  We observe that when a local patch in a radiation filled Robertson-Walker
universe inflates by some reason, outside perturbations can enter into the
inflating region. Generally, the physical wavelengths of these perturbations
become larger than the Hubble radius as they cross into the inflating space and
their amplitudes freeze out immediately. It turns out that the corresponding
power spectrum is not scale invariant. Although these perturbations cannot
reach out to a distance inner observer shielded by a de Sitter horizon, they
still indicate a curious boundary effect in local inflationary scenarios.
