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We present a novel suite of cosmological N-body simulations called theDUSTGRAIN-pathfinder, implementing simultaneously the effects of an extensionto General Relativity in the form of $f(R)$ gravity and of a non-negligiblefraction of massive neutrinos. We describe the generation of simulated weaklensing and cluster counts observables within a past light-cone extracted fromthese simulations. The simulations have been performed by means of acombination of the MG-GADGET code and a particle-based implementation ofmassive neutrinos, while the light-cones have been generated using the MapSimpipeline allowing us to compute weak lensing maps through a ray-tracingalgorithm for different values of the source plane redshift. The mockobservables extracted from our simulations will be employed for a series ofpapers focussed on understanding and possibly breaking the well-knownobservational degeneracy between $f(R)$ gravity and massive neutrinos, i.e. thefact that some specific combinations of the characteristic parameters for thesetwo 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 weaklensing statistics could allow - especially for the next generation ofwide-field surveys - to disentangle some of the models that appearstatistically indistinguishable through standard single-redshift weak lensingprobe.

Weak Lensing Light-Cones in Modified Gravity simulations with and without Massive Neutrinos