Mass-varying neutrino in light of cosmic microwave background and weak lensing

Aims. We aim to constrain mass-varying neutrino models using large scale structure observations and produce forecast for the Euclid survey. Methods. We investigate two models with different scalar field potential and both positive and negative coupling parameters beta. These parameters correspond to growing or decreasing neutrino mass, respectively. We explore couplings up to |beta| less than or similar to 5. Results. In the case of the exponential potential, we find an upper limit on Omega(v)h(2) < 0.004 at 2 sigma level. In the case of the inverse power law potential the null coupling can be excluded with more than 2 sigma significance; the limits on the coupling are beta > 3 for the growing neutrino mass and beta < -1.5 for the decreasing mass case. This is a clear sign for a preference of higher couplings. When including a prior on the present neutrino mass the upper limit on the coupling becomes |beta| < 3 at 2 sigma level for the exponential potential. Finally, we present a Fisher forecast using the tomographic weak lensing from an Euclid-like experiment and we also consider the combination with the cosmic microwave background (CMB) temperature and polarisation spectra from a Planck-like mission. If considered alone, lensing data is more efficient in constraining Omega(v) with respect to CMB data alone. There is, however, a strong degeneracy in the beta-Omega(v)h(2) plane. When the two data sets are combined, the latter degeneracy remains, but the errors are reduced by a factor similar to 2 for both parameters.