide the most elegant formulation of relativistic theories.…”

“…Understanding the structure of the constraints is helpful also for proper coupling of the gravitational field to matter. Whereas the coupling of the Yang-Mills fields to matter was considered previously [2], we here introduce a properly matched additional coupling of the tetrad fields to matter.…”