Question

Einstein-Cartan Theory with modern Cartan structural equations?

Answer 1

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✔✔The difference between Einstein's general relativity and its Cartan extension is analyzed within the scenario of asymptotic safety of quantum gravity. In particular, we focus on the four-fermion interaction which distinguishes the Einstein-Cartan theory from its Riemannian limit.



✔✔✔In the coupling of gravity to Dirac type spinor fields [1], it is at times surmised that the Einstein-Cartan (EC) theory [2] is superior to standard General Relativity (GR), inasmuch as the involved torsion tensor of Cartan [3, 4] can accommodate the spin of fundamental Fermions of electrons and quarks in gravity.

✔✔✔✔However, classically,the effects of spin and torsion cannot be detected by Lageos or Gravity Probe B [5] and



would be significant only at densities of matter that are very high but nevertheless smaller than the Planck density at which quantum gravitational effects are believed to dominate. It was even claimed [6] that EC theory may avert the problem of singularities in cosmology, but for a coupling to Dirac fields, the opposite happens [