Kinematic reconstruction of torsion as dark energy in Friedmann cosmology

TL;DR

This work investigates whether space-time torsion in Einstein–Cartan gravity can act as dark energy by reconstructing the torsion function $\phi(t)$ from low-redshift cosmological data using kinematic parameterizations of the comoving distance $D_C(z)$ and the Hubble parameter $H(z)$. It derives a Riccati equation for $\Phi=\phi/H_0$, reduces it to a Bernoulli form, and expresses the solution in terms of $E(z)$ and $D_C(z)$, enabling direct data-driven reconstruction via MCMC constrained by SN, $H(z)$, and BAO with priors on $\Omega_{m0}$. Two parameterizations are explored: a $D_C(z)$-based model and an $H(z)$-based model, both yielding non-negligible torsion contributions $\Phi(z)$ and deceleration histories $q(z)$ with a transition around $z_t\sim0.6-0.75$, while ΛCDM remains favored by Bayesian criteria due to model simplicity. The results show torsion as a viable late-time driver that can be probed further with improved priors and data, highlighting the value of data-driven, model-independent reconstructions in modified-gravity cosmologies.

Abstract

In this paper we study the effects of torsion of space-time in the expansion of the Universe as a candidate to dark energy. The analysis is done by reconstructing the torsion function along cosmic evolution by using observational data of Supernovae type Ia, Hubble parameter {and Baryon Acoustic Oscillation} measurements. We have used a kinematic model for the parameterization of the comoving distance and the Hubble parameter, then the free parameters of the models are constrained by observational data. The reconstruction of the torsion function is obtained directly from the data, using the kinematic parameterizations.

Figures (7)

• Figure 1: Contours for the joint analysis of SNe Ia, $H(z)$ and BAO data at 1$\sigma$ and 2$\sigma$ for the free parameters in the Comoving Distance parameterization (\ref{['pold']}).
• Figure 2: Reconstruction of the normalized torsion function $\Phi$ with the parameterization (\ref{['pold']}) for the Comoving Distance, with a 3$\sigma$ Planck prior (green) and with an 1$\sigma$ KiDS prior (red) over $\Omega_m$.
• Figure 3: Contours for the joint analysis of SNe Ia, $H(z)$ and BAO data at 1$\sigma$ and 2$\sigma$ for the free parameters in the Hubble parameter parameterization (\ref{['pold4']}).
• Figure 4: Reconstruction of the normalized torsion function $\Phi$ with the parameterization (\ref{['pold4']}) for the Hubble parameter $H(z)$, with a 3$\sigma$ Planck prior (green) and with an 1$\sigma$ KiDS prior (red) over $\Omega_m$.
• Figure 5: Superposition of the two different reconstructions for $\Phi$ within $1\sigma$ c.l. Left: 3$\sigma$ Planck prior over $\Omega_m$. Right: 1$\sigma$ KiDS prior over $\Omega_m$.