Gravity from entropy

Abstract

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 quantum operator, playing the role of an renormalizable effective density matrix and to describe the matter fields topologically, according to a Dirac-Kähler formalism, as the direct sum of a zero-form, a one-form and a two-form. While the geometry of spacetime is defined by its metric, the matter fields can be used to define an alternative metric, the metric induced by the matter fields, which geometrically describes the interplay between spacetime and matter. The proposed 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 from this action reduce to the Einstein equations with zero cosmological constant in the regime of low coupling. By introducing the G-field, which acts as a set of Lagrangian multipliers, the proposed entropic action reduces to a dressed Einstein-Hilbert action with an emergent small and positive cosmological constant only dependent on the G-field. The obtained equations of modified gravity remain second order in the metric and in the G-field. A canonical quantization of this field theory could bring new insights into quantum gravity while further research might clarify the role that the G-field could have for dark matter.

arXiv comment(16 pages, 1 figure)

References in corpus (29)

• Particle Dark Matter: Evidence, Candidates and Constraints
• f(R) Theories Of Gravity
• The World as a Hologram
• Thermodynamics of Spacetime: The Einstein Equation of State
• Aspects of Holographic Entanglement Entropy
• On the Origin of Gravity and the Laws of Newton
• Testing General Relativity with Present and Future Astrophysical Observations
• The Role of Relative Entropy in Quantum Information Theory
• Thermodynamical Aspects of Gravity: New insights
• On Geometric Entropy
• Quantum corrections to holographic entanglement entropy
• Entanglement Renormalization and Holography
• Holographic Entanglement Entropy: An Overview
• Black holes, gravitational waves and fundamental physics: a roadmap
• Notes on Some Entanglement Properties of Quantum Field Theory
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Emergence of a 4D World from Causal Quantum Gravity
• Prospects for Fundamental Physics with LISA
• Metric-affine f(R) theories of gravity
• Entanglement Equilibrium and the Einstein Equation
• Gravity and the Crossed Product
• Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation
• Notes on the type classification of von Neumann algebras
• What is the Entropy in Entropic Gravity?
• Spacetime thermodynamics without hidden degrees of freedom
• The information in a wave
• Von Neumann Entropy in QFT
• The mass of simple and higher-order networks
• Quantum entropy couples matter with geometry

Cited by in corpus (10)

• The quantum relative entropy of the Schwarzschild black-hole and the area law
• Squeezed gravitons from superradiant axion fields around rotating black holes
• Quantum response theory and momentum-space gravity
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• Entanglement entropy evolution during gravitational collapse
• Inflation from entropy
• Beyond holography: the entropic quantum gravity foundations of image processing
• Spherically symmetric black holes in Gravity from Entropy and spontaneous emission
• $\Lambda$-Gravity from Entropy
• Alternative Framework to Quantize Fermionic Fields