Effect of Vacuum Energy on Evolution of Primordial Black Holes in
  Einstein Gravity
  We study the evolution of primordail black holes by considering present
universe is no more matter dominated rather vacuum energy dominated. We also
consider the accretion of radiation, matter and vacuum energy during respective
dominance period. In this scenario, we found that radiation accretion
efficiency should be less than 0.366 and accretion rate is much larger than
previous analysis by B. Nayak et al. \cite{ns}. Thus here primordial black
holes live longer than previous works \cite{ns}. Again matter accretion
slightly increases the mass and lifetime of primordial black holes. However,
the vacuum energy accretion is slightly complicated one, where accretion is
possible only upto a critical time. This critical time depends on the values of
accretion efficiency and formation time. If a primordial black hole lives
beyond critical time, then its lifespan increases due to vacuum energy
accretion. But for presently evaporating primordial black holes, critical time
comes much later than their evaporating time and thus vacuum energy could not
affect those primordial black holes. We again found that the constraints on the
initial mass fraction of PBH obtained from the $\gamma$-ray background limit
becomes stronger in the presence of vacuum energy.
