The GUP corrected entropy was applied to the holographic equipartition law in a four-dimensional universe embedded in a conformally flat five-dimensional space-time.
In Section 3, the expansion of the cosmic space is treated as an emergent process and the modified Friedmann equations are retrieved from the holographic equipartition law in the absence of any dark energy component.
Field Equations Derived from the Holographic Equipartition Law
The number of degrees of freedom in bulk is said to obey the equipartition law of energy
Equation (13) is known as the holographic equipartition law. Here V = 4[pi]/3[H.sup.3] is the cosmic volume and the parameter e is defined by [38, 51]
Thus we have derived the acceleration equation from the holographic equipartition law and an extra driving term appears on the right side of the equation.
Consequences of GUP Corrected Entropy into the Holographic Equipartition Law. Here, we apply the GUP corrected entropy function [S.sub.Q] into the holographic equipartition law; i.e., we consider that
In the present work, our aim was to study the cosmic evolution in the brane world gravity with the help of the holographic equipartition law. We have applied the quantum corrected form of the entropy function derived from the Generalized Uncertainty Principle in the holographic equipartition law to derive the modified cosmological equations in a homogeneous, isotropic, and spatially flat 3-brane embedded in a five-dimensional bulk.
Second, Newton's law of gravitation can be derived by incorporating the entropic force approach together with the holographic principle and the equipartition law of energy.
Assuming that the amount of information is N bits, and combining the equipartition law of energy with the holographic principle, the number of bits N and area of horizon A obey the following relation:
Next, by adopting the equipartition law of energy, the total energy of the holographic system can be written as