Metric-Affine Cosmologies: Kinematics of Perfect (Ideal) Cosmological Hyperfluids and First Integrals

TL;DR

This paper explores the dynamics of perfect hyperfluids in metric-affine cosmology, deriving conservation laws, first integrals, and analyzing the effects of torsion and non-metricity on cosmic evolution.

Contribution

It introduces a comprehensive classification of perfect hyperfluids, derives their conservation laws, and provides a first integral of motion incorporating non-Riemannian geometric effects.

Findings

Conservation laws for pure spin, dilation, and shear hyperfluids.

First integral of motion relating hyperfluid variables with torsion and non-metricity.

Analysis of matter-connection couplings leading to spin, dilation, and shear currents.

Abstract

We consider a generic Metric-Affine Cosmological setup and classify some particularly interesting specific cases of Perfect Hyperfluids. In particular, we present the form of conservation laws for the cases of pure spin, pure dilation and pure shear fluids. We also develop the concept of an incompressible hyperfluid and pay special attention to the case of a hypermomentum preserving hyperfluid. We also give a specific example on the emergence of the spin, dilation and shear currents through matter-connection couplings. In addition, starting from the generalized acceleration equation for the scale factor including torsion and non-metricity we provide a first integral of motion relating the latter with the rest of the hyperfluid variables. These results then formalize the analysis of the non-Riemannian effects in Cosmology.