  Neutron stars explore matter at the highest densities in the universe such
that their inner cores might undergo a phase transition from hadronic to exotic
phases, e.g., quark matter. Such a transition could be associated with
non-trivial structures in the density behavior of the speed of sound such as
jumps and sharp peaks. Here, we employ a physics-agnostic approach to model the
density dependence of the speed of sound in neutron stars and study to what
extent the existence of non-trivial structures can be inferred from existing
astrophysical observations of neutron stars. For this, we exhaustively study
different equations of state, including as well those with explicit first-order
phase transitions. We obtain a large number of different EoSs which reproduce
the same astrophysical observations and obey the same physical constraints such
as mechanical stability and causality. Among them, some have non-trivial
structures in the sound speed while others do not. We conclude that
astrophysical information to date do not require the existence of a phase
transition to quark matter in the density range explored in the core of neutron
stars.
