2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33709We consider cosmological consequences of a conformal-invariant unified theory which is dynamically equivalent to general relativity and is given in a space with the geometry of similarity. We show that the conformal-invariant theory offers new explanations for to such problems as the arrow of time, initial cosmic data, dark matter and accelerating evolution of the universe in the dust stage.12 pages, talk presented at "Hot Points in Astrophysics", JINR Dubna, Russia, August 22-26, 2000General Relativity and Quantum Cosmologytext