ISW-LSS cross-correlation in coupled Dark Energy models with massive
  neutrinos
  We provide an exhaustive analysis of the Integrated Sach-Wolfe effect (ISW)
in the context of coupled Dark Energy cosmologies where a component of massive
neutrinos is also present. We focus on the effects of both the coupling between
Dark Matter and Dark Energy and of the neutrino mass on the cross-correlation
between galaxy/quasar distributions and ISW effect. We provide a simple
expression to appropriately rescale the galaxy bias when comparing different
cosmologies. Theoretical predictions of the cross-correlation function are then
compared with observational data. We find that, while it is not possible to
distinguish among the models at low redshifts, discrepancies between coupled
models and $\Lambda$CDM increase with $z$. In spite of this, current data alone
seems not able to distinguish between coupled models and $\Lambda$CDM. However,
we show that upcoming galaxy surveys will permit tomographic analysis which
allow to better discriminate among the models. We discuss the effects on
cross-correlation measurements of ignoring galaxy bias evolution, b(z), and
magnification bias correction and provide fitting formulae for b(z) for the
cosmologies considered. We compare three different tomographic schemes and
investigate how the expected signal to noise ratio, snr, of the ISW-LSS
cross-correlation changes when increasing the number of tomographic bins. The
dependence of snr on the area of the survey and the survey shot noise is also
discussed.
