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

Abstract: 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 $z > z_C$ 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 an exponential instability, the mode functions growing both as a function of comoving momentum $k$ and of conformal time $\eta$. 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 $z_C$ of transition between the two phases is constrained to be so close to zero that the model is unable to explain the supernova data.