1108.5086 (G. Jannes et al.)

The cosmological constant: a lesson from the Weyl superfluid 3He-A    [PDF]

G. Jannes, G. E. Volovik

In the bi-metric analog gravity emerging in superfluid 3He-A there is a
certain connection between the properly determined cosmological constant and
vacuum energy. This is in contrast to the effective 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
between the cosmological constant and the vacuum energy in 3He-A, as well as
its relation to the graviton masses appearing in the effective bi-metric
gravity, and compare with a fully relativistic bi-metric theory of gravity. In
3He-A, the parameter \lambda, which enters the cosmological term in the
bi-metric theory, can be considered as the cosmological constant. It 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. This however does not create a problem for cosmology: although the
cosmological constant, \lambda, is huge, the cosmological term itself vanishes
in the equilibrium vacuum, and thus the equilibrium state of any system
including the final state of the Universe is not gravitating.

View original: http://arxiv.org/abs/1108.5086