Primordial fluctuations of scale factor in closed Universe in Einstein$-$Cartan gravity

TL;DR

This paper explores how quantum uncertainty in the scale factor of a closed Universe within Einstein-Cartan gravity leads to primordial density fluctuations, resulting in a nonsingular bounce and inflation consistent with observational data.

Contribution

It introduces a model linking quantum uncertainty of the scale factor to primordial fluctuations in a nonsingular Einstein-Cartan cosmology.

Findings

Quantum uncertainty causes primordial matter density fluctuations.

The model predicts temperature fluctuations in the CMB.

Cosmic inflation arises naturally from particle production in this framework.

Abstract

We consider a homogeneous and isotropic Universe, described by the minisuperspace Lagrangian with the scale factor as a generalized coordinate. We show that the energy of a closed Universe is zero. We apply the uncertainty principle to this Lagrangian and propose that the quantum uncertainty of the scale factor causes the primordial fluctuations of the matter density. We use the dynamics of the early Universe in the Einstein$-$Cartan theory of gravity with spin and torsion, which eliminates the big-bang singularity and replaces it with a nonsingular bounce. Quantum particle production in highly curved spacetime generates a finite period of cosmic inflation that is consistent with the Planck satellite data. From the inflated primordial fluctuations, we determine the magnitude of the temperature fluctuations in the cosmic microwave background, as a function of the numbers of the thermal degrees of freedom of elementary particles and the particle production coefficient, which is the only unknown parameter.