It is known that the Bose-Einstein condensate (BEC) based Dark Matter (DM) model solves several problems of Cold Dark Matter model on the small scales, including core-cusp problem. In turn, there are some difficulties that arise in the framework of BEC DM, like overestimated a bit (up to 20%) prediction of halo mass in comparison with the values derived from observations. In ref. , the extended (via µ-deformation) µ-BEC DM model is proposed. The µ-deformed gas has the properties similar to ordinary Bose gas endowed with an additional attraction between its particles, incorporated  by the deformation parameter µ. We prove the possibility of BEC-like phase tran¬sition using the tools of thermodynamical (Ruppeiner) geometry, through analysis of singularities of scalar curvature in the thermodynamical parameters space. It is shown that the critical temperature of BEC-like transition is higher in the considered µ-Bose gas than in the ordinary Bose case. Moreover, dependence on the parameter µ gives us certain freedom enabling to treat the weak points of BEC DM model, e.g. the overestimated value of DM halo mass.
 A.M. Gavrilik, I.I. Kachurik, M.V. Khelashvili, A.V. Nazarenko Condensate of µ-Bose gas as a model of dark matter. Physica A: V.506, pp. 835-843 (2018)
 A.P. Rebesh, I.I. Kachurik, A.M. Gavrilik Elements of μ-calculus and thermodynamics of μ-Bose gas model, Ukr. J. Phys. V. 58, no.12, pp. 1182-1191 (2013)