FLRW Cosmology in Metric-Affine $F(R,Q)$ Gravity

We investigate some FLRW cosmological models in the context of Metric-Affine $F(R,Q)$ gravity, as proposed in [arXiv:1205.52666]. Here, $R$ and $Q$ are the curvature and nonmetricity scalars using non-special connections, respectively. We get the modified field equations using a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) metric. We then find a connection between the Hubble constant $H_{0}$, the density parameter $\Omega_{m0}$, and the other model parameters in two different situations involving scalars $u$ and $w$. Next, we used new observational datasets, such as the cosmic chronometer (CC) Hubble datasets and the Pantheon SNe Ia datasets, to determine the optimal model parameter values through MCMC analysis. Using these best-fit values of model parameters, we have discussed the results and behavior of the derived models. We have also discussed the AIC and BIC criteria for the derived models in the context of $\Lambda$CDM. We have found that the geometrical sector dark equation of state parameter $\omega_{de}$ behaves just like a dark energy candidate. We have found that both models are transit phase models and Model-I approaches to the Lambda CDM model in the late-time universe and Model-II approaches to quintessence scenarios.