The Matter Power Spectrum of Dark Energy Models and the Harrison-Zel'dovich Prescription

TL;DR

This paper presents a method to construct the matter power spectrum for dark energy models using the Harrison-Zel'dovich prescription, enabling predictions of large-scale structure observables without solving complex dynamical equations.

Contribution

The authors introduce a novel approach to derive matter power spectra for dark energy models from a mbda CDM baseline, simplifying the testing of these models against observational data.

Findings

The method accurately reproduces power spectra for various dark energy models.

It allows testing dark energy models using large-scale structure data.

Constraints from CMB low multipoles are discussed.

Abstract

According to the Harrison-Zel'dovich prescription, the amplitude of matter density perturbations at horizon crossing is the same at all scales. Based on this prescription, we show how to construct the matter power spectrum of generic dark energy models from the power spectrum of a $\Lambda$CDM model without the need of solving in full the dynamical equations describing the evolution of all energy density perturbations. Our approach allows to make model predictions of observables that can be expressed in terms of the matter power spectrum alone, such as the amplitude of matter fluctuations, peculiar velocities, cosmic microwave background temperature anisotropies on large angular scales or the weak lensing convergence spectrum. Then, models that have been tested only at the background level using the rate of the expansion of the Universe can now be tested using data on gravitational clustering and on large scale structure. This method can save a lot of effort in checking the validity of dark energy models. As an example of the accurateness of the approximation used, we compute the power spectrum of different dark energy models with constant equation of state parameter ($w_{DE}=-0.1$, -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.