Polynomial mixing for time-changes of unipotent flows

Let $G$ be a connected semisimple Lie group with finite centre, and let $M= \Gamma \backslash G$ compact homogeneous manifold. Under spectral gap assumption, we show that smooth time-changes of any unipotent flow on $M$ have polynomial decay correlations. Our result applies also in the case where is volume, non-compact quotient under some additional assumptions generator time-change. This generalizes by Forni Ulcigrai (JMD, 2012) for horocycle flows surfaces.