Gauge invariant theory of gravity in spacetime with gradient nonmetricity: A possible resolution of several cosmological puzzles

In this paper we apply the symmetry principle in order to search for an alternative unified explanation of several cosmological puzzles such as the present stage of accelerated expansion of the Universe and the Hubble tension issue, among others. We argue that Weyl gauge symmetry, being a manifest symmetry of gauge invariant theories of gravity operating on Weyl integrable geometry spacetimes, may be an actual (unbroken) symmetry of our present Universe. This symmetry may be at the core of a phenomenologically feasible explanation of modern fundamental issues arising within the framework of general relativity and of its known modifications.