Probing for variation of neutrino mass with current observations
  With the latest astronomical data including Cosmic Microwave Background (WMAP three year, CBI, ACBAR, VSA), Type Ia Supernova ("gold sample"), Galaxy Clustering (SDSS 3-D matter power, Lyman-$\alpha$ forest and Baryon Acoustic Oscillating (BAO)), we make a global fitting to constrain the mass varying neutrinos. We find that the parameter $\delta$, denoting time evolving of neutrino mass, is weakly constrained and the neutrino mass limit today can be relaxed at least by a factor of two. Adding data of $0\nu2\beta$ decay of Heidelberg-Moscow experiment to our analysis, we find that $\delta$ can be constrained tightly and mass varying neutrinos are favored at about 99.7% confidence level. 
Gong-Bo Zhao, Jun-Qing Xia, Xinmin Zhang