| Abstract: The Variable Chaplygin Gas (VCG) model has been extensively explored as a unified framework for dark matter and dark energy, offering a dynamical alternative to the standard ΛCDM paradigm. Over the past several years, a broad range of observational probes have been employed to test the viability of this model at the level of background cosmology. In this review, we present a consolidated overview of constraints on the VCG model obtained from Type Ia supernovae, gamma-ray bursts, baryon acoustic oscillations, Hubble parameter measurements, fast radio bursts, and gravitational wave standard sirens.
Beyond summarising background-level constraints, we highlight the limitations of expansion-only probes in fully assessing the cosmological viability of unified dark sector models. In particular, the growth of cosmic structures and the evolution of linear perturbations provide critical tests that are sensitive to the underlying microphysics of dark energy models. Motivated by this, we discuss recent progress in extending the VCG framework to the perturbative regime and outline the role of structure growth observables in breaking degeneracies present in background analyses.
Finally, we review emerging constraints from large-scale structure measurements, with particular emphasis on the growth parameter fσ8fσ8 derived from redshift-space distortion surveys. Recent observations from the Dark Energy Spectroscopic Instrument (DESI) represent a significant advancement in this direction, enabling high-precision tests of the VCG model at the perturbation level. This review thus provides a comprehensive account of the current status of Variable Chaplygin Gas cosmology, from background expansion to structure formation, and outlines future directions for testing unified dark sector models with next-generation surveys.
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