Dynamical friction shear and rotation in Chaplygin cosmology

TL;DR

This work extends the spherical collapse model in generalized Chaplygin gas cosmology by incorporating dynamical friction alongside shear and rotation within a pseudo-Newtonian, multi-fluid framework. It derives and solves the PN evolution equations for overdensities and velocity divergence, including an effective sound speed and a dynamical-friction term parameterized by $\eta=\eta_0 H$ and a rotation parameter $\beta$, to study non-linear perturbation growth. The results show that dynamical friction delays collapse and dampens growth more strongly than shear or rotation, mitigating instabilities predicted by linear GCG perturbation analyses and affecting the non-linear evolution of $w_c$, $c^2_{\rm eff}$, and the expansion rate. The findings underscore the importance of accurate frictional and non-radial terms in testing GCG as an alternative to $\Lambda$CDM, while also noting the limitations of the top-hat approach and pointing to extensions with smoother profiles for more realistic structure formation.

Abstract

In this study, we build upon the findings of Del Popolo et al. (2013) by further analyzing the influence of dynamical friction on the evolution of cosmological perturbations within the framework of the spherical collapse model (SCM) in a Universe dominated by generalized Chaplygin gas (GCG). Specifically, we investigate how dynamical friction alters the growth rate of density perturbations, the effective sound speed, the equation-of-state parameter www, and the evolution of the cosmic expansion rate. Our results demonstrate that dynamical friction significantly delays the collapse process compared to the standard SCM. Accurate computation of these parameters is crucial for obtaining consistent results and reliable physical interpretations when employing the GCG model. Furthermore, our analysis confirms that the suppression of perturbation growth due to dynamical friction is considerably more pronounced than that caused by shear and rotation, as previously indicated by Del Popolo et al. (2013). This enhanced suppression effectively addresses the instability issues, such as oscillations or exponential divergences in the dark-matter power spectrum, highlighted in linear perturbation studies, such as those by Sandvik et al. (2004).

Figures (8)

• Figure 1: Growth of perturbations, $\delta_b$. The solid lines represents $\delta_b$ with $\alpha$ increasing from 0 (bottom solid lines), to 0.5 (central solid lines), and 1 (top solid lines), for $\beta=0$. The dotted lines represent $\delta_b$, with $\beta = 0.01$ (top two panels), $\beta=0.02$ (central two panels), and $\beta=0.04$ (bottom two panels). The value of $\eta_0$ is equal to $4 \times 10^{-3}$ in all left column panels, and 0.03 in all right column panels.
• Figure 2: Growth of perturbations, $\delta_{GCG}$. Lines description is as in Fig. \ref{['fig:deltas_vs_z1']}.
• Figure 3: Evolution of $w_c$ with $z$ for GCG universes. Lines description is as in previous Figs. \ref{['fig:deltas_vs_z1']}--\ref{['fig:deltas_vs_z2']}.
• Figure 4: Evolution of $w$ with $z$ for GCG universes for $\alpha = 1$ (dashed line), 0.5 (dot-dashed line), 0 (solid line).
• Figure 5: Evolution of $c^2_{\rm eff}$ with $z$ for GCG universes. Lines description is as in previous Figs. \ref{['fig:deltas_vs_z1']}--\ref{['fig:deltas_vs_z3']}.