  We study the effects of the trans-Planckian dispersion relation on the
spectrum of the primordial density perturbations during inflation. In contrast
to the earlier analyses, we do not assume any specific form of the dispersion
relation and allow the initial state of the field to be arbitrary. We obtain
the spectrum of vacuum fluctuations of the quantum field by considering a
scalar field satisfying the linear wave equation with higher spatial derivative
terms propagating in the de Sitter space-time. We show that the power spectrum
does not strongly depend on the dispersion relation and that the form of the
dispersion relation does not play a significant role in obtaining the
corrections to the scale invariant spectrum. We also show that the signatures
of the deviations from the flat scale-invariant spectrum from the CMBR
observations due to quantum gravitational effects cannot be differentiated from
the standard inflationary scenario with an arbitrary initial state.
