Statistical and observation comparison of Weyl-type f(Q,T) models with the ΛCDM paradigm

We study the $f(Q,T)$ gravity in the framework of Weyl geometry (known as Weyl-type $f(Q,T)$ gravity), where Q denotes the non-metricity scalar, and T denotes the energy-momentum tensor trace. In this work, we consider the $f(Q,T)$ model, which is defined as $f(Q,T)=\alpha Q^{m+1}+\frac{\beta }{6{\kappa }^2}T$ and investigating two scenarios: (I) $m=0$ (linear model) and $\left(II\right)$ $m\ne 0$ (nonlinear model). For both scenarios, we find the explicit solution for the field equations by using the barotropic equation of state as $p=w\rho$, where w is the equation-of-state (EoS) parameter. Further, we study the obtained solutions statistically using the $Pantheo{n}^{+}$ (Without SHOES Calibrated) dataset with 1701 data points. For both models, the best-fit values of model parameters for $1-\sigma$ and $2-\sigma$ confidence level. The higher Hubble constant values in both models emphasize the presence of Tension. We statistically compare our models to the ΛCDM model using ${\chi }_{min}^2$, ${\chi }_{red}^2$, AIC, $\Delta AIC$, BIC and $\Delta BIC$. We also examine cosmological parameters such as deceleration and EoS parameters to determine the current acceleration expansion of the Universe. Furthermore, we test our model using Om diagnostic and compare it to the ΛCDM model to determine its dark energy profile. Finally, we draw the conclusion that statistically speaking, both linear and nonlinear models show good compatibility with the ΛCDM model.