Can the fluctuations of the quantum vacuum solve the cosmological
  constant problem?
  The cosmological constant problem arises because the magnitude of vacuum
energy density predicted by quantum mechanics is about 120 orders of magnitude
larger than the value implied by cosmological observations of accelerating
cosmic expansion. Recently, some of the current authors proposed that the
stochastic nature of the quantum vacuum can resolve this tension [Q, Wang, Z.
Zhu, and W. G. Unruh, Phys. Rev. D 95, 103504, 2017]. By treating the
fluctuations in the vacuum seriously and allowing fluctuations up to some
high-energy cutoff at which Quantum Field Theory is believed to break down, a
parametric resonance effect arises that leads to a slow expansion and
acceleration. In this work, we thoroughly examine the implications of this
proposal by investigating the resulting dynamics. First, we improve upon
numerical calculations in the original work and show that convergence issues
had overshadowed some important effects. Correct calculations reverse some of
the conclusions in [Q. Wang, Z. Zhu, and W. G. Unruh, Phys. Rev. D 95, 103504,
2017], however the premise that parametric resonance can explain a very slowly
accelerating expansion appears to remain sound. After improving the resolution
and efficiency of the numerical tests, we explore a wider range of cutoff
energies, and examine the effects of multiple particle fields. We introduce a
simple model using the Mathieu equation (a prototypical example of parametric
resonance), and find that it closely matches numerical results in regimes where
its assumptions are valid. Using this model, we extrapolate to find that in a
universe with 28 bosonic fields and a high-energy cutoff 40 times higher than
the Planck energy, the acceleration would be comparable to what is observed.
