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 [1]. 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. Firstly, 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 [1], 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.

Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

“…Therefore, in the literature such a route is usually regarded as to lead to unphysical predictions. It is worth mentioning in this regard that recent numerical calculations including 28 bosonic fields and based on the estimate of the stochastic fluctuations of the associated total quantum-vacuum energy density, rather than the energy density itself, are claimed to provide lower estimates and a resulting acceleration of the universe comparable to the observed one [72,73]. This type of studies should be regarded as complementary to the present quantum theory, although they differ from it for the following main reasons: 1) they are based on numerical calculations, and therefore are subject to the accuracy of the numerical codes actually implemented, while the theory proposed here is analytical; 2) they assume that the source of the universe expansion is the vacuum populated by bosonic fields, while in the present model the cosmological constant is shown to arise purely from quantum gravitational field with its quantum dynamics being predicted by CQG-theory, without needing to invoke any additional field; 3) they realize non-manifestly covariant solutions in which the coordinate time is singled out with respect to space coordinates, while the investigation based on CQG-theory preserves manifest covariance.…”

“…That this is indeed the case follows in fact by direct inspection of Eqs. (73), since the constraint equation (65) implies that…”

The Solution Cosmological Constant Problem

“…the vacuum can be treated classically seriously only up to this high-energy cutoff, see for example[15]. In this paper we argue that Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions[12] gives high-energy cutoff on natural way.…”

The Solution Cosmological Constant Problem. Quantum Field Theory in Fractal Space-Time with Negative Hausdorff-Colombeau Dimensions and Dark Matter Nature

“…Assumption 2 is well justified in the case of the traditional approach, because the contribution from zero-point fluctuations is on the order of 1 in Planck units and no other known contributions are as large thus, assuming no significant cancellation of terms (e.g. fine tuning of the bare cosmological constant ), the total eff should be at least on the order of the largest contribution [14]. (9.4) In contrary with standard Assumption1 in the case of the new approach introduced in this paper we assume that: (9.4.1) For simplisity though not necessary bare cosmological constant 0.…”