Abstract
This chapter is concerned with a thermodynamic analysis on a flat FLRW universe admitting both apparent and event horizons. As the physical system within the cosmological apparent horizon forms a Bekenstein system, so we have considered the Bekenstein entropy and the Hawking temperature on the apparent horizon. However, since the system bounded by the event horizon may not be a Bekenstein system, we have assumed the Clausius relation on the event horizon to determine its entropy variation. Moreover, we have assumed the modified Hawking temperature on the event horizon. Three types of dark energy cosmic fluids have been considered—a perfect fluid with a constant equation of state, an interacting holographic dark energy, and a Chaplygin gas.
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Notes
- 1.
The velocity of the event horizon is obtained by applying the Leibniz’s rule for differentiation under the integral sign to Eq. (1.26).
- 2.
Note that if either or both the horizons are static or if the fluid is equivalent to a cosmological constant, then the GSL holds but the TE does not.
- 3.
The right inequality is obtained by taking into account the fact that the sum of the last two terms inside the square bracket in Eq. (4.20) must be positive.
- 4.
The second inequality inside the braces is obtained by taking into account the fact that the sum of the first and the last terms inside the square bracket in Eq. (4.20) must be positive.
- 5.
All the figures in this chapter have been plotted with the help of Maple plotting software.
- 6.
At the level of inhomogeneities, the adiabatic sound speed of a cosmological fluid relates the pressure and density perturbations as \(c_{s}^{2}=\frac{\partial p}{\partial \rho }\), which, in our case, reduces to \(c_{s}^{2}=\frac{\dot{p}}{\dot{\rho }}\). It is generally restricted as \(0 \le c_{s}^{2} \le 1\). The lower bound does not allow DE fluctuations to grow exponentially, thus preventing unphysical situations, while the upper bound prevents propagation at superluminal speeds.
References
Saha, S., and S. Chakraborty. 2012. A redefinition of Hawking temperature on the event horizon: Thermodynamical equilibrium. Physics Letters B 717: 319.
Saha, S., and S. Chakraborty. 2014. Do recent observations favor a cosmological event horizon: A thermodynamical prescription? Physical Review D 89: 043512.
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Saha, S. (2018). Cosmological Thermodynamics in FLRW Model. In: Elements of Cosmological Thermodynamics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-74706-4_4
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