I will discuss how (broken) conformal symmetry can be used as a guiding principle to construct viable minimalistic extensions of the Standard Model. I will highlight the central role gravity (and its incarnations) plays in these considerations, with an emphasis on the Einstein-Cartan formulation. I will show that an inflationary epoch driven by the Higgs field is automatically incorporated. Moreover, the inflationary predictions may in principle be related to the electroweak physics, thus creating an intricate link between the primordial and late Universe. Finally, I will comment on the self-consistency of these constructions.