Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Abstract

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.