Context: The shape of the mass density profiles of cosmological halos informs us of the nature of DM and DM-baryons interactions. Previous estimates of the inner slope of the mass density profiles of clusters of galaxies are in opposition to predictions derived from numerical simulations of CDM. Aims: We determine the inner slope of the DM density profile of a massive cluster of galaxies, Abell S1063 (RXC J2248.7$-$4431) at $z=0.35$, with a dynamical analysis based on an extensive spectroscopic campaign carried out with the VIMOS and MUSE spectrographs at the ESO VLT. This new data set provides an unprecedented sample of 1234 spectroscopic members, 104 of which are located in the cluster core (R < 200 kpc), extracted from the MUSE integral field spectroscopy. The latter also allows the stellar velocity dispersion profile of the brightest cluster galaxy (BCG) to be measured out to 40 kpc. Methods: We used an upgraded version of the MAMPOSSt technique to perform a joint maximum likelihood fit to the velocity dispersion profile of the BCG and to the velocity distribution of cluster member galaxies over a radial range from 1 kpc to 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 after marginalizing over all the other parameters. The newly determined dynamical mass profile is found to be in excellent agreement with the mass density profiles obtained from the independent X-ray hydrostatic analysis based on deep Chandra data, as well as the strong and weak lensing analyses. Our value of gamma_{DM} is in very good agreement with predictions from cosmological CDM simulations. We will extend our analysis to more clusters in future works. If confirmed on a larger cluster sample, our result makes this DM model more appealing than alternative models.
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