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 $$a(t)=\beta t^{\alpha }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>β</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mi>α</mml:mi> </mml:msup> </mml:mrow> </mml:math> is shown to generate multiple solution branches, many of which can be considered to be “unphysical”. A hybrid solution, $$a(t)=Ct^{\alpha }e^{Dt^{\beta }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>C</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mi>α</mml:mi> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mi>D</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mi>β</mml:mi> </mml:msup> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> emerges in the special case $$g_1=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , where the quadratic Riemann–Cartan term vanishes. For $$g_1\not =0,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> 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.