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

TL;DR

This paper demonstrates how the Friedmann equation in holographic cosmology can be derived from thermodynamics when incorporating a logarithmic correction to entropy due to the generalized uncertainty principle, linking quantum gravity effects to cosmological dynamics.

Contribution

It introduces a novel connection between the GUP-induced entropy correction and the derivation of cosmological equations from thermodynamics, establishing a link between quantum gravity and holographic cosmology.

Findings

GUP leads to logarithmic entropy correction in holographic cosmology.

The thermodynamic derivation constrains the GUP parameter.

Identifies the gravity scale with the minimum position uncertainty.

Abstract

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.