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.
Similar content being viewed by others
References
Eckart, C.: Phys. Rev. 58, 267 (1940)
Eckart, C.: Phys. Rev. 58, 919 (1940)
Avelino, A., Leyva, Y., Urea-Lpez, L.A.: Phys. Rev. D 88, 123004 (2013)
Avelino, A., Nucamendi, U.: J. Cosmol. Astropart. Phys. 04, 006 (2009)
Avelino, A., Nucamendi, U.: J. Cosmol. Astropart. Phys. 08, 009 (2010)
Montiel, A., Bretn, N.: J. Cosmol. Astropart. Phys. 08, 023 (2011)
Padmanabhan, T., Chitre, S.M.: Phys. Lett. 120A, 433 (1987)
Israel, W.: Ann. Phys. (N.Y.) 100, 310 (1976)
Israel, W., Stewart, J.M.: Ann. Phys. (N.Y:) 118, 341 (1979)
Maartens, R.: Class. Quantum Gravity 12, 1455 (1995)
Zimdahl, W.: Mon. Not. R. Astron. Soc. 280, 1239 (1996)
Pavn, D.: Class. Quantum Gravity 7, 487 (1990)
Chimento, L.P., Jakubi, A.S.: Class. Quantum Gravity 10, 2047 (1993)
Maartens, R.: Causal thermodynamics in relativity, arXiv:astro-ph/9609119 (third chapter)
Weinberg, S.: ApJ 168, 175 (1971)
Cornejo-Pérez, O., Belinchón, J.A.: Int. J. Mod. Phys. D 22(6), 1350031 (2013)
Mak, M.K., Harko, T.: Int. J. Mod. Phys. D 13, 273–280 (2004)
Mak, M.K., Harko, T.: Gen. Rel. Grav. 8, 1171 (1998)
Mak, M.K., Harko, T.: Gen. Rel. Grav. D 13, 273–280 (2004)
Chimento, L.P., Jakubi, A.S., Pavon, D.: Int. J. Mod. Phys. D 9, 43–55 (2000)
Chimento, L.P., Jakubi, A.S., Méndez, V.: Int. J. Mod. Phys. D 7, 177–188 (1998)
Piattella, O., Fabris, J., Zimdahl, W.: J. Cosmol. Astropart. Phys. 1105, 029 (2011)
Maartens, R., Méndez, V.: Phys. Rev. D 55, 1937 (1997)
Chimento, L.P., Jakubi, A.S., Méndez, V.: Class. Quant. Grav. 14, 3363–3375 (1997)
Cruz, M., Cruz, N., Lepe, S.: Phys. Lett. B 769, 159–165 (2017)
Mohan, J., Sasidharan, A., Mathew, T.: Eur. Phys. J. C 77, 849 (2017)
Hiscock, W., Lindblom, L.: Ann. Phys. 151, 466 (1983)
Cruz, N., Lepe, S.: Phys. Lett. B 767, 103 (2017)
Cruz, M., Cruz, N., Lepe, S.: Phys. Rev. D 96, 124020 (2007)
Cruz, N., González, E., Lepe, S., Sáez-Chillón Gómez, D.: JCAP 12, 017–017 (2018)
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-020-02712-z