  We study the spherical collapse of an over-density of a barotropic fluid with
linear equation of state in a cosmological background. Fully relativistic
simulations are performed by using the Baumgarte-Shibata-Shapiro-Nakamura
formalism jointly with the Valencia formulation of the hydrodynamics. This
permits us to test the universality of the critical collapse with respect to
the matter type by considering the constant equation of state parameter
$\omega$ as a control parameter. We exhibit, for a fixed radial profile of the
energy-density contrast, the existence of a critical value $\omega^*$ for the
equation of state parameter under which the fluctuation collapses to a black
hole and above which it is diluting. It is shown numerically that the mass of
the formed black hole, for subcritical solutions, obeys a scaling law $M\propto
|\omega - \omega^*|^\gamma$ with a critical exponent $\gamma$ independent on
the matter type, revealing the universality. This universal scaling law is
shown to be verified in the empty Minkoswki and de Sitter space-times. For the
full matter Einstein-de Sitter universe, the universality is not observed if
conformally flat sub-horizon initial conditions are used. But when
super-horizon initial conditions computed from the long-wavelength
approximation are used, the universality appears to be true.
