Power-law entropic corrections to Newton’s law and Friedmann equations

A possible source of black hole entropy could be the entanglement of quantum fields inside and outside the horizon. The entanglement entropy of the ground state obeys the area law. However, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. Inspired by the power-law corrections to entropy and adopting the viewpoint that gravity emerges as an entropic force, we derive modified Newton's law of gravitation as well as the corrections to Friedmann equations. In a different approach, we obtained power-law-corrected Friedmann equation by starting from the first law of thermodynamics at the apparent horizon of a Friedmann-Robertson-Walker universe, and assuming that the associated entropy with apparent horizon has a power-law-corrected relation. Our study shows a consistency between the obtained results of these two approaches. We also examine the time evolution of the total entropy including the power-law-corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon and show that the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.