Probable ratio of the vacuum energy in a Schwarzchild-de Sitter space

TL;DR

This paper explores how the generalized uncertainty principle affects the thermodynamics of Schwarzschild-de Sitter spacetime, providing insights into the vacuum energy ratio and its relation to cosmological observations.

Contribution

It derives corrections to Hawking temperature and entropy due to GUP and estimates the vacuum energy ratio, connecting quantum gravity effects with cosmological data.

Findings

Probable vacuum energy ratio in a star is 2/3, aligning with observations.

The ratio decreases for black holes.

An inequality links energy density with system size, shedding light on the cosmological constant's smallness.

Abstract

The effects of the generalized uncertainty principle({\bf GUP}) on the cosmological constant problem are discussed in the Schwarzchild-deSitter spacetime, through studying the corrections to its thermodynamics. We derive the correction to the Hawking temperature of the cosmological horizon, by a heuristic method enlighten by gr-qc/0106080 . The logarithmic correction to the Bekenstein-Hawking entropy is also obtained. For an ordinary star (not a black hole), the probable ratio of the vacuum energy to the total energy within the cosmological horizon is 2/3, which roughly coincides with the evidences from the astronomical observations. For a black hole, the ratio tends to decrease. An inequality associating the energy density with the length of system is put forward for understanding the smallness of the cosmological constant, and the relation between the Bekenstein entropy bound and the Bekenstein-Hawking entropy is also briefly discussed.