Power-Law Entropic Corrections to Newton's Law and Friedmann Equations

摘要

A possible source of black hole entropy could be the entanglement of quantumfields in and out the horizon. The entanglement entropy of the ground stateobeys the area law. However, a correction term proportional to a fractionalpower of area results when the field is in a superposition of ground andexcited states. Inspired by the power-law corrections to entropy and adoptingthe viewpoint that gravity emerges as an entropic force, we derive modifiedNewton's law of gravitation as well as the corrections to Friedmann equations.In a different approach, we obtained power-law corrected Friedmann equation bystarting from the first law of thermodynamics at apparent horizon of a FRWuniverse, and assuming that the associated entropy with apparent horizon has apower-law corrected relation. Our study shows a consistency between theobtained results of these two approaches. We also examine the time evolution ofthe total entropy including the power-law corrected entropy associated with theapparent horizon together with the matter field entropy inside the apparenthorizon and show that the generalized second law of thermodynamics is fulfilledin a region enclosed by the apparent horizon.