  A metamodeling for the nucleonic equation of state (EOS), inspired from a
Taylor expansion around the saturation density of symmetric nuclear matter, is
proposed and parameterized in terms of the empirical parameters. The present
knowledge of nuclear empirical parameters is first reviewed in order to
estimate their average values and associated uncertainties, and thus defining
the parameter space of the metamodeling. They are divided into isoscalar and
isovector type, and ordered according to their power in the density expansion.
The goodness of the metamodeling is analyzed against the predictions of the
original models. In addition, since no correlation among the empirical
parameters is assumed a priori, all arbitrary density dependences can be
explored, which might not be accessible in existing functionals. Spurious
correlations due to the assumed functional form are also removed. This meta-EOS
allows direct relations between the uncertainties on the empirical parameters
and the density dependence of the nuclear equation of state and its
derivatives, and the mapping between the two can be done with standard Bayesian
techniques. A sensitivity analysis shows that the more influential empirical
parameters are the isovector parameters $L_{sym}$ and $K_{sym}$, and that
laboratory constraints at super-saturation densities are essential to reduce
the present uncertainties. The present metamodeling for the EOS for nuclear
matter is proposed for further applications in neutron stars and supernova
matter.
