Growth-of-Structure Constraints on the Variable Chaplygin Gas Model
A unified description of dark matter and the late-time acceleration of the Universe offers an attractive framework for explaining the dark sector. Among such models, the Variable Chaplygin Gas (VCG) model provides a unified description but faces challenges, particularly in the evolution of cosmological perturbations. We investigate the evolution of linear density perturbations in the VCG model assuming adiabatic perturbations and constrain its parameters using recent $fσ_8$ growth measurements within a Markov Chain Monte Carlo (MCMC) framework. Gaussian priors are adopted from our previous analysis of background observations, including Type Ia supernovae (Pantheon), baryon acoustic oscillations (BAO), Hubble parameter $H(z)$ measurements, fast radio bursts (FRB), and gamma-ray bursts (GRB). We find that growth data favour a markedly different region of the parameter space than the background observations. In particular, the growth analysis prefers a substantially larger value of the model parameter $n$ ($n \simeq 2.3$) compared with the background constraint ($n \sim 1$). This tension indicates that parameter values providing an excellent fit to the background expansion fail to simultaneously reproduce the observed growth of cosmic structures. Our results demonstrate that growth-of-structure observations provide a stringent and independent test of unified dark sector models and underscore the importance of combining background and perturbation data when assessing the cosmological viability of the Variable Chaplygin Gas model.