[Paper Review] Gravity through the prism of condensed matter physics

G. E. Volovik|arXiv (Cornell University)|Jul 25, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes that gravity, cosmological constant, and black hole entropy emerge from condensed matter physics analogs, using tetrads as bilinear fermion operators and Weyl points to model quantum vacuum structure. It suggests that the small cosmological constant arises from symmetry breaking and topological protection, while emergent gravity predicts extensions to the Standard Model with four generations and asymmetric dark matter.

ABSTRACT

In the paper "Life, the Universe, and everything--42 fundamental questions", Roland Allen and Suzy Lidström presented personal selection of the fundamental questions. Here, based on the condensed matter experience, we suggest the answers to some questions concerning the vacuum energy, black hole entropy and the origin of gravity. In condensed matter we know both the many-body phenomena emerging on the macroscopic level and the microscopic (atomic) physics, which generates this emergence. It appears that the same macroscopic phenomenon may be generated by essentially different microscopic backgrounds. This points to various possible directions in study of the deep quantum vacuum of our Universe.

Motivation & Objective

• To address fundamental questions in quantum gravity and cosmology using condensed matter analogs.
• To resolve the hierarchy problem of the cosmological constant by leveraging vacuum energy nullification in many-body systems.
• To explain black hole entropy and horizon thermodynamics through analogies with de Sitter space and two-fluid dynamics.
• To propose emergent gravity scenarios based on tetrads derived from fermionic bilinears and Weyl point structures.
• To extend the Standard Model via topological and symmetry-based mechanisms inspired by condensed matter systems.

Proposed method

• Model the vacuum as a many-body quantum system with emergent spacetime via tetrads constructed from bilinear fermion operators.
• Use the Weyl point construction in 3D and 4D momentum-frequency space to realize 8 or 16 massless fermions, corresponding to 4 generations.
• Apply the Gibbs-Duhem relation to de Sitter thermodynamics to derive black hole entropy and horizon temperature.
• Introduce dimensionless physics where Planck’s constant ℏ is reinterpreted as a length scale within the tetrad framework.
• Analyze phase coexistence and relaxation processes to explain the small observed cosmological constant.
• Explore topological defects such as cosmic domain walls and Alice strings as analogs of condensed matter textures in 3He-B and 3He-A.

Experimental results

Research questions

• RQ1 Why is the cosmological constant so small compared to the Planck-scale prediction?
• RQ2 How can black hole entropy and temperature emerge from vacuum thermodynamics?
• RQ3 What is the origin of gravity in terms of condensed matter analogs?
• RQ4 Can the Standard Model be extended via topological and symmetry-based mechanisms from condensed matter?
• RQ5 What are the implications of emergent tetrads and Weyl fermions for quantum gravity and dark matter?

Key findings

• The cosmological constant problem is resolved by vacuum energy nullification via symmetry and phase coexistence, consistent with observed small values.
• Black hole entropy arises from the de Sitter thermodynamics of the vacuum, with entropy proportional to horizon area via the Gibbs-Duhem relation.
• Tetrads emerge as bilinear forms of fermion operators, suggesting they are more fundamental than the metric in emergent gravity.
• The Weyl point construction in 4D momentum-frequency space yields 16 massless fermions, supporting a Pati-Salam-type grand unification with four generations.
• Massive neutrinos arise from spontaneous breaking of symmetry K, with small masses due to exponential suppression typical in condensed matter phase transitions.
• Topological analogs of cosmic strings, domain walls, and magnetic quarks in 3He-A mirror predicted cosmological objects, linking condensed matter to astrophysics.