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.

9 pages, 2 figures, text is modified, references updated and version accepted for publication in Phys. Rev. D