A new class of equations of state (EoS) for strongly interacting matter is
presented which is characterized by a density-dependent stiffening of the
hadronic phase due to the quark substructure of baryons (Pauli blocking on
the quark level between baryons) and by a density-dependent stiffening in
the quark matter phase after the chiral/deconfinement transition due to
higher order (8-quark) interactions in the scalar and vector current
channels.
It is demonstrated that such an EoS can describe high-mass twin compact
stars as a unique feature of identifying a strong first-order phase
transition in mass and radius observations of compact stars, thus
supporting the existence of a critical endpoint in the QCD phase diagram.
Furthermore, rotating compact star configurations are considered which
reveal a unique feature of this new hybrid EoS for scenarios of hybrid star
formation in either accreting LMXBs or spinning-down isolated pulsars.