Can the fluctuations of the quantum vacuum solve the cosmological constant problem?

Abstract

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.