  At the ultra-high densities existing in the core of neutron stars, it is
expected that a phase transition from baryonic to deconfined quark matter may
occur. Such a phase transition would affect the underlying equation of state
(EoS) as well as the observable astrophysical properties of neutron stars.
Comparison of EoS model predictions with astronomical data from multi-messenger
signals then provides us an opportunity to probe the behaviour of dense matter.
In this work, we restrict the allowed parameter space of EoS models in neutron
stars for both nucleonic (relativistic mean field model) and quark matter (bag
model) sectors by imposing state-of-the-art constraints from nuclear
calculations, multi-messenger astrophysical data and perturbative QCD (pQCD).
We systematically investigate the effect of each constraint on the parameter
space of uncertainties using a cut-off filter scheme, as well as the
correlations among the parameters and with neutron star astrophysical
observables. Using the constraints, we obtain limits for maximum NS mass,
maximum central density, as well as for NS radii and tidal deformability.
Although pQCD constraints are only effective at very high densities, they
significantly reduce the parameter space of the quark model. We also conclude
that astrophysical data supports high values of the bag parameter B and
disfavors the existence of a pure quark matter core in hybrid stars.
