METRIC-AFFINE SCALE-COVARIANT GRAVITY

We propose a gravitational theory based on the complete relaxing of Riemannian constraints (which force the connection to be symmetric and metric compatible) combined with the requirement of local conformal invariance. To reach this goal we generalize original Dirac's formalism of co-covariant calculus on spaces with arbitrary torsion and nonmetricity. The resulting gravitational theory turns out to be independent of the choice of measuring standards. Nevertheless there exists a mechanism of spontaneous gauge fixing through which all the masses in the universe could be generated. It is shown that field equations of the theory admit of a de Sitter solution with no cosmological constant, both in a vacuum case and in the presence of matter without proper hypermomentum. Various possible developments of the proposed theory are discussed in brief.