The use of $\mu$-Bose gas model for effective modeling of dark matter
  For the recently introduced $\mu$-deformed analog of Bose gas model
($\mu$-Bose gas model), its thermodynamical aspects e.g. total number of
particles and the partition function are certain functions of the parameter
$\mu$. This basic $\mu$-dependence of thermodynamics of the $\mu$-Bose gas
arises through the so-called $\mu$-calculus, an alternative to the known
$q$-calculus (Jackson derivative, etc.), so we include main elements of
$\mu$-calculus. Likewise, virial expansion of EOS and virial coefficients, the
internal energy, specific heat and the entropy of $\mu$-Bose gas show
$\mu$-dependence. Herein, we study thermodynamical geometry of $\mu$-Bose gas
model and find the singular behavior of (scalar) curvature, signaling for
Bose-like condensation. The critical temperature of condensation $T^{(\mu)}_c$
depending on $\mu$ is given and compared with the usual $T_c$, and with known
$T_c^{(p,q)}$ of $p,q$-Bose gas model. Using the results on
$\mu$-thermodynamics we argue that the condensate of $\mu$-Bose gas, like the
earlier proposed infinite statistics system of particles, can serve for
effective modeling of dark matter.
