Quantum cosmology, minimal length and holography

Abstract

We study the effects of a generalized uncertainty principle on the classical and quantum cosmology of a closed Friedmann Universe whose matter content is either a dust or a radiation fluid. More concretely, assuming the existence of a minimal length, we show that the entropy will constitute a Dirac observable. In addition, 't Hooft conjecture on the cosmological holographic principle is also investigated. We describe how this holographic principle is satisfied for large values of a quantum number, $n$. This occurs when the entropy is computed in terms of the minimal area.

7 pages, no figures, to appear in Phys. Rev. D

References in corpus (10)

• Discreteness of Space from the Generalized Uncertainty Principle
• Natural extension of the Generalised Uncertainty Principle
• Cosmological apparent and trapping horizons
• Quantum FRW cosmological solutions in the presence of Chaplygin gas and perfect fluid
• Perfect fluid quantum Universe in the presence of negative cosmological constant
• Signature change from Schutz's canonical quantum cosmology and its classical analogue
• Effects of the Modified Uncertainty Principle on the Inflation Parameters
• A canonical transformation and the tunneling probability for the birth of an asymptotically DeSitter universe with dust
• Entropy of gravitationally collapsing matter in FRW universe models
• Self-Relative (or Machian) Information: Entropy-Area Relation

Cited by in corpus (5)

• Generalized uncertainty principle and the conformally coupled scalar field quantum cosmology
• On the relation between boundary proposals and hidden symmetries of the extended pre-big bang quantum cosmology
• Gödel-type solutions in $f(R,T,R_{\mu \nu }{T}^{\mu \nu }$) gravity
• Bound states in the continuum are universal under the effect of minimal length
• Minimal length implications on the Hartree-Fock theory