A cosmological model with logarithmic f(T) gravity and H(z) quadratic expansion

TL;DR

This study investigates late-time cosmic acceleration within a modified teleparallel gravity framework by adopting a logarithmic f(T) function and a quadratic H(z) expansion. The authors perform a model-independent analysis, fitting $H_{0}$, $\alpha$, and $\beta$ to Hubble data, Pantheon+SH0ES, and BAO, obtaining a present-day deceleration parameter $q(0)\approx -0.435$ that confirms acceleration, and a competitive $H_{0}$ value near the local measurements. They derive the effective geometric fluid with density $\rho_{g}$, pressure $p_{g}$, and equation of state $\omega_{g}$, showing that the model can emulate quintessence or phantom behavior depending on the exponent $n$, with $\omega_{g}\to -1$ for early and late times. Overall, the work demonstrates that logarithmic f(T) gravity, combined with a data-driven H(z) parametrization, can reproduce ΛCDM-like acceleration while providing a dynamical equation of state and a purely geometric origin for dark energy, consistent with current cosmological data.

Abstract

We study the late-time cosmological expansion of a modified teleparallel gravity model of type logarithmic type. This modified gravitational lagrangian yields a cosmological constant term and also power-law corrections to the teleparallel equivalent of general relativity (TEGR) for small $λ$. By using the cosmological chronometers and the type Ia supernove data from the Pantheon+SH0ES dataset, we fit the parameters of the modified gravitational dynamics assuming $H(z)$ parametrized by a quadratic expansion. The results exhibit an accelerated expansion with parameter $q = - 0.435 \pm 0.028$. In addition, we analyzed the effective energy density, pressure and state parameter $ω$. It turns out that, this modified gravitational theory produces solutions similar to the quintessence and phantom models.

Figures (7)

• Figure 1: Comparison between two possible parameterizations for $H(z)$, where one represents the simplified $\Lambda CDM$ model for a universe containing only dust-like matter. Both parameterizations were tested for the same Hubble dataset represented by the black bars.
• Figure 2: Comparison between two possible parameterizations for $H(z)$ used to construct the apparent magnitude $\mu(z)$ represented in equation (22). Both parameterizations were tested for the same Pantheon+SH0ES dataset represented by the black bars.
• Figure 3: Contours of the confidence regions of the quadratic expansion model $H(z)$ tested for data from Pantheon+, BAO and Hubble datasets in the maximization of likelihood method. The regions from outside to inside represent respectively $1\sigma$ and $2\sigma$.
• Figure 4: Deceleration parameter $q$ for the parameterized $H(z)$ and $\Lambda CDM$ models. The best-fit values presented in Table II for each model were used to generate the plot.
• Figure 5: Graphical representation of the effective $\rho_{g}$ behaviors for different values of $n$. The best-fits of $H_0$, $\alpha$ and $\beta$ present in Table II were used to construct the figure, and for behavior analysis purposes, we assume numerically $\lambda = 10^{-3}$ and $\Lambda = 1$.