Alternative Theory of Gravity

Although Einstein’s theory of gravity is among the most beautiful and successfully tested theories in physics, it has serious problems at the very small and large length scales: its unwavering resistance to quantization and the present need to search for dark energy are the symptoms that motivate the exploration of alternative theories of gravity. To obtain an alternative theory with geometric beauty, we develop a composite Yang-Mills theory in which the gauge-vector fields are expressed in terms of more basic variables and their derivatives [1]. The basic ideas behind composite higher derivative theories can be found in [2,3].

We propose to “downgrade” the full space-time metric of general relativity to a relativistic anisotropy of the mass tensor characterizing the velocity-momentum relation. The “square root” of the metric or mass tensor is used to construct a composite Yang-Mills theory with Lorentz symmetry group, thus building an elegant bridge to the present theories of electroweak and strong interactions. The coupling to matter is given by the expression for the conserved currents of the Yang-Mills theory with Lorentz symmetry group in terms of the energy-momentum tensor [4].

The proposed theory reproduces the famous high-precision predictions of Einstein’s general relativity, such as the deflection of light by the sun and the anomalous precession of the perihelion of Mercury, but makes black holes less singular.

The natural constraints for the weak-field approximation to composite gravity have been analyzed in detail within a canonical Hamiltonian approach [5]. Although this higher derivative theory involves a large number of fields, only few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The structure of the constraints is found to be such that the quantization of the theory is expected to be straightforward.