Abstract
The appearance of the quantum gravitational effects in a very high energy regime necessitates some corrections to the thermodynamics of Friedmann-Robertson-Walker (FRW) universe. The modified dispersion relation (MDR) as a phenomenological approach to investigate the high energy physics provides a perturbation framework upon which the FRW universe thermodynamics can be corrected. In this letter, we obtain the corrected entropy-area relation of the apparent horizon of FRW universe by utilizing the extra dimensional form of MDR, leading to the modification of Friedmann equations. The influence of MDR on the Friedmann equations provides a good insight into the understanding of the FRW universe dynamics in the final quantum gravity theory.
Highlights
Nowadays a black hole is known as a thermodynamical object which obeys the four laws of thermodynamics
Since modified dispersion relation (MDR) can yield to a deeper understanding of the ultimate quantum gravity proposal, we have investigated the 4-dimensional form of MDR in the context of the black holes thermodynamics in [15]
One may be interested in finding the dynamics of the FRW universe in the era of Planck time as an important part of this history
Summary
Nowadays a black hole is known as a thermodynamical object which obeys the four laws of thermodynamics. Using the entropy-area relation and the temperature relation of the black hole, the first law of thermodynamics can reproduce the gravitational field equations [1]. One may find a deep connection between three seemingly different branches of science: thermodynamics, gravity, and quantum mechanics in the black holes This connection has been investigated extensively for FRW universe [6]. If one applies the first law of thermodynamics to the apparent horizon of any finite dimensional FRW universe with any spatial curvature, the Friedmann equations can be derived [6]. Using the corrected entropy-area relation of the apparent horizon, the first law of thermodynamics may be cast to the modified Friedmann equations. The modified Friedmann equations can certainly result in a better understanding of FRW universe dynamics
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