Analytic study of cosmological perturbations in a unified model of dark matter and dark energy with a sharp transition

We study cosmological perturbations in a model of unified dark matter and dark energy with a sharp transition in the late-time universe. The dark sector is described by a dark fluid which evolves from an early stage at redshifts z > zC when it behaves as cold dark matter (CDM) to a late time dark energy (DE) phase (z < zC) when the equation of state parameter is w=−1+ϵ, with a constant ϵ which must be in the range 0 < ϵ < 2/3. We show that fluctuations in the dark energy phase suffer from an exponential instability, the mode functions growing both as a function of comoving momentum k and of conformal time η. In order that this exponential instability does not lead to distortions of the energy density power spectrum on scales for which we have good observational results, the redshift zC of transition between the two phases is constrained to be so close to zero that the model is unable to explain the supernova data.