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Journal of Physical Studies 13(1), Article 1902 [12 pages] (2009)
DOI: https://doi.org/10.30970/jps.13.1902 EVOLUTION OF SCALAR PERTURBATIONS IN COSMOLOGY WITH QUINTESSENTIAL DARK ENERGYB. Novosyadlyj, O. Sergijenko
Astronomical Observatory of Ivan Franko National University
of Lviv, |
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The dynamics of the expansion of the Universe and evolution of scalar perturbations are discussed for the quintessential scalar fields $Q$ with the classical Lagrangian $L=\frac{1}{2}Q_{;i}Q^{;i}-U(Q)$ satisfying the additional condition $w={\rm const}$ or $c^2_a=0$. Both quintessential fields are studied for the same cosmological model. It is shown that the accelerated expansion of the Universe is caused by the effect of the rolling down of the field to the minimum. At the early epoch the contribution to dynamics of the quintessence with $w={\rm const}$ is negligible (like that of the cosmological constant) while the quintessence with $c^2_a=0$ mimics dust matter. In the future a scalar field with $c^2_a=0$ will mimic the cosmological constant.
The systems of evolution equations for gauge-invariant perturbations of metric, matter and quintessence have been analysed analytically 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 similarly in both models (likewise in the $Λ$CDM-model), but time dependences of different amplitudes of quintessence perturbations are varied: gauge-invariant variables $D_g^{(Q)}$ and $D_s^{(Q)}$ decay from the initial constant value after the particle horizon entry while $D^{(Q)}$ and $V^{(Q)}$ grow at an early stage before the horizon entry and decay after that in the quintessence-dominated epoch when the gravitational potential starts to decay so that at the current epoch they are approximately two orders lower than the matter ones on supercluster scales. Therefore, on the subhorizon scales 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 $Λ$CDM ones -- such a suppression is scale dependent and more visible for the quintessence with $c^2_a=0$.
PACS number(s): 95.36.+x, 98.80.-k