  A relativistic Hartree-Fock Lagrangian including a chiral potential and
nucleon polarisation is investigated in hopes of providing a better description
of dense nuclear matter. We fully consider the contribution of the exchange
Fock term to the energy and the self-energies, and in addition we investigate
the nucleon's compositeness and finite size effects (confinement and form
factors) and short range correlations modeled by a Jastrow ansatz. These
effects are added step by step, such that their impact on the dense matter
properties can be analysed in details. The parameters of the model are adjusted
to reproduce fundamental properties related to the QCD theory at low energy,
such as the chiral symmetry breaking, nucleon's quark substructure and
Lattice-QCD predictions, as well as two empirical properties at saturation: the
binding energy and the density. All other empirical parameters, e.g., symmetry
energy and its slope, incompressibility modulus, effective mass, as well as
spin-isospin Landau-Midgal parameter are predictions of the models and can be
used to evaluate the gain of the different approximation schemes in describing
nuclear properties. Bayesian statistics is employed in order to propagate
parameter uncertainties into predictions for the nuclear matter properties. We
show that the splitting of the effective Landau mass is largely influenced by
the value of the $\rho^T$ coupling, and we show that the fit to the symmetry
energy, which induces an increase of the coupling constant $g_\rho$ by about
20-25% compared to the case where it is fixed by the quark model, provides a
very good EoS compatible with the present nuclear physics knowledge.
