Reconstructing $f(T)$ Gravity From Hubble Parameterization Constraints

TL;DR

The work addresses late-time cosmic acceleration within $f(T)$ gravity by adopting a simple, well-motivated $f(T)$ form and a parametric Hubble history $H(z)=H_0 \sqrt{(z-a)(bz+1)+(a+1)}$, then constrains the parameters $H_0$, $a$, $b$ using cosmological data via Bayesian MCMC. It derives the dark-energy sector quantities $\rho_{de}$, $p_{de}$ and $\omega_{de}$, and analyzes kinematic diagnostics such as the deceleration parameter $q(z)$ and statefinders $(j,s)$ to compare with $\Lambda$CDM. The results show present values $H_0$ in the range $[69.8,74.2]$ and $q_0$ around $-0.54$ to $-0.74$, with $q(z)\to -1$ at late times; the statefinder trajectory approaches the $\Lambda$CDM point, while the dark-energy EoS remains negative (roughly $\omega_{de}(0)\approx -0.914$). Energy conditions indicate SEC violation (as expected for acceleration) and dataset-dependent behavior for NEC/DEC. Overall, the study provides a viable teleparallel $f(T)$ framework that reproduces late-time acceleration in agreement with current observations and offers diagnostic insight via $j$ and $s$.

Abstract

In this paper, we have presented the cosmological model of the Universe that represents late time cosmic acceleration in torsion based gravitational theory, the $f(T)$ gravity. A well motivated parametrization for the Hubble parameter has been introduced and the free parameters involved are constrained using the cosmological datasets. With the constrained values of the free parameters, other geometrical parameters such as deceleration parameter, jerk parameter, and snap parameter are analyzed and confronted with the prescribed value of the cosmological observations. In addition, the dynamical parameters are analyzed in some non-linear form of $f(T)$ and the energy conditions are also studied and confirmed with the violation of the strong energy condition. The obtained cosmological model provides late time phantom behavior of the Universe.

Figures (9)

• Figure 1: Two dimensional contour diagram extracted from $H(z)$ data demonstrate the favored parameter ranges and uncertainty contours (up to $3 \sigma$) for $H_0$, $a$, and $b$.
• Figure 2: Two dimensional contour diagram extracted from BAO data demonstrate the favored parameter ranges and uncertainty contours (up to $3 \sigma$) for $H_0$, $a$, and $b$.
• Figure 3: Two dimensional contour diagram extracted from Pantheon+SH0ES data demonstrate the favored parameter ranges and uncertainty contours (up to $3 \sigma$) for $H_0$, $a$, and $b$.
• Figure 4: Two dimensional contour diagram extracted from combined ($H(z)$ + BAO + Pantheon+SH0ES) data demonstrate the favored parameter ranges and uncertainty contours (up to $3 \sigma$) for $H_0$, $a$, and $b$.
• Figure 5: (i) Upper panel: Error bar plot of Hubble parameter in redshift; Lower panel: Error bar plot of distance modulus in redshift. The curves are based on the constraints from $H(z)$, BAO, Pantheon+SH0ES and Combined datasets.