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

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, $a(t)=C{t}^{\alpha }{e}^{D{t}^{\beta }}$ emerges in the special case $g_1=0$, where the quadratic Riemann-Cartan term vanishes. For $g_1\ne 0,$ 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.

This manuscript is 11 pages long and contains no figures

References in corpus (14)

• The Confrontation between General Relativity and Experiment
• Cosmology with torsion: An alternative to cosmic inflation
• Torsion Cosmology and the Accelerating Universe
• Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein-Cartan theory
• Motion of test bodies in theories with nonminimal coupling
• First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: Lagrangian and first integrals
• Analytical results for binary dynamics at the first post-Newtonian order in Einstein-Cartan theory with the Weyssenhoff fluid
• Radiative losses and radiation-reaction effects at the first post-Newtonian order in Einstein-Cartan theory
• First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: equations of motion
• The dark side of the torsion: Dark Energy from propagating torsion
• Torsional dark energy in quadratic gauge gravity
• Ehrenfest Theorem in Precanonical Quantization
• Torsion driving cosmic expansion
• Torsion cosmology in the light of DESI, supernovae and CMB observational constraints