Bulk viscous matter in $f(T)$ gravity: A path to cosmic acceleration
In this paper, we investigate the effects of varying bulk viscosity coefficients $ζ(t)=ζ_{0}+ζ_{1}H$ on cosmic evolution within the framework of $f(T)$ teleparallel gravity. We focus on two cases: (i) $ζ_{1} \neq0$ and (ii) $ζ_{1} =0$, deriving the Hubble parameter $H$ as a function of redshift $z$ using a linear $f(T)$ model ($f(T) = αT$ where $α\neq 0$). Using the combined $H(z)+Pantheon^{+}+BAO$ dataset, we obtain observational constraints on model parameters. For Case I ($ζ_1 \neq 0$), best-fit values are $H_0=60.0^{+2.0}_{-1.9}$ km/s/Mpc, $α=1.01^{+0.10}_{-0.098}$, $ζ_0=40.1^{+1.9}_{-2.0}$, and $ζ_1=0.123^{+0.093}_{-0.088}$, while for Case II ($ζ_1 = 0$), they are $H_0=67.5^{+1.3}_{-1.3}$ km/s/Mpc, $α=0.94^{+0.14}_{-0.13}$, and $ζ_0=34.7^{+2.0}_{-2.0}$. The analysis reveals a transition in the deceleration parameter, indicating a shift from deceleration to acceleration of the universe's expansion, with present-day values of $q_{0} \approx -0.49$ and $q_{0} \approx -0.32$ for the respective cases. The jerk parameter $j(z)$ and effective EoS for the cosmic viscous fluid also support the cosmic acceleration, with trajectories aligning with the quintessence scenario. These findings underscore the potential of our $f(T)$ model dominated by bulk viscous matter in explaining cosmic acceleration.