Linear perturbations in a universe with a cosmological constant

There are now evidences that the cosmological constant $\Lambda$ 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 $-\rho\leq p \buildrel<\over\sim-0.6 \rho$. Since $p=-\rho$ is equivalent to the pure cosmological constant model, it is appropriate to analyze 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 analyze the single-fluid and the 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 slower in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime, the perturbations stop growing.