Cosmic Dynamics in Einstein-Cartan Theory: Analysing Hubble Tension through Curvature and Torsion field

Abstract: The Hubble tension refers to the significant discrepancy in the Hubble constant $H_{0}$ obtained from two different measurement methods in cosmology. One method derives data from the Cosmic Microwave Background (CMB) observations by the Planck satellite, yielding a value of $67.4\pm{0.5} \ \mathrm{km\ s^{-1}} \mathrm{Mpc^{-1}} $, while the other method relies on direct measurements of Type Ia supernovae, producing a value $73.04\pm{1.04} \ \mathrm{km\ s^{-1}} \mathrm{Mpc^{-1}} $. This issue has persisted for several years. To theoretically explore potential solutions to this problem, this paper examines a model within the framework of Einstein-Cartan (EC) theory, where torsion is introduced with spin as the corresponding entity, allowing for the assumption $H = -\alpha \phi$. By employing the Markov Chain Monte Carlo (MCMC) algorithm and utilizing Cosmic Chronometers (CC) data, we impose parameter constraints on various parameters in the Friedmann equations, particularly focusing on the curvature density parameter $\Omega_k$, to assess whether the model remains stable under this assumption and whether the estimated parameters align more closely with either of the observational results. In conclusion, we find that the parameter constraints in the model incorporating torsion ($ H_0 = 67.6^{+2.1}_{-2.7} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under the Big Bang Nucleosynthesis (BBN) constraint with $\Omega_{k}=0$; $ H_0 = 66.2^{+4.4}_{-2.9} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under same constraint but set $\Omega_{k}$ as a free variable; $ H_0 = 68.8^{+2.9}_{-4.2} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under the Planck constraint) are more consistent with the value derived from CMB data, favoring the lower $H_0$ value.