Late cosmic acceleration by matter creation cosmology in modified gravity

In this article, we explore the expansion of the Universe powered by the gravitationally induced ‘adiabatic’ matter creation, a non-equilibrium thermodynamical process in $f\left(Q\right)$ gravity in the background dynamics of a flat Friedmann–Lemaître–Robertson–Walker spacetime geometry. The action of $f\left(Q\right)$ gravity involves a general function of nonmetricity scalar $Q$. As the Universe expanding, the gravitational field of this expanding Universe is acting on the quantum vacuum, which results in a continuous creation of matter particles. Under the formalism of $f\left(Q\right)$ gravity, we obtain the analytical solutions of the cosmological quantities by assuming the ‘generalized Chaplygin gas’ (GCG)equation of state. A particular case of GCG equation of state is also studied. We analyze how matter creations play an effective role in the late-time evolution of the Universe in modified gravity. By using the latest observational datasets, including the type Ia supernovae (Pantheon), Cosmic Chronometer $H\left(z\right)$ data, and Baryonic Acoustic Oscillations (BAO) we also perform a statistical analysis to test the observational viability of two models. The best-fit parameters are used to compare both models to $\Lambda$CDM by means of the evolution of cosmological quantities, stability, and information selection criteria, namely, the Akaike information criterion and the Bayesian information criterion. We conclude that a flat Universe in our models with GCG is still supported by current observational data. Furthermore, the data shows a phantom nature of the equation of state for GCG model and de-Sitter model for Chaplygin gas in late-time evolution.