We have previously demonstrated that an affine connection resulting in non-metricity can bring in two new scalar fields into the Einstein-Palatini action. These scalar fields can play crucial roles in elucidating inflation and dark energy. In this chapter, we have explored potential coupling of these fields with scalar, gauge and Dirac fields. We have demonstrated that the above mentioned scalar fields may be excluded from the actions of gauge theories interacting with Dirac fields through conserved currents. A similar aspect holds true for scalar fields. The connection- scalars can be coupled with ordinary matter and gauge fields by incorporating suitable interaction terms. We have also found that Stokes’ theorem necessitates the inclusion of right handed neutrinos in the electroweak theory in curved spacetime, even when we use only the Levi-Civita connection. This inclusion is essential for obtaining consistent equations of motion and a conserved vector current for the neutrinos. Axial vector currents for different Dirac fields may remain anomalous depending on the theory. The right handed neutrinos can be significant in explaining neutrino oscillation and dark matter.