Cosmic degeneracies - I. Joint N-body simulations of modified gravity and massive neutrinos

We present the first suite of cosmological N-body simulations that simultaneously include the effects of two different and theoretically independent extensions of the standard Lambda cold dark matter (Lambda CDM) cosmological scenario - namely an f (R) theory of modified gravity and a cosmological background of massive neutrinos - with the aim to investigate their possible observational degeneracies. We focus on three basic statistics of the large-scale matter distribution, more specifically the non-linear matter power spectrum, the halo mass function, and the halo bias. Our results show that while these two extended models separately determine very prominent and potentially detectable features in all the three statistics, when we allow them to be simultaneously at work these features are strongly suppressed. In particular, when an f (R) gravity model with f(R0) = -1 x 10(-4) is combined with a total neutrino mass of Sigma(i)m(nu i) = 0.4 eV, the resulting matter power spectrum, halo mass function, and bias at z = 0 are found to be consistent with the standard model's predictions at the less than or similar to 10, less than or similar to 20, and less than or similar to 5 per cent accuracy levels, respectively. Therefore, our results imply an intrinsic theoretical limit to the effective discriminating power of present and future observational data sets with respect to these widely considered extensions of the standard cosmological scenario.