Abstract
The effect of bulk viscosity on the early evolution of Universe for a spatially homogeneous and isotropic Robertson-Walker model is considered. Einstein’s field equations are solved by using ‘gamma-law’ equation of state p = (γ − 1)ρ, where the adiabatic parameter gamma (γ) depends on the scale factor of the model. The ‘gamma’ function is defined in such a way that it describes a unified solution of early evolution of the Universe for inflationary and radiation-dominated phases. The fluid has only bulk viscous term and the coefficient of bulk viscosity is taken to be proportional to some power function of the energy density. The complete general solutions have been given through three cases. For flat space, power-law as well as exponential solutions are found. The problem of how the introduction of viscosity affects the appearance of singularity, is briefly discussed in particular solutions. The deceleration parameter has a freedom to vary with the scale factor of the model, which describes the accelerating expansion of the Universe.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C Eckart, Phys. Rev. 58, 919 (1940)
L D Landau and E M Lifshitz, Fluid mechanics (Butterworth Heinemann, New York, 1987)
W Israel, Ann. Phys. 100, 310 (1976)
W Israel and J M Stewart, Phys. Lett. A58, 213 (1976)
S Weinberg, Gravitation and cosmology (Wiley, New York, 1972)
J D Nightingale, Astrophys. J. 185, 105 (1973)
M Heller and Z Klimek, Astrophys. Space Sci. 33, L37 (1975)
M Heller, Z Klimek and L Suszyeki, Astrophys. Space Sci. 20, 205 (1973)
G L Murphy, Phys. Rev. D8, 4231 (1973)
V A Belinskii and I M Khalatnikov, Sov. Phys. JETP 43, 205 (1976)
V A Belinskii and I M Khalatnikov, Sov. Phys. JETP 49, 401 (1975)
J D Barrow, Phys. Lett. B180, 335 (1986)
J D Barrow, Nucl. Phys. B310, 743 (1988)
N O Santos, R S Dias and A Banerjee, J. Math. Phys. 26, 876 (1985)
Ø Grøn, Astrophys. Space Sci. 173, 191 (1990)
D Pavo’n, J Bafaluy and D Jou, Class. Quantum Grav. 8, 347 (1991)
D Pavo’n and W Zimdahl, Phys. Lett. A179, 261 (1993)
A Burd and A Coley, Class. Quant. Grav. 11, 83 (1994)
R Maartens, Class. Quant. Grav. 12, 1455 (1995)
W Zimdahl, Phys. Rev. D53, 5483 (1996)
W Zimdahl, Mon. Not. R. Astron. Soc. 280, 1239 (1996)
L P Chimento, A S Jakubi and D Pavon, Phys. Rev. D62, 063508 (2000)
L P Chimento, A S Jakubi and D Pavon, Phys. Rev. D67, 087302 (2003)
J C Fabris, S V B Goncalves and R S Ribeiro, Gen. Relativ. Gravit. 38, 495 (2006)
M K Mak and T Harko, Int. J. Mod. Phys. D12, 925 (2003)
A A Sen, S Sen and S Sethi, Phys. Rev. D63, 107501 (2001)
M Cataldo, N Cruz and S Lepe, Phys. Lett. B619, 5 (2005)
N Carlevaro and G Mod. Montani, Phys. Lett. A20, 1729 (2005)
J C Carvalho, Int. J. Theor. Phys. 35, 2019 (1996)
S Ram and C P Singh, Int. J. Theor. Phys. 37, 1141 (1998)
S Ram and C P Singh, Astrophys. Space Sci. 254, 143 (1997)
C P Singh, S Kumar and A Pradhan, Class. Quant. Grav. 24, 455 (2007)
C P Singh, Nuovo Cimento B122, 89 (2007)
P C W Davies, Class. Quant. Grav. 4, L225 (1987)
Z Klimek, Acta Cosmol. 10, 7 (1981)
S Hawking and R Penrose, Proc. R. Soc. London Ser. A314, 529 (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, C.P. Bulk viscous cosmology in early Universe. Pramana - J Phys 71, 33–48 (2008). https://doi.org/10.1007/s12043-008-0139-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-008-0139-4