The matter power spectrum of dark energy models and the Harrison-Zel'dovich prescription

Abstract

According to the Harrison-Zel'dovich prescription, the amplitudeof matter density perturbations at horizon crossing is the same atall scales. Based on this prescription, we show how to constructthe matter power spectrum of generic dark energy models fromthe power spectrum of a ΛCDM model without the need ofsolving in full the dynamical equations describing the evolutionof all energy density perturbations. Our approach allows to makemodel predictions of observables that can be expressed in terms ofthe matter power spectrum alone, such as the amplitude of matterfluctuations, peculiar velocities, cosmic microwave backgroundtemperature anisotropies on large angular scalesor the weak lensing convergence spectrum.Then, models that have been tested only at the background levelusing the rate of the expansion of the Universe can now be testedusing data on gravitational clustering and on large scalestructure. This method can save a lot of effort in checking thevalidity of dark energy models. As an example of the accurateness of theapproximation used, we compute the power spectrum of different dark energy models with constant equation of state parameter (wDE = −0.1, -0.5 and -0.8, ruled out by observations but easy to compare to numerical solutions) using our methodology and discuss the constraints imposed by the low multipoles of the cosmic microwave background.