  Recently H. Georgi suggested that a scale invariant unparticle
${\mathcal{U}}$ sector with an infrared fixed point at high energy can couple
with the SM matter via a higher-dimensional operator suppressed by a high
cut-off scale. Intense phenomenological search of this unparticle sector in the
collider and flavour physics context has already been made. Here we explore
it's impact in cosmology, particularly it's possible role in the supernovae
cooling. We found that the energy-loss rate (and thus the cooling) is strongly
dependent on the effective scale \LdaU and the anomalous dimension \dU of this
unparticle theory.
