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General Relativity and Quantum Cosmology, gr-qc, Condensed Matter, Quantum Gases, cond-mat.quant-gas
Abstract:
The cosmological constant is one of the most pressing problems in modern
physics. In this Letter, we address the issue of its nature and computation
using an analogue gravity standpoint as a toy model for an emergent gravity
scenario. Even if it is well known that phonons in some condense matter systems
propagate like a quantum field on a curved spacetime, only recently it has been
shown that the dynamics of the analogue metric in a Bose-Einstein condensate
can be described by a Poisson-like equation with a vacuum source term
reminiscent of a cosmological constant. Here we directly compute this term and
confront it with the other energy scales of the system. On the gravity side of
the analogy, this model suggests that in emergent gravity scenarios it is
natural for the cosmological constant to be much smaller than its naif value
computed as the zero-point energy of the emergent effective field theory. The
striking outcome of our investigation is that 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. A
proper computation would require the knowledge of both the full microscopic
quantum theory and a detailed understanding about how Einstein equations emerge
from such a fundamental theory. In this light, the cosmological constant
appears even more a decisive test bench for any quantum/emergent gravity
scenario.
