The cosmological model incorporating viscous fluid within the framework of general relativity
DOI:
https://doi.org/10.5269/bspm.78158Abstract
Dark matter and dark energy, elusive elements of the universe, exert gravitational forces of attraction or repulsion, influencing the cosmological model. This phenomenon, known as cosmic acceleration, has been the subject of theoretical and observational studies spanning many decades. In this paper we have presented the cosmological models in presence of viscous fluid. Incorporation of cosmological constant and gravitational constant makes model more realistic. We solve the model in two phases: with case first, we assume that the viscosity of fluids is a power function of density. While another case comprises that the viscosity of the cosmological model is to be considered as the form of scalar expansion. To get the deterministic model, we have assumed a power law of gravitational constant . The relationship between viscosity and density; and with viscosity and scalar expansion determines the existence of dark energy. The geometrical aspect of the cosmological models also discussed.
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32. Xing–xiang W., Bianchi type-III string cosmological model with bulk viscosity and magnetic field, 23(2006), Chinese physics letters, No.7, 1702. https://iopscience.iop.org/article/10.1088/0256-307X/23/7/013/meta
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2. Perlmutter S., et al., 517(1999), Astrophys. J., No. 565. https://iopscience.iop.org/article/10.1086/307221/meta
3. Riess A.G., Filippenko A.V., challis P., Clocchiatti A., et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, 116(1998), The astronomical journal , No.3, 1009. https://iopscience.iop.org/article/10.1086/300499/meta
4. Riess A.G., Strolger L.G., Tonry J., et al., Type Ia supernova discoveries at z ¿ 1 from the Hubble Space Telescope: Evidence for past deceleration and constraints on dark energy evolution, 607(2004), The Astrophysical Journal, No.2, 665. https://iopscience.iop.org/article/10.1086/383612/meta
5. Ali N., Bulk viscous Bianchi type-V cosmological model with time function G and lambda (Λ), arXiv preprint arXiv:2305.10535 (2023). https://doi.org/10.48550/arXiv.2305.10535
6. Bali R., and Tinker S., Bianchi type III bulk viscous barotropic fluid cosmological models with variable G and Λ, 26 (2009), Chinese Physics Letters, No.2, 029802. https://iopscience.iop.org/article/10.1088/0256-307X/26/2/029802/meta
7. Linde A.D., Is the cosmological constant really constant?, 19(1974), Pisma v Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki , No.320-322. https://ui.adsabs.harvard.edu/abs/1974PZETF..19..320L/abstract
8. Weinberg S., Implications of dynamical symmetry breaking: an addendum, 19(1979), Physical Review D, No. 4, 1277. https://doi.org/10.1103/PhysRevD.19.1277
9. Pavon D., jou J., and Bafaluy D., 8(1991) Class. Quant. Grav. , No. 357. https://iopscience.iop.org/article/10.1088/0264-9381/8/2/014
10. Maartens R., Dissipative cosmology, 12(1995), Classical and Quantum Gravity, No.6, 1455. https://iopscience.iop.org/article/10.1088/0264-9381/12/6/011/meta
11. Pradhan A., Yadav V.K., and Chakrabarty I., Bulk viscous FRW cosmology in Lyra geometry, 10(2001), International Journal of Modern Physics D, No. 03, 339-349. https://doi.org/10.1142/S0218271801000767
12. Kumar S., Yadav M.K., Gangele R.K., et al., Bianchi type-I viscous fluid and interacting dark energy cosmological model in general relativity, 96(2022), Pramana Journal of Physics, No. 195. https://doi.org/10.1007/s12043-022-02434-8
13. Klimek Z., Entropy per particle in the early Bianchi type I universe, 35(1976), Nuovo Cimento B Serie, No.249-258. https://ui.adsabs.harvard.edu/link.gateway/1976NCimB..35..249K/doi:10.1007/BF02724062
14. Murphy G.I., Big-bang model without singularities, 8(1973), Physical Review D, No.12, 4231. https://doi.org/10.1103/PhysRevD.8.4231
