  In this work, we study the evolution of primordial black holes within the
context of Brans-Dicke theory by considering the presence of a dark energy
component with a super-negative equation of state called phantom energy as a
background. Besides Hawking evaporation, here we consider two type of
accretions - radiation accretion and phantom energy accretion. We found that
radiation accretion increases the lifetime of primordial black holes whereas
phantom accretion decreases the lifespan of primordial black holes.
Investigating the competition between the radiation accretion and phantom
accretion, we got that there is an instant during the matter-dominated era
beyond which phantom accretion dominates radiation accretion. So the primordial
black holes which are formed in the later part of radiation dominated era and
in matter dominated era are evaporated at a quicker rate than the Hawking
evaporation. But for presently evaporating primordial black holes, radiation
accretion and Hawking evaporation terms are dominant over phantom accretion
term and hence presently evaporating primordial black holes are not much
affected by phantom accretion.
