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Context: The shape of the mass density profiles of cosmological halos informsus of the nature of DM and DM-baryons interactions. Previous estimates of theinner slope of the mass density profiles of clusters of galaxies are inopposition to predictions derived from numerical simulations of CDM. Aims: Wedetermine the inner slope of the DM density profile of a massive cluster ofgalaxies, Abell S1063 (RXC J2248.7$-$4431) at $z=0.35$, with a dynamicalanalysis based on an extensive spectroscopic campaign carried out with theVIMOS and MUSE spectrographs at the ESO VLT. This new data set provides anunprecedented sample of 1234 spectroscopic members, 104 of which are located inthe cluster core (R < 200 kpc), extracted from the MUSE integral fieldspectroscopy. The latter also allows the stellar velocity dispersion profile ofthe brightest cluster galaxy (BCG) to be measured out to 40 kpc. Methods: Weused an upgraded version of the MAMPOSSt technique to perform a joint maximumlikelihood fit to the velocity dispersion profile of the BCG and to thevelocity distribution of cluster member galaxies over a radial range from 1 kpcto the virial radius (~ 2.7 Mpc). Results: We find a value of $\gamma_{DM}=0.99 \pm 0.04$ for the inner logarithmic slope of the DM density profile aftermarginalizing over all the other parameters. The newly determined dynamicalmass profile is found to be in excellent agreement with the mass densityprofiles obtained from the independent X-ray hydrostatic analysis based on deepChandra data, as well as the strong and weak lensing analyses. Our value of\gamma_{DM} is in very good agreement with predictions from cosmological CDMsimulations. We will extend our analysis to more clusters in future works. Ifconfirmed on a larger cluster sample, our result makes this DM model moreappealing than alternative models.

CLASH-VLT: a full dynamical reconstruction of the mass profile of Abell S1063 from 1 kpc out to the virial radius