The energy and momentum of the Universe

Abstract

The Einstein$-$Cartan$-$Sciama$-$Kibble theory of gravity naturally extends general relativity to include quantum-mechanical, intrinsic angular momentum of matter by equipping spacetime with torsion. Using the Einstein energy$-$momentum pseudotensor for the gravitational field in this theory, we show that the energy and momentum of the closed Universe are equal to zero. Since the positive energy from mass and motion of the observed matter in the Universe exceeds in magnitude the negative energy from gravity, the Universe must contain another form of matter whose energy is negative. This form, which cannot be composed from particles, might be the observed dark matter.