Structure Formation by Fifth Force I: N-Body vs. Linear Simulations

Abstract

We lay out the frameworks to numerically study the structure formation in both linear and nonlinear regimes in general dark-matter-coupled scalar field models, and give an explicit example where the scalar field serves as a dynamical dark energy. Adopting parameters of the scalar field which yield a realistic CMB spectrum, we generate the initial conditions for our N-body simulations, which follow the spatial distributions of the dark matter and the scalar field by solving their equations of motion using the multilevel adaptive grid technique. We show that the spatial configuration of the scalar field tracks well the voids and clusters of dark matter. Indeed, the propagation of scalar degree of freedom effectively acts a fifth force on dark matter particles, whose range and magnitude are determined by the two model parameters (mu, gamma), local dark matter density as well as the background value for the scalar field. The model behaves like the LCDM paradigm on scales relevant to the CMB spectrum, which are well beyond the probe of the local fifth force and thus not significantly affected by the matter-scalar coupling. On scales comparable or shorter than the range of the local fifth force, the fifth force is perfectly parallel to gravity and their strengths have a fixed ratio 2gamma^2 determined by the matter-scalar coupling, provided that the chameleon effect is weak; if on the other hand there is a strong chameleon effect (i.e., the scalar field almost resides at its effective potential minimum everywhere in the space), the fifth force indeed has suppressed effects in high density regions and shows no obvious correlation with gravity, which means that the dark-matter-scalar-field coupling is not simply equivalent to a rescaling of the gravitational constant or the mass of the dark matter particles.