Ok .. so now I've read the complete paper, I'm even more interested.
... so here comes the controversy ... oh no !!
)
"There is however surprisingly little direct evidence that the Universe is expanding. As mentioned in Section 1, searches for time dilation in gamma-ray bursts do not provide a conclusive test. Supernova light curves on the other hand appear to show convincing evidence of time dilation (Foley et al. 2005), which would rule out a non-expanding universe as an explanation for the results presented here for quasar light curves. Although this result has been challenged in an interesting paper by Crawford (2009) on the basis of bias in the sampling procedure, it seems fair to say that the result is still generally accepted."
So,
GRBs => not a conclusive test for universe expansion,
Supernova light curves => convincing evidence of expanding universe (with an outstanding challenge);
Quasar light curves => no dilation but not evidence for a static universe.
So that's a pretty up-to-date summary of where things stand at the moment.
Fascinating !
Cheers