We investigate a cosmological scenario in which the dark matter particles can be created during the evolution of the Universe. By regarding the Universe as an open thermodynamic system and using non-equilibrium thermodynamics, we examine the mechanism of gravitational particle production. In this setup, we study the large-scale structure (LSS) formation of the Universe in the Newtonian regime of perturbations and derive the equations governing the evolution of the dark matter overdensities. Then, we implement the cosmological data from Planck 2018 CMB measurements, SNe Ia and BAO observations, as well as the Riess et al. (2019) local measurement for H0 to provide some cosmological constraints for the parameters of our model. We see that the best case of our scenario (χtot2=3834.40) fits the observational data better than the baseline ΛCDM model (χtot2=3838.00) at the background level. We moreover estimate the growth factor of linear perturbations and show that the best case of our model (χfσ82=39.85) fits the LSS data significantly better than the ΛCDM model (χfσ82=45.29). Consequently, our model also makes a better performance at the level of the linear perturbations compared to the standard cosmological model. Although the improvement in χtot for Model 2 compared to ΛCDM at the background level may arise somewhat from the additional degree of freedom, the better consistency of this model at the level of linear perturbations results mainly from the impact of particle production on the sound speed at low redshifts.
