FLRW cosmology in Weyl type f(Q) gravity and observational constraints

Inspired by various works in a Weyl type $f\left(Q\right)$ gravity to reduce some serious problems in General Relativity Theory (GR), we develop a model of the universe in a Weyl type $f\left(Q\right)$ gravity which shows the transition from a decelerating state to an accelerating state of the universe at present when we consider a particular functional form of the $f\left(Q\right)$ gravity as $f\left(Q\right)=\left({H_0}^2\right)({\alpha }_1+{\alpha }_{2}log(H_0^{-2}Q\left)\right)$. We numerically solve Weyl type $f\left(Q\right)$ gravity field equations and obtain the numerical solutions to the Hubble parameter, deceleration parameter, distance modulus, and the apparent magnitudes of stellar objects using Ia Supernovae. Also, we obtain numerical solutions for the Weyl vector w, non-metricity scalar Q, and the Lagrangian multiplier λ appearing in the action of $f\left(Q\right)$ gravity. We compare our model with the error bar plots of the observed Hubble dataset of 77 points, SNIa datasets of 580 points, and 1048 supernova Pantheon datasets of the apparent magnitudes, and the statistical analysis using Baryon Acoustic Oscillations (BAO). It is found that our results fit well with the observed values. The model envisages a unique feature: although the universe is filled with perfect fluid as dust whose pressure is zero, the Weyl vector dominance $f\left(Q\right)$ creates acceleration.