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

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 $\lambda$. 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 $\omega$. It turns out that, this modified gravitational theory produces solutions similar to the quintessence and phantom models.