Interacting dark sector with quadratic coupling: theoretical and observational viability
Models proposing a non-gravitational interaction between dark energy (DE) and dark matter (CDM) have been extensively studied as alternatives to the standard cosmological model. A common approach to describing the DE-CDM coupling assumes it to be linearly proportional to the dark energy density. In this work, we consider the model with interaction term $Q=3Hγ{ρ_{x}^{2}}/{(ρ_{c}+ρ_{x})}$. We show that for positive values of $γ$ this model predicts a future violation of the Weak Energy Condition (WEC) for the dark matter component, and for a specific range of negative values of $γ$ the CDM energy density can be negative in the past. We perform a parameter selection analysis for this model using data from Type Ia supernovae from the Pantheon sample, $H(z)$ measurements from the Cosmic Chronometers sample, Baryon Acoustic Oscillations from the DESI survey, and Cosmic Microwave Background data from the Planck combined with the Hubble constant $H_0$ prior. Imposing a prior to ensure that the WEC is not violated, our model is consistent with $Λ$CDM in 2$σ$ C.L., yet exhibits a preference for smaller values of $σ_8$, alleviating the $σ_8$ tension between the CMB results from Planck 2018 and the weak gravitational lensing observations from the KiDS-1000 cosmic shear survey.