^{3}.

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.

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 [

Since a common feature of all promising candidates for quantum theory of gravity is the existence of a minimal observable length [

Previously, FRW universe had been considered to modify the Friedmann equations from the generalized uncertainty principle (GUP) in 4 dimensions [

The modified dispersion relation in 4 dimensions can be written as [

Alternatively, one may be interested in using the extra dimensional form of MDR which is not studied enough yet. We have investigated the modified dispersion relation in theories with extra dimensions in our previous work [

As another point, we have shown in [

We consider an

Then it can be shown that the first law of thermodynamics

In this work, we are interested in finding the modified Friedmann equations in a very high energy regime. To obtain the modified Friedmann equations, we start by deriving the corrections to the entropy of FRW universe via MDR. Let us consider the extra dimensional form of MDR as

Let us now consider that a particle with energy

As another point, we can refer to the absence of the fractional powers of

Anyway, the quantum gravity effects are so important in the early universe. The appearance of the correction terms in the entropy-area relation, coming from MDR, plays an important role in studying the FRW universe in the Planck time. In addition, one may be interested in finding the modified Friedmann equations within MDR. Using the MDR-corrected entropy of FRW universe, the first law of thermodynamics can reproduce the modified Friedmann equations.

In an

It is important to point that the modification to the entropy-area relation leads to the modification to Friedmann equations [

For

Finding the whole evolution history of the FRW universe is one of the most important goals in cosmology. To reach this goal, 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. Since the early universe experiences a very high energy regime, the effects of quantum gravity should not be forgotten there. In this letter, the modified dispersion relation as an appropriate phenomenological approach to study the quantum gravitational effects has been used to study the FRW universe. We have obtained the corrections to the entropy of a FRW universe via the extra dimensional form of MDR. We have found that the logarithmic correction term, whose existence is still somewhat mysterious, may only emerge in a FRW universe with even dimensions (odd

The author declares that there is no conflict of interests regarding the publication of this paper.