Evolution of scalar perturbations in cosmology with quintessential dark energy

TL;DR

This paper analyzes how scalar perturbations evolve in cosmological models with quintessential dark energy, showing that such fields suppress matter growth and have scale-dependent effects distinct from the standard Lambda-CDM model.

Contribution

It provides analytical and numerical analysis of scalar perturbations in quintessential dark energy models with constant w or zero sound speed, highlighting their impact on structure formation.

Findings

Quintessence perturbations decay after horizon entry, unlike matter perturbations.

Quintessence suppresses matter density growth, especially at subhorizon scales.

Suppression of gravitational potential is scale-dependent in QCDM models.

Abstract

The dynamics of expansion of the Universe and evolution of scalar perturbations are studied for the quintessential scalar fields $Q$ with the classical Lagrangian satisfying the additional condition $w=const$ or $c^2_a=0$. Both quintessential fields are studied for the same cosmological model. The systems of evolutionary equations for gauge-invariant perturbations of metrics, matter and quintessence have been analysed analyticaly for the early stage of the Universe life and numerically up to the present epoch. It is shown that amplitudes of the adiabatic matter density perturbations grow like in $\Lambda$CDM-model but time dependences of amplitudes of the quintessence perturbations are more varied: gauge-invariant variables $D_g^{(Q)}$ and $D_s^{(Q)}$ decay from initial constant value after entering the particle horizon while $D^{(Q)}$ and $V^{(Q)}$ grow at the early stage before entering the horizon and decay after that -- in the quintessence-dominated epoch, when gravitational potential starts to decay -- so, that at the current epoch they are approximately two orders lower than matter ones at the supercluster scale. Therefore, at the subhorizon scales the quintessential scalar fields are smoothed out while the matter clusters. It is also shown that both quintessential scalar fields suppress the growth of matter density perturbations and the amplitude of gravitational potential. In these QCDM-models -- unlike $\Lambda$CDM ones -- such suppression is scale dependent and more visible for the quintessence with $c^2_a=0$.