# Viscosity in Modified Gravity

## Abstract

**:**

## 1. Introduction

## 2. Fundamental Formalism

## 3. Special Cases

#### 3.1. Einstein Action

#### 3.2. Modified Gravity Action

## 4. On the Possibility of a Phase Transition in the Late Universe

## 5. Conclusions

## References

- Nojiri, S.; Odintsov, S.D. Introduction to modified gravity and gravitational alternative for dark energy. Int. J. Geom. Methods Mod. Phys.
**2007**, 4, 115–146. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models. Phys. Rep.
**2011**, 505, 59–144. [Google Scholar] [CrossRef] - Bamba, K.; Capozziello, S.; Nojiri, S.; Odintsov, S.D. Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests. Astrophys. Space Sci.
**2012**, 342, 155–228. [Google Scholar] [CrossRef] - Eckart, C. The thermodynamics of irreversible processes. Phys. Rev.
**1940**, 58, 919–924. [Google Scholar] [CrossRef] - Müller, I. Zum Paradoxen der Wärmeleitungstheorie. Zeitschrift für Physik A
**1967**, 198, 329–344. [Google Scholar] [CrossRef] - Israel, W. Nonstationary reversibel thermodynamics: A causal relativistic theory. Ann. Phys. (N.Y.)
**1976**, 100, 310–331. [Google Scholar] [CrossRef] - Israel, W.; Stewart, J.M. Transient relativistic thermodynamics and kinetic theory. Ann. Phys. (N.Y.)
**1979**, 118, 341–372. [Google Scholar] [CrossRef] - Brevik, I.; Grøn, Ø. Relativistic viscous universe models. In preparation.
- Brevik, I.; Gorbunova, O.; Shaido, Y.A. Viscous FRW cosmology in modified gravity. Int. J. Mod. Phys.
**2005**, 14, 1899–1906. [Google Scholar] [CrossRef] - Brevik, I. Crossing of the w = − 1 barrier in viscous modified gravity. Int. J. Mod. Phys.
**2006**, 15, 767–775. [Google Scholar] [CrossRef] - Brevik, I. Viscous modified gravity on a RS brane embedded in AdS
_{5}. Eur. Phys. J. C**2008**, 56, 579–583. [Google Scholar] [CrossRef] - Brevik, I.; Elizalde, E.; Nojiri, S.; Odintsov, S.D. Viscous little rip cosmology. Phys. Rev. D
**2011**, 84, 103508. [Google Scholar] [CrossRef] - Brevik, I.; Myrzakulov, R.; Nojiri, S.; Odintsov, S.D. Turbulence and little rip cosmology. Phys. Rev. D
**2012**, 86, 063007. [Google Scholar] [CrossRef] - Abdalla, M.C.B.; Nojiri, S.; Odintsov, S.D. Consistent modified gravity: Dark energy, acceleration and the absence of cosmic doomsday. Class. Quantum Grav.
**2005**, 22, L35–L42. [Google Scholar] [CrossRef] - Brevik, I.; Nojiri, S.; Odintsov, S.D.; Vanzo, L. Entropy and universality of the Cardy-Verlinde formula in a dark energy universe. Phys. Rev. D
**2004**, 70, 043520. [Google Scholar] [CrossRef] - Nakamura, K.; Particle Data Group Collaboration. Review of Particle Physics. J. Phys. G
**2010**, 37, 075021. [Google Scholar] [CrossRef] - Amanullah, R.; Lidman, C.; Rubin, D.; Aldering, G.; Astier, P.; Barbary, K.; Burns, M.S.; Conley, A.; Dawson, K.S.; Deustua, S.E.; et al.; Supernova Cosmology Project Collaboration Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation. Astrophys. J.
**2010**, 716, 712–738. [Google Scholar] - Vikman, A. Can dark energy evolve to the phantom? Phys. Rev. D
**2005**, 71, 023515. [Google Scholar] [CrossRef] - Koivisto, K. A note on covariant conservation of energy-momentum in modified gravities. Class. Quantum Grav.
**2006**, 23, 4289–4296. [Google Scholar] [CrossRef] - Elizalde, E.; Nojiri, S.; Odintsov, S.D.; Sebastiani, L.; Zerbini, S. Nonsingular exponential gravity: A simple theory for early- and late- time accelerated expansion. Phys. Rev. D
**2011**, 83, 086006. [Google Scholar] [CrossRef] - Brevik, I.; Gorbunova, O. Dark energy and viscous cosmology. Gen. Relativ. Gravit.
**2005**, 37, 2039–2045. [Google Scholar] [CrossRef] - Ren, J.; Meng, X.H. Modified equation of state, scalar field, and bulk viscosity in Friedmann universe. Phys. Lett. B
**2006**, 636, 5–12. [Google Scholar] [CrossRef] - Mostafapoor, N.; Grøn, Ø. Viscous ΛCDM universe models. Astrophys. Space Sci.
**2011**, 333, 357–368. [Google Scholar] [CrossRef] - Brevik, I. Crossing the w = − 1 barrier in two-fluid viscous modified gravity. Gen. Relativ. Gravit.
**2006**, 38, 1317–1328. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Brevik, I.
Viscosity in Modified Gravity. *Entropy* **2012**, *14*, 2302-2310.
https://doi.org/10.3390/e14112302

**AMA Style**

Brevik I.
Viscosity in Modified Gravity. *Entropy*. 2012; 14(11):2302-2310.
https://doi.org/10.3390/e14112302

**Chicago/Turabian Style**

Brevik, Iver.
2012. "Viscosity in Modified Gravity" *Entropy* 14, no. 11: 2302-2310.
https://doi.org/10.3390/e14112302