Temperature evolution of the FRW Universe in the viscous generalised Chaplygin gas model

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Abstract

In this paper, we study the temperature evolution of the Friedmann–Robertson–Walker (FRW) Universe filled with viscous generalised Chaplygin gas (VGCG) as a model of dark energy. We started the thermodynamical treatment of the VGCG, which is given by the equation of state $p = - \frac{A}{ρ^{α}}$ with bulk viscosity in the framework of the Eckart theory. We investigated it in the cosmological model using the FRW metric in flat space–time, and we were able to determine its temperature as a function of redshift z. Besides, the expression for the fluid’s temperature in terms of redshift and the viscosity parameter $ξ_{0}$ is derived. In our computation, we assumed that the value of the parameter $Ω_{x}$ would be 0.7 and that the current value of the temperature of the microwave background radiation would be given by $T_{0} = 2.7$ K. Using the decoupling redshift value $(z \approx 1100)$ and the viscous parameter, the decoupling temperature is computed. The optimum choices for the remaining parameters are $α = 0.25$ , $Ω_{x} = 0.75$ , $ξ_{0} = - 0.1930$ , yielding a decoupling temperature of $T (z = 1100) \approx 4000$ K and a redshift of $z \approx 0.25$ . We also compute the decoupling temperature in this model at $\ddot{a} = 0$ and $T_{0} = 2.7$ K. In terms of z and $ξ_{0}$ , we also examined other parameters, such as the Hubble parameter, the equation of state parameter, the adiabatic speed of sound, jerk, snap and Om diagnostic parameters. These values are then compared with the outcomes of earlier research on modified Chaplygin gas (MCG) and other Chaplygin gas. We have shown that this model is thermodynamically stable for $ξ_{0} < 0$ in the FRW Universe and studied the validity of the generalised second law of thermodynamics on the apparent and event horizons of the Universe in the FRW Universe dominated by various Chaplygin gas fluids. However, a perfect fluid with $ω_{e f f} < - \frac{1}{3}$ would produce an acceleration phase but might not produce a feasible dark energy epoch in the early and late stages of the Universe that is consistent with the observational data.

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Computational Cosmology
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Acknowledgements

The author would like to thank the Vice-Chancellor of Alipurduar University for the necessary research facilities to initiate the work.

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Authors and Affiliations

Department of Physics, Alipurduar University, Alipurduar Court, Alipurduar, 736122, India

Abhinath Barman

Corresponding author

Correspondence to Abhinath Barman.

Appendix

The expression of redshift in the dust phase $(p_{e f f} = 0)$ can be written as

(48)

The expression of redshift in the transition of the expansion of the Universe from deceleration to acceleration (i.e., $\ddot{a} = 0$ ) can be written as

(49)

The jerk parameter j(t), related to the third-order time derivative of the scale factor a(t), is defined as

(50)

which may be expressed in terms of redshift and Hubble parameter as

(51)

The snap parameter s is related to the fourth-order time derivative of scale factor a(t) as

(52)

which is related to j and q by the relation

(53)

The Om diagnostic is defined in terms of redshift and Hubble parameter as

(54)

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Barman, A. Temperature evolution of the FRW Universe in the viscous generalised Chaplygin gas model. Pramana – J Phys 99, 100 (2025). https://doi.org/10.1007/s12043-025-02959-8

Received 05 September 2024
Revised25 February 2025
Accepted 15 April 2025
Published 14 July 2025
DOI https://doi.org/10.1007/s12043-025-02959-8

Keywords

Cosmology
Chaplygin gas
bulk viscosity
thermodynamics
dark matter and dark energy

PACS Nos.

95.35.+d
98.80.−k
98.80.Es

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