Exact analytical solution for an Israel–Stewart cosmology

Abstract

In this article we report a novel analytic solution describing a cosmological model with a matter content represented by a one dissipative fluid component, in the framework of the causal Israel–Stewart theory. The dissipative fluid is described by a barotropic equation of state \(p= (\gamma -1) \rho \) and the bulk viscosity has been assumed of the form \(\xi =\xi _{0}\rho ^{s}\). We study within the parameter space which label the solution, a suited region compatible with an accelerated expansion of the universe for late times, as well as stability properties of the solution at the critical parameter value \( \gamma = 1\) and for \( s = 1/2 \). We study as well the consequences that arise from the positiveness of the entropy production along the time evolution. We found that the solution for pressureless dark matter, \( \gamma = 1\), can well describe a universe with a transition from a decelerated expansion to an accelerated one at late times, but with a very large non-adiabatic contribution to speed of sound. Finally, the kinematics and thermodynamics properties of the solutions are discussed in terms of the type of expansion and entropy production.

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Acknowledgements

This article was partially supported by Dicyt from Universidad de Santiago de Chile, through Grants No. 041831PA (G.P.) and No. 041831CM (N.C.). E.G. was supported by Proyecto POSTDOC_DICYT, código 041931CM_POSTDOC and partially supported by CONICYT-PCHA/Doctorado Nacional/2016-21160331.

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Correspondence to Guillermo Palma.

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Cruz, N., González, E. & Palma, G. Exact analytical solution for an Israel–Stewart cosmology. Gen Relativ Gravit 52, 62 (2020). https://doi.org/10.1007/s10714-020-02712-z

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Keywords

  • Analytical solutions
  • Israel–Stewart dissipative cosmology
  • Universe expansion transition
  • Entropy production