  We investigate the stochastic gravitational wave background produced by
primordial black hole binaries during their early inspiral stage while
accreting high-density radiation surrounding them in the early universe. We
first show that the gravitational wave amplitude produced from a primordial
black hole binary has correction terms because of the rapid rate of increase in
masses of the primordial black holes. These correction terms arise due to
non-vanishing first and second time derivatives of the masses and their
contribution to the overall second time derivative of quadrupole moment tensor.
We find that some of these correction terms are not only significant in
comparison with the main term but even dominant over the main term for certain
ranges of time in the early Universe. The significance of these correction
terms is not only for the gravitational wave amplitude produced from an
individual PBH-binary, but persists for the overall stochastic gravitational
wave background produced from them. We show that the spectral density produced
from such accreting primordial black hole binaries lie within the detectability
range of some present and future gravitational wave detectors.
