Cosmology in the De Donder-Weyl Formulation of Einstein-Cartan Gravity

TL;DR

This paper explores torsion effects in Einstein-Cartan gravity using De Donder-Weyl formalism, deriving modified Friedmann equations and analyzing their solutions, revealing limitations of common power-law assumptions in cosmological models.

Contribution

It introduces a De Donder-Weyl Hamiltonian approach to Einstein-Cartan cosmology, deriving new torsion-modified Friedmann equations and analyzing solution branches.

Findings

Multiple solution branches for power-law scale factors, many unphysical.

A hybrid exponential-power law solution emerges when quadratic Riemann-Cartan terms vanish.

Nonlinear equations for non-zero quadratic terms limit analytic solutions.

Abstract

We investigate torsion-driven cosmological dynamics within the framework of Einstein-Cartan gravity using the De Donder-Weyl Hamiltonian formalism, where the tetrad and Lorentz connection act as independent variables and the Hamiltonian includes quadratic Riemann Cartan corrections. Embedding this theory in an FLRW background, we derive the corresponding torsion-modified Friedmann equations and analyze their solutions across radiation and matter-dominated epochs. The commonly assumed power law form $a(t)=\beta t^{\alpha}$ is shown to generate multiple solution branches, many of which can be considered to be 'unphysical'. A hybrid solution, $a(t)=Ct^{\alpha}e^{Dt^{\beta}}$ emerges in the special case $g_1=0$, where the quadratic Riemann-Cartan term vanishes. For $g_1\not=0,$ the equations become nonlinear, precluding closed-form analytic solutions. These findings highlight the limitations of the power-law approximation and identify the restricted conditions under which torsion can coherently drive cosmic expansion.