  In this paper, we study the viscous $f(T, B)$ gravity model as a source of
dark energy, and the Extended Bose-Einstein Condensate (EBEC) as a source of
dark matter, in a flat-FRW metric. In the presence of bulk viscosity, we obtain
Friedmann equations and write two continuity equations of dark energy and dark
matter by interacting them. Using the generalized Gross-Pitaeveskii equation,
we earn Equation of State (EoS) of dark matter by EBEC regime as $p_m = \alpha
\rho_{m} + \beta \rho_{m}^2$ in which the both of terms are respectively
introduced as normal dark matter and dark matter halo. The innovation of the
work is that we can simultaneously describe the nature of the dark parts of the
universe with the viscous $f(T, B)$ gravity and the EBEC regime, which leads to
a deep understanding of the different epochs of the universe from early to late
times. In what follows, the energy density and the pressure of dark energy are
reconstructed in terms of the redshift parameter, and then we fit the obtained
results with 53 supernova data from the Hubble data constraints. Next, we plot
the cosmological parameters in terms of the redshift parameter and conclude
that the current universe is in an accelerated phase. Finally, we analyze the
stability and instability of the current model with the sound speed parameter
as well as we draw the density parameter values for dark energy in terms of the
redshift parameter.
