Could a so far ignored symmetry of the classical laws of gravity explain the cosmological puzzles?

Abstract

We show that if the masses of timelike fields are point-dependent quantities transforming under conformal transformations as $m\rightarrow\Omega^{-1}m$, so the energy density of perfect fluids transforms as $\rho\rightarrow\Omega^{-4}\rho$, form-invariance under Weyl transformations could be an actual symmetry of the gravitational interactions of matter. That is, under the mentioned circumstances, Weyl symmetry allows any matter field to be coupled to gravity. The phenomenological and physical consequences of the novel result, including the ``many worlds'' interpretation of gauge freedom, are drawn. We explore, in particular, a possible explanation of two major cosmological puzzles: dark matter and dark energy, as a consequence of Weyl symmetry. Quantum-mechanical removal of the spacetime singularities in this framework is briefly discussed as well.