Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory

TL;DR

This paper explores Einstein-Cartan cosmology with intrinsic spin, showing how torsion influences universe geometry, gravitational wave generation, and accelerated expansion, but cannot fully replace dark energy.

Contribution

It provides a detailed analysis of Einstein-Cartan cosmology, deriving new theorems on universe geometry, gravitational waves, and the role of torsion in cosmic acceleration.

Findings

Universe must be flat or open, excluding closed models.

Intrinsic spin leads to gravitational wave emission.

Torsion contributes to positive accelerated expansion.

Abstract

We start by presenting the general set of structure equations for the 1+3 threading spacetime decomposition in 4 spacetime dimensions, valid for any theory of gravitation based on a metric compatible affine connection. We then apply these equations to the study of cosmological solutions of the Einstein-Cartan theory in which the matter is modeled by a perfect fluid with intrinsic spin. It is shown that the metric tensor can be described by a generic FLRW solution. However, due to the presence of torsion the Weyl tensors might not vanish. The coupling between the torsion and Weyl tensors leads to the conclusion that, in this cosmological model, the universe must either be flat or open, excluding definitely the possibility of a closed universe. In the open case, we derive a wave equation for the traceless part of the magnetic part of the Weyl tensor and show how the intrinsic spin of matter in a dynamic universe leads to the generation and emission of gravitational waves. Lastly, in this cosmological model, it is found that the torsion tensor, which has an intrinsic spin as its source, contributes to a positive accelerated expansion of the universe. Comparing the theoretical predictions of the model with the current experimental data, we conclude that torsion cannot completely replace the role of a cosmological constant.