7.9 The cosmological constant problem

The condensed matter analogies offer us an important lesson concerning the cosmological constant problem [660]. Sakharov’s induced gravity not only can give rise to an Einstein–Hilbert term under certain conditions, it also gives rise to a cosmological term. This contribution would depend on the cut-off as E4 P, so if there were not additional contributions counterbalancing this term, emergent gravity in condensed-matter-like systems will always give place to an enormous cosmological constant inducing a strongly-repulsive force between quasiparticles.

However, we know that at low temperatures, depending on the microscopic characteristics of the system we can have quite different situations. Remarkably, liquid systems (as opposed to gases) can remain stable on their own, without requiring any external pressure. Their total internal pressure at equilibrium is (modulo finite-size effects) always zero. This implies that, at zero temperature, if gravity emerges from a liquid-like system, the total vacuum energy Λ ∝ ρV = − pV will be automatically forced to be (relatively) small, and not a large number. The E4 P contribution coming from quasiparticle fluctuations will be exactly balanced by contributions from the microphysics or “trans-Planckian” contributions.

If the temperature is not zero there will be a pressure pM associated with the thermal distribution of quasiparticles, which constitute the matter field of the system. Then, at equilibrium one will have pM + pV = 0, so that there will be a small vacuum energy Λ ∝ pM. This value is not expected to match exactly the preferred value of Λ obtained in the standard cosmological model (ΛCDM) as we are certain to be out of thermodynamic equilibrium. However, it is remarkable that it matches its order of magnitude, (at least for the current epoch), albeit any dynamical model implementing this idea will probably have to do so only at late times to avoid possible tension with the observational data. Guided by these lessons, there are already a number of heuristic investigations about how a cosmological term could dynamically adapt to the evolution of the matter content, and which implications it could have for the evolution of the universe [27, 350, 349, 351].

As final cautionary remark let us add that consideration of an explicit toy model for emergent gravity [252] shows that the quantity that actually gravitates cannot be so easily predicted without an explicit derivation of the analogue gravitational equations. In particular in [198] it was shown that the relevant quantity entering the analogue of the cosmological constant is a contribution coming only from the excitations above the condensate.

  Go to previous page Go up Go to next page