  The evolution of primordial black holes in a flat Friedmann universe with a
massless scalar field is investigated in fully general relativistic numerical
relativity. A primordial black hole is expected to form with a scale comparable
to the cosmological apparent horizon, in which case it may go through an
initial phase with significant accretion. However, if it is very close to the
cosmological apparent horizon size, the accretion is suppressed due to general
relativistic effects. In any case, it soon gets smaller than the cosmological
horizon and thereafter it can be approximated as an isolated vacuum solution
with decaying mass accretion. In this situation the dynamical and inhomogeneous
scalar field is typically equivalent to a perfect fluid with a stiff equation
of state $p=\rho$. The black hole mass never increases by more than a factor of
two, despite recent claims that primordial black holes might grow substantially
through accreting quintessence. It is found that the gravitational memory
scenario, proposed for primordial black holes in Brans-Dicke and scalar-tensor
theories of gravity, is highly unphysical.
