ON CERTAIN RELATIONSHIPS BETWEEN COSMOLOGICAL OBSERVABLES IN THE EINSTEIN-CARTAN GRAVITY

We show that if one takes into account Penrose's conformal technique i n the Einstein-Cartan gravity, it is possible to obtain a relation bet ween Hubble's expansion and Birch's rotation of the Universe at space- like infinity. This relation also leads to the final reduction of the gravitational coupling to a dimensionless quantity of order unity at s pace-like infinity. Initial-value equations at space-like infinity in the Einstein-Cartan gravity can be used as a starting point to study t he structure formation and evolution of the Universe with Omega=1. Cur rent measurements of the expansion and rotation of the Universe favour the massive spinning particle as a candidate particle for dark matter .