Weyl type $f(Q,T)$ gravity observational constrained cosmological model

In this paper, we have studied the dynamical aspects of the cosmological model of the Universe in the Weyl type $f(Q,T)$ gravity, which is an extension of symmetric teleparallel gravity. The non-metricity scalar $Q$ has been expressed in standard Weyl form and can be determined by a vector field $w_{\mu}$ and the trace of energy momentum tensor denoted as $T$. The logarithmic form of the Hubble parametrization has been incorporated and the best fit values of the free parameters have been determined using $32~CC$ sample points, $1701~Pantheon^{+}$ and $6~BAO$ data points. The present value of the $H_{0}\approx 70.2\pm 4.6$, $H_{0}\approx 68.69_{-0.59}^{+0.67}$ and $H_{0}\approx 69.26_{-0.53}^{+0.57}$ respectively for $CC~Sample$, $CC + Pantheon^{+}$ and $CC + Pantheon^{+} + BAO$ datasets. With the constrained values of the free parameters, the cosmographic parameters are constrained and the present value of each parameter has been noted. The deceleration parameter for $CC~Sample$, $CC + Pantheon^{+}$ and $CC + Pantheon^{+} + BAO$ datasets provides $-0.5221$, $-0.5477$ and $-0.5691$ respectively at present time. We have considered exponential and non-linear form of the Weyl type function $f(Q,T)$ to assess the dynamical behaviour of the model. The accelerating cosmological models show the quintessence behaviour at present time as we get the present EoS parameter values obtained as $\omega\approx -0.7068$ and $\omega\approx -0.6828$ for $CC~Sample$, $\omega\approx -0.6991$ and $-0.6949$ for $CC + Pantheon^{+}$ and $\omega\approx -0.7001$ and $-0.7084$ for $CC + Pantheon^{+} + BAO$ respectively.