  In this paper we discuss on the phenomenological footprints of gauge
invariant theories of gravity where the gravitational effects are due not only
to spacetime curvature, but also to vectorial nonmetricity. We explore the
possibility that vectorial nonmetricity and gauge symmetry may survive after
$SU(2)\times U(1)$ (electroweak) symmetry breaking, so that these may have
impact on the explanation of certain cosmological puzzles, such as the nature
of the dark matter and of the dark energy. We show that this is possible only
for theories with gradient nonmetricity, i. e., when the vectorial nonmetricity
amounts to a gradient of a scalar. The possibility that vectorial nonmetricity
may have played a role in the quantum epoch is not ruled out. We also present
an alternative interpretation of gauge invariance of theories with vectorial
nonmetricity which we call as ``many-worlds'' interpretation due to its overall
similitude with the known interpretation of quantum physics.
