The conceptual beauty of cEDF is to connect the saturation mechanism at the origin of the existence of finite nuclei and the spin-orbit interaction, see for instance [Chanfray2020], at the origin of the magic numbers and element abundance in the universe to the properties of two strong scalar and vector fields. In our project, nuclear data will be employed to calibrate new cEDF models, as well as first-principle results, such as Lattice-QCD, the quark model and the vector dominance model. Our methodology is the following:

While relativistic Lagrangians have existed since the first models by Walecka, almost 50 years ago, new conceptual ideas have emerged recently, as well as new data from exotic beam facilities, contributing to the discovery of about 20 new isotopes every year, for about 20 years. Relativistic Hartree-Fock approaches were blocked by their loose reproduction of finite nuclei ground state [Bouyssy1987]. This obstacle has been overcome with the introduction of density-dependent coupling constants [Long2006], which are also used in relativistic Hartree approaches. The chiral feature of the nuclear interaction originating from the spontaneous symmetry breaking of QCD at low-density, where QCD is non-perturbative, is one of the most recent advances in the understanding of the emergence of the residual nuclear interaction. It has created a new avenue in the understanding of nuclear forces with the chiral effective field theory being one of the most visible new concepts leading to progresses in the description of nuclear matter at low-density and in finite nuclei. The breakdown density of this low-energy theory is estimated to be ~1-2ρ

Astrophysical data will also be employed to select among various dense matter modeling, including the onset of new degrees of freedom above ρ

- Radio astronomy, which is continuously pushing up the lowest bound of the maximal NS mass, will be compared to the solution of the TOV equations using our EoS.
- NICER observatory has released masses and radii for two millisecond pulsars, and at least 2 other measurements are expected for the near future. We will solve TOV equations to compare our cEDF with these data.
- Binary NS (BNS) mergers produce gravitational waves (GW) detected by the LIGO-Virgo collaboration since 2017. We will compare the tidal deformability from BNS with the one predicted by our cEDF. New data are also expected from O4 and O5 observing runs.
- GW170817, AT2017gfo, GRB170817A are also one of the very few examples of the young multi-messenger astronomy. We will employ empirical relations deduced from numerical relativity simulations to relate our EoS to these data.

- WP1: Management and coordination
- WP2: Development of new Lagrangians
- WP3: Modeling of physical systems (finite nuclei and neutron stars) and comparison to data
- WP4: Results, outreach and open access and open sources

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