Antony Lewis wrote: not the case for quintessence.
This statement is too strong, whether scalar field perturbations are adiabatic or isocurvature depends on the initial conditions, which we think are set by inflation.
If the quintessence field is a decay product of the inflaton the perturbations in the quintessence will be adiabatic, which means that not only the perturbations of the quintessence field relative to the other fluids
(S_q f =0) initially vanish, but also the scalar field intrinsic entropy perturbation (Gamma_q =0) is initially zero.
If these conditions are verified at an initial time the conservation of the energy momentum tensor (which provide the equation of motion for the perturbations) impose that they are verified at any other time (no matter the gauge, actually everything can be formulated in gauge invariant language as S and Gamma are gauge invariant variables).
In other words adiabaticity is preserved by the flow equations and no matter what is the background scalar field evolution or the choice of the gauge, the scalar field perturbations will remain adiabatic (Gamma_q=0 always) as those in the other fluids.
This can be inferred from General Relativity arguments in the context of the Separate Universe Approach (Wands, Malik, Lyth and Liddle,
astro-ph/0003278).
More specifically we have shown this by directly looking at the flow equations in the gauge invariant formulation (Bartolo, Corasaniti, Liddle, Malquarti,
astro-ph/0311503).
Also we have found that if the initial conditions are isocurvature ones, which could be the case if the quintessence or k-essence or whatever is not a decay product of the inflaton, then the evolution of the isocurvature quintessence mode depends on the dynamics of the background. In particular during kination regimes the isocurvature mode is amplified, while it decays during tracker ones. This implies that only those quintessence scenarios with initial isocurvature perturbations and with the field undergoing a long kination phase followed by a short period of tracking can give rise to a cosmologically relevant isocurvature perturbation that can survive at present time. (The specific time evolution of this isocurvature mode can be different in the case of k-essence, since the two scenarios (Q <-> K) can be mapped one into the other only at the homogeneus level).
I tend to accept the fact that c_s^2, as a free parameter for an effective fluid description of scalar field perturbations, is a simple way of parametrizing something which depends on initial conditions, however from a pure physical point of view I find this effective description rather misleading, so one should have always in mind the microscopic description of the scalar field whatsoever is its lagrangian.
Pier-Stefano