Cui, Weiguang; Baldi, Marco; Borgani, Stefano, 2012, MNRAS, 424, 993C
Making use of the public halo catalogues of the CoDECS simulations, we derive the halo mass function for several different types of coupled dark energy scenarios, based on both the friends-of-friends algorithm and the spherical overdensity halo identification for different values of the overdensity threshold Δc. Our results show that the standard fitting functions still reproduce both the friends-of-friends and spherical overdensity halo mass functions of interacting dark energy cosmologies reasonably well at intermediate masses and low redshifts, once rescaled to the characteristic amplitude of linear density perturbations of each specific model as given by σ8. However, we also find that such apparent degeneracy with σ8 is broken by both the high-mass tail and the redshift evolution of our halo mass functions, with deviations beyond ˜10 per cent for most of the models under investigation.
Upper figure shows the relative difference between the simulated HMF_{fof, DE}/HMF_{fof, LCDM} and fitted HMF_{fof, DE}/HMF_{fof, LCDM}. Different colorful lines indicate different DE simulations (please look at the online paper for details). Even scaled the relative difference, we can see that the fitting function is not working properly for the dark energy models, especially at higher redshift.
Similar to the first figure, this upper figure shows the relative difference for the SO (instead of FoF) HMF at overdensity \Delta_c = 500. The results are very similar.
Cui, Weiguang; Zhang, Pengjie; Yang, Xiaohu, 2010, PhRvD, 81j, 3528C
We modify the Gadget-2 code by including a monotonic parameter ζ to simplify modified gravity models and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. the nonlinear power spectra can differ by ˜30% for 10% deviation from GR (|ζ-1|=0.1) where the r.m.s. density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.
Left figure shows the power spectrum difference between modified gravity (ζ != 1) and GR (ζ = 1). Different colourful lines show the results at different redshifts. As shown in the figure, the linear power spectra are the same between these different colourful lines (the redshifts are chose by an analytical method with purpose). However, these non-linear power spectra show significant difference!