Gauge gravitation theory in Riemann-Cartan space-time and the nonsingular Universe

TL;DR

This work investigates gauge gravitation theory in Riemann–Cartan space-time (GTRC) as a classical route to resolving cosmological singularities and explaining late-time acceleration without dark energy. By formulating isotropic cosmology equations from a Lagrangian including curvature and torsion invariants, the authors show that torsion can generate a limiting energy density, leading to a Friedmann-like expansion with an effective cosmological constant $\Lambda_{eff} = \frac{(1 - b/f_0)^2}{8 b \alpha_G}$ and a vacuum energy density $\varepsilon_{vac} = \frac{1}{4 \alpha_G}(1 - b/f_0)^2$. They analyze homogeneous isotropic models in a dimensionless framework, obtaining numerical solutions for flat, open, and closed universes near the limiting density; results indicate a transition from gravitational compression to expansion (a bounce) and a subsequent standard-like expansion, with the early dynamics depending on $\omega$, $\alpha_G$, and $b$. The findings suggest that torsion-induced repulsion can address singularities and early-universe acceleration, while vacuum torsion–spin couplings may have observable implications for astrophysical objects and dark matter phenomena, highlighting the potential of GTRC as a viable alternative extension of general relativity. Key expressions include $\Lambda_{eff} = \\frac{(1 - b/f_0)^2}{8 b \alpha_G}$ and $\varepsilon_{vac} = \\frac{1}{4 \alpha_G}(1 - b/f_0)^2$.

Abstract

The gauge gravitation theory in the Riemann-Cartan space-time is investigated in order to solve the fundamental problems of the general relativity theory. The constraints for indefinite parameters of the theory under which solutions of isotropic cosmology describe a nonsingular accelerating Universe are given. Numerical solutions of cosmological equations near the limiting energy density by transition from gravitational compression to expansion in dependence on energy density in the case of flat, closed and open models are obtained. Some physical consequences of gauge gravitational theory in the Riemann-Cartan space-time in astrophysics are discussed.

Figures (5)

• Figure 1: Parameter $\tilde{H}=\tilde{H}_\pm$ as function of $\tilde{\varepsilon}$ for flat model (solid lines) and for closed model (dashed lines): $\tilde{H}_+$ (red line), $\tilde{H}_-$ (blue line)
• Figure 2: Time derivative $\tilde{H}'$ and acceleration parameter $\tilde{H}' + \tilde{H}^2$ as functions of $\tilde{\varepsilon}$ near limiting energy density
• Figure 3: Energy density $\tilde{\varepsilon}$ as function of time $\tilde{t}$ near limiting energy density
• Figure 4: Energies $\tilde{\varepsilon}_{\rm max}$, $\tilde{\varepsilon}_1$, $\tilde{\varepsilon}_2$, $\tilde{\varepsilon}_3$ as functions of parameter $\omega$ for flat and closed models
• Figure 5: Parameter $\tilde{H}=\tilde{H}_\pm$ as function of $\tilde{\varepsilon}$ for $\omega=1$ and $k=0$ (solid lines) and for $\omega=1$, $k=-1$, and $C_1 = 15$ (dashed lines): $\tilde{H}_+$ (red line), $\tilde{H}_-$ (blue line)