One-parameter dynamical dark-energy from the generalized Chaplygin gas

The fact that Einstein's equations connect the space-time geometry to the total matter content of the cosmic substratum, but not to individual contributions of the matter species, can be translated into a degeneracy in the cosmological dark sector. Such degeneracy makes it impossible to distinguish cases where dark energy (DE) interacts with dark matter (DM) from a dynamical non-interacting scenario using observational data based only on time or distance measurements. In this paper, based on the non-adiabatic generalized Chaplygin gas (gCg) model, we derive and study some cosmological consequences of a varying one-parameter dynamical DE parameterization, which does not allow phantom crossing. We perform a parameter selection using the most recent public available data, such as the data from Planck 2018, eBOSS DR16, Pantheon and KiDS-1000. We find that current observations provide strong constraints on the model parameters, leading to values very close to the $\Lambda$CDM cosmology, at the same time that the well-known $\sigma_8$ tension is reduced from $\sim 3\sigma$ to $\sim 1\sigma$ level.