  Primordial black holes (PBHs) in the mass range $10^{17} - 10^{23}~{\rm gm}$
are considered as possible dark matter candidates as they are not subject to
big-bang nucleosynthesis constraints and behave like cold dark matter. If PBHs
are indeed dark matter, they cannot be treated as isolated objects in
asymptotic flat space-time. Furthermore, when compared to stellar-mass black
holes, the rate at which the Hawking particles radiate out from PBHs is
significantly faster. In this work, we obtain an exact time-dependent solution
that models evaporating black holes in the cosmological background. As a
result, the solution considers all three aspects of PBHs -- mass-loss due to
Hawking radiation, black hole surrounded by mass distribution, and cosmological
background. Furthermore, our model predicts that the decay of PBHs occurs
faster for larger masses; however, \emph{the decay rate reduces for lower
mass}. Finally, we discuss the implications of theoretical constraints on PBHs
as dark matter.
