General relativity with spin and torsion and its deviations from Einstein's theory

The field equations of general relativity with spin and torsion ($U_4$ theory) are considered to describe correctly the gravitational properties of matter on a microphysical level. By an averaging procedure one arrives at a macroscopic field equation, which under normal matter densities coincides with Einstein's equation of conventional general relativity. For very high matter densities, even if the spin are randomly distributed, Einstein's equation breaks down and $U_4$ theory must be applied. It is shown how the singularity theorems of Penrose and Hawking must be modified to apply in $U_4$ theory. All known cosmological models in $U_4$ theory which prevent singularities are shown to violate an energy condition of a singularity theorem.