Abstract

We investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase space and reconstruct the cosmological history of a spatially flat Friedmann-Lemaitre-Robertson-Walker universe within scalar-nonmetricity theory in both the Jordan and Einstein frames. A detailed analysis is conducted for three connections defined in the coincident and non -coincident gauges. Our findings reveal the existence of a unique one-to-one correspondence for equilibrium points in the two frames. Furthermore, we demonstrate that solutions describing accelerated universes remain invariant under the transformation that relates these conformally equivalent theories.