Quantum phenomenological gravitational dynamics: A general view from thermodynamics of spacetime

TL;DR

This paper derives quantum-modified gravitational equations from thermodynamic principles, incorporating quantum gravity effects via entropy corrections, and explores their implications for cosmology and singularity resolution.

Contribution

It introduces a general quantum phenomenological framework for gravitational dynamics based on thermodynamics, including quantum gravity modifications to entropy.

Findings

Derived equations generalize unimodular gravity with second derivatives of the metric.

Quantum gravity effects modify Bekenstein entropy with a logarithmic term.

Application to cosmology suggests a resolution of classical singularities.

Abstract

In this work we derive general quantum phenomenological equations of gravitational dynamics and analyse its features. The derivation uses the formalism developed in thermodynamics of spacetime and introduces low energy quantum gravity modifications to it. Quantum gravity effects are considered via modification of Bekenstein entropy by an extra logarithmic term in the area. This modification is predicted by several approaches to quantum gravity, including loop quantum gravity, string theory, AdS/CFT correspondence and generalised uncertainty principle phenomenology, giving our result a general character. The derived equations generalise classical equations of motion of unimodular gravity, instead of the ones of general relativity, and they contain at most second derivatives of the metric. We provide two independent derivations of the equations based on thermodynamics of local causal diamonds. First one uses Jacobson's maximal vacuum entanglement hypothesis, the second one Clausius entropy flux. Furthermore, we consider questions of diffeomorphism and local Lorentz invariance of the resulting dynamics and discuss its application to a simple cosmological model, finding a resolution of the classical singularity.