Are H 0 and σ 8 Tensions Generic to Present Cosmological Data?

Yes, for a wide range of cosmological models (ΛCDM, non-interacting w _z CDM, w _z WDM, or a class of interacting DMDE). Recently there have been attempts to solve the tension between direct measurements of H ₀ and {σ }₈\sqrt{{{{Ω }}}_0{{m}}} from respective low-redshift observables and indirect measurements of these quantities from observations of the cosmic microwave background (CMB). In this work we construct a quasi-model-independent framework that reduces to different classes of cosmological models under suitable choices of parameters. We test this parameterization against the latest Planck CMB data combined with recent measurements of baryon acoustic oscillations (BAO) and supernovae, and direct measurements of H ₀. Our analysis reveals that a strong positive correlation between H ₀ and σ ₈ is more or less generic for most of the cosmological models. The present data slightly prefer a phantom equation of state for dark energy and a slightly negative effective equation of state for dark matter (a direct signature of interacting models), with a relatively high H ₀ consistent with Planck+R16 data and simultaneously a consistent {{{Ω }}}_0{{m}}. Thus, even though the tensions cannot be fully resolved, a class of interacting models with phantom w _DE get a slight edge over w _z CDM for the present data. However, although they may resolve the tension between high-redshift CMB data and individual low-redshift data sets, these data sets have inconsistencies between them (e.g., between BAO and H ₀, supernovae and BAO, and cluster counts and H ₀).