  In this paper we investigate power spectrum of a smoothed scalar field. The
smoothing leads to the regularisation of the UV divergences and can be related
with the internal structure of the considered field or the space itself. We
apply procedure of smoothing to the quantum fluctuations generated during the
phase of cosmic inflation. We study whether this effect can be probed
observationally and conclude that the modifications of the power spectrum due
to the smoothing on the Planck scale are negligible and far beyond the
observational abilities. Subsequently we investigate whether smoothing in any
other form can be probed observationally. We introduce phenomenological
smoothing factor $e^{-k^2\sigma^2}$ to the inflationary spectrum and
investigate its effects on the spectrum of CMB anisotropies and polarisation.
We show that smoothing can lead to suppression of high multipoles in the
spectrum of the CMB. Based on five years observations of WMAP satellite we
indicate that the present scale of high multipoles suppression is constrained
by $\sigma < 2.86$ Mpc (95% CL). This corresponds to the constraint $\sigma <
100 \mu$m at the end of inflation. Despite this value is far above the Planck
scale, the other processes of smoothing can be possibly studied with this
constraint, e.g. diffusion or decoherence of primordial perturbations.
