Holographic Cosmology from the First Law of Thermodynamics and the Generalized Uncertainty Principle

Details Holographic Cosmology from the First Law of Thermodynamics and the Generalized Uncertainty Principle Holographic Cosmology from the First Law of Thermodynamics and the Generalized Uncertainty Principle

2009-11-17

arxiv.org/abs/0911.3286v1

Physics

High Energy Physics

High Energy Physics - Theory

4 pages

Scientific paper

The cosmological Friedmann equation sourced by the trace anomaly of a conformal field theory that is dual to the five-dimensional Schwarzschild-AdS geometry can be derived from the first law of thermodynamics if the apparent horizon of the boundary spacetime acquires a logarithmically-corrected Bekenstein-Hawking entropy. It is shown that such a correction to the entropy can arise when the generalized uncertainty principle (GUP) is invoked. The necessary condition for such a thermodynamic derivation directly relates the GUP parameter to the conformal anomaly. It is consistent with the existence of a gravitational cutoff for a theory containing $n$ light species. The absolute minimum in position uncertainty can be identified with the scale at which gravity becomes effectively five-dimensional.

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