Linear perturbations in a universe with a cosmological constant

Abstract

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 $-ρ\leq p \buildrel<\over\sim-0.6 ρ$. 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.

23 pages, 1 figure, latex; references added, extended introduction

References in corpus (5)

• The Case for a Positive Cosmological Lambda-term
• The Cosmological Constant
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• The Cosmic Triangle: Revealing the State of the Universe
• Quintessence and Gravitational Waves

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• Density perturbation in the models reconstructed from jerk parameter
• Perturbations In Some Dark Energy Models
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models