Weak Lensing Light-Cones in Modified Gravity simulations with and
  without Massive Neutrinos
  We present a novel suite of cosmological N-body simulations called the
DUSTGRAIN-pathfinder, implementing simultaneously the effects of an extension
to General Relativity in the form of $f(R)$ gravity and of a non-negligible
fraction of massive neutrinos. We describe the generation of simulated weak
lensing and cluster counts observables within a past light-cone extracted from
these simulations. The simulations have been performed by means of a
combination of the MG-GADGET code and a particle-based implementation of
massive neutrinos, while the light-cones have been generated using the MapSim
pipeline allowing us to compute weak lensing maps through a ray-tracing
algorithm for different values of the source plane redshift. The mock
observables extracted from our simulations will be employed for a series of
papers focussed on understanding and possibly breaking the well-known
observational degeneracy between $f(R)$ gravity and massive neutrinos, i.e. the
fact that some specific combinations of the characteristic parameters for these
two phenomena (the $f_{R0}$ scalar amplitude and the total neutrino mass
$\Sigma m_{\nu}$) may result indistinguishable from the standard
$\mathrm{\Lambda CDM}$ cosmology through several standard observational probes.
In particular, in the present work we show how a tomographic approach to weak
lensing statistics could allow - especially for the next generation of
wide-field surveys - to disentangle some of the models that appear
statistically indistinguishable through standard single-redshift weak lensing
probe.
