1205.6905 (Ivan Arraut)

The Planck length as a duality of the Cosmological Constant: S-dS and
S-AdS thermodynamics from a single expression    [PDF]

Ivan Arraut

Is the Cosmological Constant $\Lambda$ a fundamental quantity? What is the relation between the Planck scale and the Cosmological Constant one? In this paper we suggest that the Planck length $l_{pl}$ and the Cosmological Constant scale $r_\Lambda=\frac{1}{\sqrt{\Lambda}}$ could in principle be dual each other if we take seriously the so-called q-Bargmann Fock space representation as has been previously suggested by Kempf and others and if additionally we introduce $l_{pl}$ as an ultraviolet cut-off and $r_\Lambda=\frac{1}{\sqrt{\Lambda}}$ as an infrared one. As a consequence, it is possible to demonstrate that a Generalized Uncertainty Principle (GUP) given by $\Delta X \Delta P\geq \frac{\hbar}{2}+\frac{l_{pl}^2}{2\hbar}(\Delta P)^2+\frac{\hbar}{2r_\Lambda^2}(\Delta X)^2$, can reproduce appropriately the thermodynamic for both, the Schwarzschild Anti de-Sitter (S-AdS) and the Schwarzschild de-Sitter (S-dS) space without making any analytical extension for the coefficient (parameter) related to the minimum uncertainty in momentum (already suggested in the literature). This is possible if the physics (Black Hole) and as a consequence, the coordinate system is described with respect to the Static Observer for the S-dS case.

View original: http://arxiv.org/abs/1205.6905