Deformed Boson Condensate as a Model of Dark Matter

We consider the condensate of $q$-deformed bosons as a model of dark matter. Our observations demonstrate that for all $q$ values, the system condenses below a $q$-dependent critical temperature $T^{q}_c$. The critical temperature interestingly tends to infinity when $q\rightarrow 0$, so that the $q$- deformed boson gas is always in the condensed phase in this limit irrespective to the temperature. We argue that this has remarkable outcomes, e.g. on the entropy of the system, and also the fraction of the particles in the ground state. Especially, by direct evaluation of the entropy of the system we reveal that it tends to zero at this limit for all temperatures, and also the fraction of particles in the ground state becomes unity. These observations prove the consistency of the model, put it in the list of appropriate candidates for the dark matter. Also, the lower and upper bounds of mass are evaluated using the phase space density and observational data for $q$ deformed Bose-Einstein condensate ($q$-BEC) model.