COSMOLOGICAL SINGULARITY AND BOUNCE IN EINSTEIN-CARTAN-KIBBLE-SCHIAMA GRAVITY
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In this thesis we consider a generalised Einstein-Cartan theory, and the effects of including space-time torsion in the description of grav- ity. We add the most general covariant dimension four operators to general relativity coupling torsion with fermionic fields, with arbi- trary strength. If the gravitational action is taken to be he Einstein- Hilbert action, torsion is local and non dynamical and can be inte- grated out to yield to an effective four-fermion interaction. In this theory we study the dynamics of a collapsing universe that begins in a thermal state and find that – instead of a big crunch singularity – the Universe with torsion undergoes a bounce. We solve the dynami- cal equations (a) classically (without particle production); (b) includ- ing the production of fermions in a fixed background in the Hartree- Fock approximation and (c) including the quantum backreaction of fermions onto the background space-time. In the first and last cases the Universe undergoes a bounce. The production of fermions due to the coupling to a contracting homogeneous background speeds up the bounce, implying that the quantum contributions from fermions is negative. When compared with former works on the subject, our treatment is fully microscopic (namely, we treat fermions by solving the corresponding Dirac equations), and quantum (in the sense that we include fermionic loop contributions).