Linear perturbations in a universe with a cosmological constant

There is now evidence that the cosmological constant A has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density rho and the pressure p of this fluid are constrained by -rho less than or equal to p less than or similar to -0.6 rho. As p = -rho is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further. We study the linear theory of perturbations in a Friedmann-Robertson-Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.