Kinematics of Einstein-Cartan universes

TL;DR

This paper investigates how nonzero torsion in Einstein-Cartan gravity affects the kinematic behavior of cosmological spacetimes, providing a comprehensive geometric framework that includes matter spin effects.

Contribution

It develops a general geometric approach to analyze the kinematics of Einstein-Cartan universes without initial restrictions on matter or torsion-spin couplings.

Findings

Derived evolution equations for observer kinematics with torsion

Identified effects of torsion on cosmological kinematic variables

Recovered known results for Weyssenhoff fluid in Einstein-Cartan theory

Abstract

We analyse the kinematics of cosmological spacetimes with nonzero torsion, in the framework of the classical Einstein-Cartan gravity. After a brief introduction to the basic features of spaces with non-vanishing torsion, we consider a family of observers moving along timelike worldlines and focus on their kinematic behaviour. In so doing, we isolate the irreducible variables monitoring the observers' motion and derive their evolution formulae and associated constraint equations. Our aim is to identify the effects of spacetime torsion, and the changes they introduce into the kinematics of the standard, torsion-free, cosmological models. We employ a fully geometrical approach, imposing no restrictions on the material content, or any a priori couplings between torsion and spin. Also, we do not apply the familiar splitting of the equations, into a purely Riemannian component plus a torsion/spin part, at the start of our study, but only introduce it at the very end. With the general formulae at hand, we use the Einstein-Cartan field equations to incorporate explicitly the spin of the matter. The resulting formulae fully describe the kinematics of dynamical spacetimes within the framework of the Einstein-Cartan gravity, while in the special case of the so-called Weyssenhoff fluid, they recover results previously reported in the literature.