  Bearing holographic dark energy hypothesis in mind, the ability of vacuum
energy in describing the current accelerated universe is studied in the
framework of Rastall theory. Here, in addition to the ordinary approach in
which it is expected that this energy plays the role of dark energy, we also
address a new approach where the sum of this energy and Rastall term is
responsible for the current accelerated universe. We also investigate the
cosmological outcomes of using Tsallis entropy in quantifying the energy of
fields in vacuum for both mentioned approaches. The implications of considering
an interaction between the various segments of cosmic fluid have been addressed
in each studied cases. The normalized Hubble parameter for the models have also
been plotted and compared that with the H(z) data consisting of 41 data points
in the redshift range of 0.07< z<2.36.
