The Mass Power Spectrum in Quintessence Cosmological Models

We present simple analytic approximations for the linear and fully evolved nonlinear mass power spectrum for spatially flat cold dark matter (CDM) cosmological models with quintessence (Q). Quintessence is a time evolving, spatially inhomogeneous energy component with negative pressure and an equation of state w_Q < 0. It clusters gravitationally on large length scales but remains smooth like the cosmological constant on small length scales. We show that the clustering scale is determined by the Compton wavelength of the Q-field and derive a shape parameter, Γ_Q, to characterize the linear mass power spectrum. The growth of linear perturbations as functions of redshift, w_Q, and matter density Ω_m is also quantified. Calibrating to N-body simulations, we construct a simple extension of the formula by Ma (1998) that closely approximates the nonlinear power spectrum for a range of plausible QCDM models.