Nonlinearities in modified gravity cosmology I: signatures of modified gravity in the nonlinear matter power spectrum

A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter \zeta, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (\zeta = 1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance to include the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size and initial redshift). We find that, the nonlinear power spectra can differ by ~30% for 10% deviation from GR (|\zeta-1| = 0.1) where the rms 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.