Emergence of quadratic gravity from entanglement equilibrium

TL;DR

This paper demonstrates how quadratic gravity equations can emerge from entanglement equilibrium principles, using a model-independent approach based on horizon entanglement entropy corrections, avoiding assumptions about gravitational dynamics.

Contribution

It introduces a novel derivation of linearised quadratic gravity from entanglement entropy without relying on the Wald prescription or prior gravitational assumptions.

Findings

Quadratic gravity equations emerge from entanglement equilibrium.

Logarithmic entropy corrections influence the sign of gravity correction terms.

Negative entropy correction sign avoids tachyonic instabilities.

Abstract

In this work, we derive the linearised equations of quadratic gravity from entanglement equilibrium of local causal diamonds. Rather than starting from the Wald entropy prescription (which depends on the gravitational Lagrangian), we employ a model independent approach based on the logarithmic corrections to horizon entanglement entropy. In this way, we are able to show the emergence of linearised quadratic gravity from entanglement equilibrium without using any a priori knowledge about gravitational dynamics. If the logarithmic correction to entropy has a negative sign, as predicted by replica trick calculations of entanglement entropy, we find that the quadratic gravity correction terms have the sign necessary to avoid tachyonic instabilities of the theory.