Nonlinear interacting cosmological models after Planck 2018 legacy release and the $H_0$ tension

Interacting dark energy models are widely renowned for giving an explanation to the cosmic coincidence problem as well as several observational issues. According to the recent observational data, and so far we are concerned with the literature, the choice of the interaction function between dark matter and dark energy is always questionable since there is no such underlying theory that could derive it. Thus, in this work we have raised this issue by proposing two new nonlinear interaction functions and constrain them using cosmic microwave background (CMB) from Planck 2018, baryon acoustic oscillations (BAO), dark energy survey and a measurement of the Hubble constant $H_0$ from Hubble Space Telescope (HST) 2019. The dark energy equation of state is considered to be constant throughout the work and the geometry of the universe is assumed to be homogeneous and isotropic with zero spatial curvature. Our analyses report that a non-zero interaction is always allowed by the observational data and the dark energy equation of state is bent towards the phantom regime. In particular, when $H_0$ from HST is added to Planck 2018+BAO, we find an evidence for a non-zero coupling at more than $2\sigma$ confidence level. Our analyses also report that for both the models, $H_0$ is close to its local measurements and thus alleviating the $H_0$ tension. In particular, one of the interacting models perfectly solves the $H_0$ tension.