Quantum cosmology, minimal length and holography

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.

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