15. Padmanabhan T. and Chitre S.M., Viscous universes, 120(1987), Physics Letters A, No.9, 433-436. https://doi.org/10.1016/0375-9601(87)90104-6
16. Arbab I., Bianchi type I viscous universe with variable G and Λ, 30(1998), General Relativity and Gravitation, No.9, 1401-1405. https://doi.org/10.1023/A:1018856625508
17. Beesham A., Ghosh G.S., and Lombard R.G., Anisotropic viscous cosmology with variable G and Λ, 32 (2000), General Relativity and Gravitation, No.471-477. https://doi.org/10.1023/A:1001924300321
18. Bali, R. and Tinker S., Bianchi type III bulk viscous barotropic fluid cosmological models with variable G and Λ, 26 (2009), Chinese Physics Letters, No.2, 029802. https://iopscience.iop.org/article/10.1088/0256-307X/26/2/029802/meta
19. Bali R. and Pradhan A., Bianchi type-III string cosmological models with time dependent bulk viscosity, 24(2007), Chinese Physics Letters, No.2, 585. https://iopscience.iop.org/article/10.1088/0256-307X/24/2/079/meta
20. Thomas L.H., The Radiation field in a fluid of motion,1(1930), Q. J. Math ., No. 239- 251. https://doi.org/10.1093/qmath/os-1.1.239
21. Dunn K.A. and Tupper B.O.J, Tilting and viscous models in a class of Type VI/0/cosmologies, 222(1978), The Astrophysical Journal, No. 405-411. https://adsabs.harvard.edu/full/record/seri/ApJ../0222/1978ApJ...222..405D.html
22. Mukherjee G., A Bianchi type I tilted universe, 4(1983), Journal of Astrophysics and Astronomy , No. 295-300. https://doi.org/10.1007/BF02714923
23. Pawar D.D., and Dagwal V.J., Conformally flat tilted cosmological models in general relativity, 37(2010), Bulg. J. Phys., No.165-175. https://www.researchgate.net/publication/267401093
24. Dagwal V.J. and Pawar D.D., Two-fluid sources in F (T) theory of gravity, 35(2020), Modern Physics Letters A, No.04,1950357. https://doi.org/10.1142/S0217732319503577
25. Berman M.S. and Gomide F.D.M., Cosmological models with constant deceleration parameter, 20(1988), General Relativity and Gravitation, No. 191-198. https://doi.org/10.1007/BF00759327
26. Akarsu O and Dereli T., Cosmological models with linearly varying deceleration parameter, 51(2012), International Journal of Theoretical Physic, No.612-621. https://doi.org/10.1007/s10773-011-0941-5
27. Singh T. and Singh G.P., Some cosmological models with constant deceleration parameter, (1971-1996) (1991), Il Nuovo Cimento B, No.106 617-622. https://doi.org/10.1007/BF02813228
28. Bali R., and Yadav M.K., Bianchi type-IX viscous fluid cosmological model in general relativity, 64(2005), Pramana, No.187-196. https://doi.org/10.1007/BF02704873
29. Bali R., Singh P. and Singh J.P., Bianchi Type V viscous fluid cosmological model in presence of decaying vacuum energy, 341(2012), Astrophys. and Space Sci., No.701. https://doi.org/10.1007/BF02704873
30. Pawar D.D., and Dagwal V.J., Two fluids tilted cosmological models in general relativity, 53(2014), International Journal of Theoretical Physics, No.2441-2450. https://doi.org/10.1007/s10773-014-2043-7
31. Dagwal V.J. and Pawar D.D., Tilted two fluids cosmological models with variable G and Λ in General Relativity, arXiv preprint arXiv:1704.07107 (2017). https://doi.org/10.48550/arXiv.1704.07107
32. Xing–xiang W., Bianchi type-III string cosmological model with bulk viscosity and magnetic field, 23(2006), Chinese physics letters, No.7, 1702. https://iopscience.iop.org/article/10.1088/0256-307X/23/7/013/meta
33. Tiwari R.K., and Dwivedi U.K., Bianchi type-III string cosmological models with bulk viscosity and time-dependent Λ term, 18(2009) Fizika B: Journal of experimental and theoretical physics, No.3,181-188. https://hrcak.srce.hr/304582
34. Chokyia K.K., and Chattopadhyay S., Testing generalized second law of thermodynamics in cosmological models with bulk viscosity and modified gravity, 85,771(2025), Eur. Phys. J. C, https://doi.org/10.1140/epjc/s10052-025-14478-2
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2025-12-06
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