# Cosmological singularities and bounce in Cartan-Einstein theory

## Abstract

We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh ( in-in ) formalism. We then apply the renormalized theory to 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 dynamical equations (a) classically (without particle production); (b) including 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, presumably because fermion production contributes negatively to the energy-momentummore »

- Authors:

- Institute for Theoretical Physics, Spinoza Institute and EMME$\Phi$, Utrecht University, Postbus 80.195, 3508 TD Utrecht (Netherlands)

- Publication Date:

- OSTI Identifier:
- 22667623

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL MODELS; COUPLING; DIRAC EQUATION; ENERGY-MOMENTUM TENSOR; EXPANSION; FERMI INTERACTIONS; FERMIONS; GENERAL RELATIVITY THEORY; HARTREE-FOCK METHOD; INFLATIONARY UNIVERSE; PARTICLE PRODUCTION; RENORMALIZATION; SINGULARITY; SPACE-TIME; SPIN; TORSION; UNIVERSE; VELOCITY

### Citation Formats

```
Lucat, Stefano, and Prokopec, Tomislav, E-mail: s.lucat@students.uu.nl, E-mail: t.prokopec@uu.nl.
```*Cosmological singularities and bounce in Cartan-Einstein theory*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/10/047.

```
Lucat, Stefano, & Prokopec, Tomislav, E-mail: s.lucat@students.uu.nl, E-mail: t.prokopec@uu.nl.
```*Cosmological singularities and bounce in Cartan-Einstein theory*. United States. doi:10.1088/1475-7516/2017/10/047.

```
Lucat, Stefano, and Prokopec, Tomislav, E-mail: s.lucat@students.uu.nl, E-mail: t.prokopec@uu.nl. Sun .
"Cosmological singularities and bounce in Cartan-Einstein theory". United States.
doi:10.1088/1475-7516/2017/10/047.
```

```
@article{osti_22667623,
```

title = {Cosmological singularities and bounce in Cartan-Einstein theory},

author = {Lucat, Stefano and Prokopec, Tomislav, E-mail: s.lucat@students.uu.nl, E-mail: t.prokopec@uu.nl},

abstractNote = {We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh ( in-in ) formalism. We then apply the renormalized theory to 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 dynamical equations (a) classically (without particle production); (b) including 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, presumably because fermion production contributes negatively to the energy-momentum tensor. 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).},

doi = {10.1088/1475-7516/2017/10/047},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 10,

volume = 2017,

place = {United States},

year = {Sun Oct 01 00:00:00 EDT 2017},

month = {Sun Oct 01 00:00:00 EDT 2017}

}