Physical Review D - Particles and Fields
We present a systematic treatment of the initial conditions and evolution of cosmological perturbations in a universe containing photons, baryons, neutrinos, cold dark matter, and a scalar quintessence field. By formulating the evolution in terms of a differential equation involving a matrix acting on a vector comprised of the perturbation variables, we can use the familiar language of eigenvalues and eigenvectors. As the largest eigenvalue of the evolution matrix is fourfold degenerate, it follows that there are four dominant modes with a nondiverging gravitational potential at early times, corresponding to adiabatic, cold dark matter isocurvature, baryon isocurvature and neutrino isocurvature perturbations. We conclude that quintessence does not lead to an additional independent mode.
Doran, Michael; Müller, Christian M.; Schäfer, Gregor; and Wetterich, Christof, "Gauge-Invariant Initial Conditions and Early Time Perturbations in Quintessence Universes" (2003). Open Dartmouth: Faculty Open Access Articles. 1953.