Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity

TL;DR

This paper investigates gauge invariant gravity theories with vectorial nonmetricity, exploring their potential phenomenological signatures and implications for cosmology, dark matter, and dark energy, especially after electroweak symmetry breaking.

Contribution

It introduces the concept of gradient nonmetricity in gauge invariant gravity theories and proposes a novel 'many-worlds' interpretation of gauge invariance in this context.

Findings

Vectorial nonmetricity can survive electroweak symmetry breaking.

Gradient nonmetricity is essential for phenomenological impact.

Possible role of vectorial nonmetricity in the quantum epoch.

Abstract

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.