Observational constraints on soft dark energy and soft dark matter: challenging $\Lambda$CDM

Soft cosmology is an extension of standard cosmology allowing for a scale-dependent equation-of-state (EoS) parameter in the dark sectors, which is one of the properties of soft materials in condensed-matter physics, that may arise either intrinsically or effectively. We use data from Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillations (BAO), Supernovae Type Ia (SNIa), and Redshift space distrotion (RSD) probes, in order to impose observational constraints on soft dark energy and soft dark matter. We examine three simple models, corresponding to the minimum extensions of $\Lambda$CDM scenario, namely we consider that at large scales the dark sectors have the EoS's of $\Lambda$CDM model (dust dark matter and cosmological constant respectively), while at intermediate scales either dark energy or dark matter or both, may have a different EoS according to constant "softness" parameters $s_{de}$ and $s_{dm}$. The observational confrontation shows that for almost all datasets the softness parameters deviate from their $\Lambda$CDM values, in a prominent way for soft dark energy and mildly for soft dark matter, and thus the data favor soft cosmology. Finally, performing a Bayesian evidence analysis we find that the examined models are certainly preferred over $\Lambda$CDM cosmology.