Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-08-25
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages, no figures
Scientific paper
Topological matter with Weyl points, such as superfluid 3He-A, provide an explicit example where the properly determined vacuum energy and the cosmological constant appearing in the effective gravity are directly connected. 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)). 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. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating.
Jannes Gil
Volovik Grigori E.
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