The cosmological constant: A lesson from the effective gravity of topological Weyl media

TL;DR

This paper explores how topological Weyl media, like superfluid 3He-A, provide insights into the cosmological constant by linking vacuum energy to emergent effective gravity, highlighting differences from Bose-Einstein condensates.

Contribution

It demonstrates that in topological matter, the vacuum energy directly relates to the cosmological constant and clarifies the role of bi-metric gravity and vacuum states in emergent gravity models.

Findings

The parameter , analogous to the cosmological constant, matches the vacuum energy difference between states.

The cosmological constant in topological media is large but naturally non-constant and vanishes in equilibrium.

Emergent gravity in topological matter closely resembles real gravity, unlike in Bose-Einstein condensates.

Abstract

Topological matter with Weyl points, such as superfluid 3He-A, provide an explicit example where there is a direct connection between the properly determined vacuum energy and the cosmological constant of the effective gravity emerging in condensed matter. This is in contrast to the acoustic gravity emerging in Bose-Einstein condensates, where the "value of this constant cannot be easily predicted by just looking at the ground state energy of the microscopic system from which spacetime and its dynamics should emerge" (S. Finazzi, S. Liberati and L. Sindoni, The cosmological constant: a lesson from Bose-Einstein condensates, Phys. Rev. Lett. 108, 071101 (2012)). The advantage of topological matter is that the relativistic fermions and gauge bosons emerging near the Weyl point obey the same effective metric and thus the effective gravity is more closely related to real gravity. We study this connection in the bi-metric gravity emerging in 3He-A, and its relation to the graviton masses, by comparison with a fully relativistic bi-metric theory of gravity. This shows that the parameter \lambda, which in 3He-A is the bi-metric generalization of the cosmological constant, coincides with the difference in the proper energy of the vacuum in two states (the nonequilibrium state without gravity and the equilibrium state in which gravity emerges) and is on the order of the characteristic Planck energy scale of the system. Although the cosmological constant \lambda\ is huge, the cosmological term itself is naturally non-constant and vanishes in the equilibrium vacuum, as dictated by thermodynamics. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating.