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We study cosmological perturbations in a model of unified dark matter anddark energy with a sharp transition in the late-time universe. The dark sectoris described by a dark fluid which evolves from an early stage at redshifts $z> z_C$ when it behaves as cold dark matter (CDM) to a late time dark energy(DE) phase ($z < z_C$) when the equation of state parameter is $w = -1 +\epsilon$, with a constant $\epsilon$ which must be in the range $0 < \epsilon< 2/3$. We show that fluctuations in the dark energy phase suffer from anexponential instability, the mode functions growing both as a function ofcomoving momentum $k$ and of conformal time $\eta$. In order that thisexponential instability does not lead to distortions of the energy densitypower spectrum on scales for which we have good observational results, theredshift $z_C$ of transition between the two phases is constrained to be soclose to zero that the model is unable to explain the supernova data.

Analytic Study of Cosmological Perturbations in a Unified Model of Dark Matter and Dark Energy with a Sharp Transition