a rXiv:as tr o-ph/ 11477v2 29 Nov 2 CMBR in G¨o del Universe with torsion:A possible test to Einstein-Cartan Gravity?L.C.Garcia de Andrade 1Abstract A rotating universe represented by the G¨o del metric in spacetimes with Cartan torsion is investigated where the Cosmic Microwave Back-ground Radiation (CMBR)is computed from the G¨o del rotation of the universe and the spin density of the spinning fluid in Einstein-Cartan gravity.The autoparallel equation in Riemann-Cartan space-time is shown to lead to the evolution equation of the cosmological per-turbation where the spin-rotation coupling is the source of the growth of inhomogeneities.It is shown that temperature anisotropy is withinthe limits of COBE constraint yielding a value of δT1Departamento de F´ısica Teorica-UERJ.Rua S˜a o Fco.Xavier 524,Rio de Janeiro,RJ Maracan˜a ,CEP:20550-003,Brasil.E-Mail.:garcia@dft.if.uerj.br