The problem lies at the interface of GR and QM.
GR does not predict
any density of the false vacuum, not even 10
-120 that suggested by QM.
The hugh OOM fine tuning problem occurs when the false vacuum is identified with the cosmological constant suggested by the standard cosmological paradigm. This is an attractive hypothesis as \Lambda and false vacuum have the same equation of state:
p=-\rho,
however strictly in GR the false vacuum ought to be entered into the right hand side of the field equation, as a component of the energy-momentum tensor of the matter field, rather than on the left hand side as a component of space-time curvature,
R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R+\Lambda g_{\mu\nu}=8\pi GT_{\mu\nu}.
i.e. \Lambda should not be confused with
T!
There is a resolution of this huge fine tuning problem, in the theory http://www.kluweronline.com/oasis.htm/5092775, the field equation requires a moderate false vacuum density
in vacuo dependent on the curvature of space-time.
T_v is the trace of the Einstein Frame Vacuum energy momentum tensor and which in this theory is required to be generally non-zero by Equation (166). In this case I therefore suggest that there is a false vacuum made up of contributions of zeropoint energy from every quantum matter field which has a natural renormalised ‘cut-off’ E_{max} determined, and therefore limited, by the above solutions to the local gravitational equations.
(page 712)
There are two, (the gravitational and the scalar), field equations to be satisfied in SCC. In flat space-time their solutions converge consistently, however the presence of curvature separates the solutions slightly and consistency between them requires a small false vacuum energy density. It is this that is being probed by the Casimir force.
This is testable; the Casimir force should "bottom out" in the solar gravitational field with present experimental sensitivity somewhere between the orbits of Jupiter and Saturn.
What is true of the local spherically symmetric solution is also true of the cosmological solution thereby predicting a small and precisely determined cosmological false vacuum. The cosmological solution thus requires a moderate amount of "Dark Energy" (here identified as false vacuum) \Omega_{fv}=0.11.
The requirement on the Case 2 equation of state; Equation (213), together with Equation (231) mean the total cosmological pressure is given by
p=-\frac{1}{3} \rho_0 exp(H_0t)
To explain this it is again suggested that a component of the cosmological pressure and density is made up of false vacuum. That is there is a ‘remnant’ vacuum energy made up of contributions of zero-point energy from every mode of every quantum field which would have a natural energy ‘cut-off’ E_{max} which in the cosmological case is determined, and limited, by the solution to the cosmological equations.
(page 725)
Garth
