[Paper Review] Viscous Cosmology

C. M. S. Barbosa, J. C. Fabris+3 more|arXiv (Cornell University)|Dec 3, 2015

Solar and Space Plasma Dynamics4 citations

TL;DR

This paper investigates viscous cosmology by modeling dark matter as a bulk-viscous fluid to address small-scale issues in the ΛCDM model, such as the cusp-core problem and overabundance of substructures. Using Eckart and Müller-Israel-Stewart formalisms, it shows that viscous dissipation suppresses power in small-scale structures, significantly reducing substructure abundance by nearly an order of magnitude for $ M \sim 10^9 M_\odot $, while maintaining good background fit to SN Ia and 2dFGRS data, though CMB constraints remain challenging without a cosmological constant.

ABSTRACT

We discuss the possibility to implement a viscous cosmological model, attributing to the dark matter component a behaviour described by bulk viscosity. Since bulk viscosity implies negative pressure, this rises the possibility to unify the dark sector. At the same time, the presence of dissipative effects may alleviate the so called small scale problems in the $Λ$CDM model. While the unified viscous description for the dark sector does not lead to consistent results, the non-linear behaviour indeed improves the situation with respect to the standard cosmological model.

Motivation & Objective

• To address the small-scale problems of the ΛCDM model, such as the cusp-core problem and overproduction of substructures in galaxies and clusters.
• To explore whether bulk viscosity in dark matter can unify the dark sector, similar to the Generalised Chaplygin Gas model.
• To evaluate the viability of viscous cosmology using both non-causal Eckart and causal Müller-Israel-Stewart formalisms in the context of background and perturbative evolution.
• To assess whether viscous models can simultaneously fit background data (e.g., SN Ia, 2dFGRS) and perturbative observations (e.g., CMB, ISW effect).
• To determine whether a cosmological constant is necessary to reconcile viscous models with CMB observations, especially the ISW effect.

Proposed method

• Models dark matter as a bulk-viscous fluid using the Eckart formalism, where viscous pressure is $ p_v = -\xi(\rho) u^\mu_{;\mu} $, with $ \xi = \xi_0 \rho^\nu $.
• Applies the causal Müller-Israel-Stewart (MIS) formalism with a relaxation time $ \tau $, using the truncated form $ \tau \Pi^\bullet + \Pi = -\theta \xi $ to avoid acausality.
• Imposes a background evolution with $ \rho = \rho_v + \rho_b + \rho_\Lambda $, where $ \rho_b \propto a^{-3} $, $ \rho_\Lambda = \text{const} $, and $ \rho_v $ evolves via the viscous continuity equation.
• Performs perturbative analysis using the spherical collapse model to study non-linear structure formation and substructure abundance.
• Compares model predictions with observational data: SN Ia for background evolution, 2dFGRS power spectrum for large-scale structure, and CMB for ISW effect and gravitational potential evolution.
• Evaluates the Integrated Sachs-Wolfe (ISW) effect by comparing the evolution of the gravitational potential in viscous models versus ΛCDM across different wavenumbers $ k $.

Experimental results

Research questions

• RQ1 Can bulk viscosity in dark matter alleviate the small-scale problems of the ΛCDM model, such as the overproduction of substructures and the cusp-core discrepancy?
• RQ2 Does a viscous dark matter model with bulk viscosity unify the dark sector in a way analogous to the Generalised Chaplygin Gas model, and is such a unification viable?
• RQ3 How do the Eckart and Müller-Israel-Stewart formalisms compare in their ability to describe viscous cosmology, particularly regarding causality and perturbative stability?
• RQ4 To what extent can viscous models fit background data (e.g., SN Ia, 2dFGRS) while remaining consistent with CMB observations, especially the ISW effect?
• RQ5 Is the inclusion of a cosmological constant necessary to reconcile viscous models with CMB data, particularly in light of the ISW suppression of power?

Key findings

• The viscous model with $ \bar{\xi}_0 \sim 10^{-8} $ reduces the abundance of substructures with masses $ M \sim 10^9 M_\odot $ by nearly one order of magnitude compared to ΛCDM, significantly alleviating the small-scale overproduction problem.
• The Eckart formalism yields a background evolution similar to the Generalised Chaplygin Gas model, but perturbative behavior differs, offering hope that viscous models may avoid the GCG model’s perturbative instabilities.
• The ISW effect in viscous models leads to a strong suppression of power in the gravitational potential, particularly at late times, which conflicts with the observed plateau in the CMB spectrum.
• The inclusion of a cosmological constant ($ \Omega_\Lambda = 0.7 $) improves the fit to CMB data, suggesting that a $ \Lambda v\text{CDM} $ model—viscous dark matter with a cosmological constant—can be viable despite issues in the unified viscous model.
• The truncated MIS formalism produces results comparable to the full MIS formalism, indicating that the simplified approach is sufficient for studying viscous cosmology in the context of this work.
• The viscous model shows good agreement with SN Ia and 2dFGRS data, indicating that background evolution is well-fitted, but tension arises when combining background and perturbative constraints.