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.

arXiv comment7 pages, no figures, to appear in Phys. Rev. D

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• Kinetic inflation in deformed phase space Brans-Dicke cosmology
• Phase space analysis of the bouncing universe with stringy effects
• The minimal length and the Shannon entropic uncertainty relation
• Fractional Einstein-Gauss-Bonnet scalar field cosmology
• Cosmology from String T-duality and zero-point length
• Resolution of challenging problems in quantum cosmology with electromagnetic radiation
• On the relation between boundary proposals and hidden symmetries of the extended pre-big bang quantum cosmology
• On the thermodynamics of reconciling quantum and gravity
• Gödel-type solutions in $f(R,T,R_{\mu \nu }{T}^{\mu \nu }$) gravity
• Phase space noncommutativity, power-law inflation and quantum cosmology
• Bound states in the continuum are universal under the effect of minimal length
• Minimal length implications on the Hartree-Fock theory