Cosmic degeneracies - II. Structure formation in joint simulations of warm dark matter and f (R) gravity

We present for the first time the outcomes of a cosmological N-body simulation that simultaneously implements a warm dark matter (WDM) particle candidate and a modified gravitational interaction in the form of f(R) gravity, and compare its results with the individual effects of these two independent extensions of the standard Lambda CDM scenario, and with the reference cosmology itself. We consider a rather extreme value of the WDM particle mass (m(WDM) = 0.4 keV) and a single realization of f(R) gravity with |(f) over bar (R0)| = 10(-5), and we investigate the impact of these models and of their combination on a wide range of cosmological observables with the aim to identify possible observational degeneracies. Differently from the case of combining f(R) gravity with massive neutrinos, we find that most of the considered observables do not show any significant degeneracy due to the fact that WDM and f(R) gravity are characterized by individual observational signatures with a very different functional dependence on cosmic scales and halo masses. In particular, this is the case for the non-linear matter power spectrum in real space, for the halo and subhalo mass functions, for the halo density profiles and for the concentration-mass relation. However, other observables - like e.g. the halo bias - do show some level of degeneracy between the two models, while a very strong degeneracy is observed for the non-linear matter power spectrum in redshift space, for the density profiles of small cosmic voids, and for the voids abundance as a function of the void core density.