relativistic Fermi liquid in the sense of Landau theory [@FW2019]. The density-dependent leading Landau parameters show the characteristic behaviour of a strongly correlated fermionic many-body system, albeit less extreme in comparison with another well-known Fermi system at low temperature, namely liquid $^3$He. Alternative descriptions of neutron star matter involve a (possibly smooth) transition from hadronic matter to some form of quark matter [@Baym2018; @Baym2019; @McLerran2019; @FFM2019].

The required stiffness of the EoS implies strong restrictions on the appearance of hyperons in neutron star matter and for the underlying hyperon-nuclear interactions. A naive introduction of $\Lambda$ hyperons, with only two-body $\Lambda N$ interactions, would appear to be energetically favorable by replacing neutrons at baryon densities around 2-3 $\rho_0$ (in terms of the equilibrium density of normal nuclear matter, $\rho_0 = 0.16$ fm$^{-3}$). However, then the EoS of neutron star matter would become far too soft to satisfy the two-solar-mass constraint [@Djapo2010; @Hell2014; @Lonardoni2015]. A phenomenological analysis [@BS2015], taking into account constraints from both hypernuclear physics and neutron star observations, points out indeed that the interaction between $\Lambda$ hyperons and dense matter has to become repulsive at densities below three times $\rho_0$.

The aim of the present work is to investigate whether 