  The low density nuclear matter equation of state is strongly constrained by
nuclear properties, however, for constraining the high density equation of
state it is necessary to resort to indirect information obtained from the
observation of neutron stars, compact objects that may have a central density
several times nuclear matter saturation density, $n_0$. Taking a meta-modelling
approach to generate a huge set of equation of state that satisfy nuclear
matter properties close to $n_0$ and that do not contain a first order phase
transition, the possibility of constraining the high density equation of state
was investigated. The entire information obtained from the GW170817 event for
the probability distribution of $\tilde{\Lambda}$ was used to make a
probabilistic inference of the EOS, which goes beyond the constraints imposed
by nuclear matter properties. Nuclear matter properties close to saturation,
below $2n_0$, do not allow us to distinguish between equations of state that
predict different neutron star (NS) maximum masses. This is, however, not true
if the equation of state is constrained at low densities by the tidal
deformability of the NS merger associated to GW170817. Above $3n_0$,
differences may be large, for both approaches, and, in particular, the pressure
and speed of sound of the sets studied do not overlap, showing that the
knowledge of the NS maximum mass may give important information on the high
density EOS. Narrowing the maximum mass uncertainty interval will have a
sizeable effect on constraining the high density EOS.
