Abstract
Bulk viscosity in cold dark matter is an appealing feature that introduces distinctive phenomenological effects in the cosmological setting as compared to the \(\Lambda \)CDM model. Under this view, we propose a general parametrization of the bulk viscosity of the form \(\xi \sim H^{1-2s} \rho _{m}^{s}\), Some advantages of this novel parametrization are: first, it allows to write the resulting equations of cosmological evolution in the form of an autonomous system for any value of s, so a general treatment of the fixed points and stability can be done, and second, the bulk viscosity effect is consistently handled so that it naturally turns off when matter density vanishes. As a main result we find, based on detailed dynamical system analysis, one-parameter family of de Sitter-like asymptotic solutions with non-vanishing bulk viscosity coefficient during different cosmological periods. Numerical computations are performed jointly along with analytical phase space analysis in order to assess more quantitatively the bulk viscosity effect on the cosmological background evolution. Finally, as a first contact with observation we derive constraints on the free parameters of some bulk viscosity models with specific s-exponents from Supernovae Ia and observations of the Hubble parameter, by performing a Bayesian statistical analysis thought the Markov Chain Monte Carlo method.
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Notes
It does not mean however that the cosmological constant evolves itself since the condition \({\dot{\rho }}_{\Lambda }=0\) is preserved at any time.
Notice however that all components are (minimally) coupled to gravity whereby the latter acts as a messenger between them. This is an indirect way where the bulk viscosity effects may be present in different cosmological stages.
Another physical interpretation can be given in terms of an effective pressure for DE that arises due to the contribution of the bulk viscosity pressure in the acceleration equation Eqn. (3). Accordingly, deviation of \(\omega _{\textrm{DE}}=-1\) is possible, leading to an artificial phantom scenario.
In the extreme case of large bulk viscosity values, which is achieved for large negative values of s, the presence of dark energy is not required to accelerate the expansion. This physical situation corresponds indeed to an unified dark fluid scenario, and it is another natural convergence of this viscous model.
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Acknowledgements
G.G acknowledges financial support from Vicerrectoría de Investigación, Desarrollo e Innovación - Universidad de Santiago de Chile, Proyecto DICYT, Código 042031 CM\(\_\)POSTDOC. G.P. acknowledges financial support by Dicyt-USACH Grant No. 042231PA. E.G. thanks to Vicerrectoría de Investigación y Desarrollo Tecnológico (VRIDT) at Universidad Católica del Norte (UCN) by the scientific support of Núcleo de Investigación No. 7 UCN-VRIDT 076/2020, Núcleo de Modelación y Simulación Científica (NMSC). A.R. acknowledges Universidad de Santiago de Chile for financial support through the Proyecto POSTDOCDICYT, Código 043131 CM-POSTDOC.
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Gómez, G., Palma, G., González, E. et al. A new parametrization for bulk viscosity cosmology as extension of the \(\Lambda \)CDM model. Eur. Phys. J. Plus 138, 738 (2023). https://doi.org/10.1140/epjp/s13360-023-04367-6
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DOI: https://doi.org/10.1140/epjp/s13360-023-04367-6