Gravity from entropy

Gravity is derived from an entropic action coupling matter fields with geometry. The fundamental idea is to relate the metric of Lorentzian spacetime to a density matrix. The matter fields curve spacetime, defining a metric induced by the matter fields. The entropic action is the quantum relative entropy between the metric of spacetime and the metric induced by the matter fields. The modified Einstein equations obtained reduce to the Einstein equations in the regime of low coupling. To simplify the theory, exclusively scalar matter fields are considered. This theoretical framework can be extended in different directions, for instance by including fermionic matter fields and gauge fields. A canonical quantization of this field theory could bring new insights into quantum gravity.