Sensitivity of the cosmic microwave background anisotropy to initial conditions in quintessence cosmology

We analyze the evolution of energy density fluctuations in cosmological scenarios with a mixture of cold dark matter and quintessence, in which the quintessence field is modeled by a constant equation of state. We obtain analytic expressions for the time evolution of the quintessence perturbations in models with light fields. The fluctuations behave analogously to a driven harmonic oscillator, where the driving term arises from the inhomogeneities in the surrounding cosmological fluid. We demonstrate that the homogeneous solution, determined by the initial conditions, is completely subdominant to the inhomogeneous solution for physically realistic scenarios. Thus we show that the cosmic microwave background anisotropy predicted for such models is highly insensitive to the initial conditions in the quintessence field.