On Certain Relationships between Cosmological Observables in the Einstein-cartan Gravity

We show that if one takes into account Penrose’s conformal technique in the Einstein-Cartan gravity, it is possible to obtain a relation between Hubble’s expansion and Birch’s rotation of the Universe at spacelike infinity. This relation also leads to the final reduction of the gravitational coupling to a dimensionless quantity of order unity at spacelike infinity. Initial-value equations at spacelike infinity in the Einstein-Cartan gravity can be used as a starting point to study the structure formation and evolution of the Universe with Ω=1. Current measurements of the expansion and rotation of the Universe favour the massive spinning particle as a candidate particle for the dark matter .