  With the recent dawn of the multi-messenger astronomy era a new window has
opened to explore the constituents of matter and their interactions under
extreme conditions. One of the pending challenges of modern physics is to probe
the microscopic equation of state (EoS) of cold and dense matter via
macroscopic neutron star observations such as their masses and radii. Still
unanswered issues concern the detailed composition of matter in the core of
neutron stars at high pressure and the possible presence of e.g. hyperons or
quarks. By means of a non-perturbative functional renormalization group
approach the influence of quantum and density fluctuations on the quark matter
EoS in $\beta$-equilibrium is investigated within two- and three-flavor
quark-meson model truncations and compared to results obtained with common
mean-field approximations where important fluctuations are usually ignored. We
find that they strongly impact the quark matter EoS.
