  Recently, a resonant state of four neutrons (tetraneutron) with an energy of
$E_{4n}=2.37\pm 0.38 \rm{(stat)} \pm 0.44 \rm{(sys)}$ MeV and a width of
$\Gamma=1.75\pm 0.22 \rm{(stat)} \pm 0.30 \rm{(sys)}$ MeV was reported. In this
work, we analyse the effect of including such an exotic state on the yields of
other light clusters, that not only form in astrophysical sites, such as
core-collapse supernovae and neutron star mergers, but also in heavy-ion
collisions. To this aim, we use a relativistic mean-field formalism, where we
consider in-medium effects in a two-fold way, via the couplings of the clusters
to the mesons, and via a binding energy shift, to compute the low-density
equation of state for nuclear matter at finite temperature and fixed proton
fraction. We consider five light clusters, deuterons, tritons, heliums,
$\alpha$-particles, and $^6$He, immersed in a gas of protons and neutrons, and
we calculate their abundances and chemical equilibrium constants with and
without the tetraneutron. We also analyse how the associated energy of the
tetraneutron would influence such results. We find that the low-temperature,
neutron-rich systems, are the ones most affected by the presence of the
tetraneutron, making neutron stars excellent environments for their formation.
Moreover, its presence in strongly asymmetric matter may increase considerably
the proton and the $\alpha$-particle fractions. This may have an influence on
the dissolution of the accretion disk of the merger of two neutron stars.
