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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_{rm WDM}=0.4$ keV) and a single realisation of $f(R)$ gravity with $|bar{f}_{R0}|=10^{-5}$, 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. In particular, we focus on the large-scale matter distribution, as well as on the statistical and structural properties of collapsed halos and cosmic voids. Differently from the case of combining $f(R)$ gravity with massive neutrinos -- previously investigated in Baldi et al. (2014) -- 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 characterised by individual observational footprints with a very different functional dependence on cosmic scales and halo masses. In particular, this is the case for the nonlinear matter power spectrum in real space, for the halo and sub-halo 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 nonlinear matter power spectrum in redshift space, for the density profiles of small cosmic voids -- with radius below $approx 5$ Mpc$/h$ -- and for the voids abundance as a function of the void core density.
Using N-body simulations, we measure the power spectrum of the effective dark matter density field, which is defined through the modified Poisson equation in $f(R)$ cosmologies. We find that when compared to the conventional dark matter power spectru
We introduce the idea of {it effective} dark matter halo catalog in $f(R)$ gravity, which is built using the {it effective} density field. Using a suite of high resolution N-body simulations, we find that the dynamical properties of halos, such as th
The logarithmic $R^2$-corrected $F(R)$ gravity is investigated as a prototype model of modified gravity theories with quantum corrections. By using the auxiliary field method, the model is described by the general relativity with a scalaron field. Th
We use the Copernicus Complexio (COCO) high resolution $N$-body simulations to investigate differences in the properties of small-scale structures in the standard cold dark matter (CDM) model and in a model with a cutoff in the initial power spectrum
Modifications of the equations of general relativity at large distances offer one possibility to explain the observed properties of our Universe without invoking a cosmological constant. Numerous proposals for such modified gravity cosmologies exist,