CMBR in G\"{o}del Universe:A possible test to Einstein-Cartan gravity?

A rotating universe represented by the G\"{o}del metric in spacetimes with Cartan torsion is investigated where the Cosmic Microwave Background 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 spacetime is shown to lead to the evolution equation of the cosmological perturbation where the spin-rotation coupling is the source of the growth of inhomogeneities.It is shown that temperature anisotropy is within the limits of COBE constraint yielding a value of $\frac{{\delta}T}{T}=10^{-7}$.This result opens the possibility of testing Einstein-Cartan gravity from a cosmological experiment such as PLANCK or MAP.