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 filled with two fluids, namely, dust and radiation, non-interacting. More concretely, assuming the existence of a minimal length, we show that a corresponding minimal area will constitute a Dirac observable. In addition, ’t Hooft conjecture on the cosmological holographic principle is also investigated for either the case of dust or radiation being present. 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.