Perfect fluid dynamics with observational constraint in the framework of f(T) gravity

Abstract

In this study, we explore cosmological models within the framework of $f\left(T\right)$ gravity by utilizing the energy–momentum tensor for a perfect fluid to solve the corresponding field equations. We derive key cosmological parameters, including the Hubble parameter $H$. Parameter constraints were applied using the $R^2$ test, resulting in best-fit values of $\beta =108.51_{-0.40}^{+0.41}$ and ${\xi }_1=-{0.14717}_{-0.00096}^{+0.00094}$, with a strong alignment with the $\Lambda$CDM model ($R^2=0.9280$; RMSE = 11.4068). The deceleration parameter, calculated in terms of cosmic time and redshift, indicates a transition from deceleration to acceleration, consistent with current observations of an accelerating universe. Additionally, we examined the pressure $p$, energy density $\rho$, and equation of state parameter $\omega$ for two specific models: Model-I for $f\left(T\right)=\lambda T$ and Model-II for $f\left(T\right)=T+\beta T^2$. The Om diagnostic plotted against redshift for ${\xi }_1$ shows that $\Omega \left(z\right)$ stabilizes around 0.3 after a slight deviation at $z\approx 0$, with a narrow uncertainty band. The model closely aligns with $\Lambda$CDM at higher redshifts. The pair of statefinder diagnostics $r$ vs. $s$ is also discussed, and our model for $(r,s)=(1,0)$ represents the $\Lambda$CDM model.