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Phenomenological signatures of gauge invariant theories of gravity with vectorial and gradient nonmetricity

Israel Quiros
Aug 2022
In this paper we discuss on the phenomenological footprints of theories wherethe gravitational effects are due not only to spacetime curvature, but also tononmetricity. These theories are characterized by gauge invariance. Due totheir simplicity, here we focus in theories with vectorial nonmetricity. Wemake special emphasis in gradient nonmetricity theories which are based in Weylintegrable geometry (WIG) spaces. While arbitrary and vectorial nonmetricitiesmay have played a role in the quantum epoch, gradient nonmetricity can beimportant for the description of gravitational phenomena in our classical worldinstead. This would entail that gauge symmetry may be an actual symmetry of ourpast, present and future universe, without conflict with the standard model ofparticles (SMP). We show that, in a gauge invariant world modeled by WIGspacetime, the vacuum energy density is a dynamical quantity, so that thecosmological constant problem (CCP) may be avoided. Besides, due to gaugeinvariance, and to the fact that photons and radiation do not interact withnonmetricity, the accelerated pace of cosmic expansion can be explained withoutthe need for the dark energy. We also discuss on the ``many-worlds''interpretation of the resulting gauge invariant framework, where generalrelativity (GR) is just a specific gauge of the theory. The unavoidablediscrepancy between the present value of the Hubble parameter computed on theGR basis and its value according to the gauge invariant theory, may explain theHubble tension issue. It will be shown also that, due to gauge freedom,inflation is not required in order to explain the flatness, horizon and relictparticles abundance problems within the present framework.