Vacuum fluctuation, microcyclic universes, and the cosmological constant problem

Abstract

We point out that the standard formulation of the cosmological constant problem itself is problematic since it is trying to apply the very large scale homogeneous cosmological model to very small (Planck) scale phenomenon. At small scales, both the spacetime and the vacuum stress energy are highly inhomogeneous and wildly fluctuating. This is a version of Wheeler's "spacetime foam". We show that this "foamy" structure would produce a large positive contribution to the average macroscopic spatial curvature of the Universe. In order to cancel this contribution to match the observation, the usually defined effective cosmological constant $\lambda_{\mathrm{eff}}=\lambda_B+8\pi G\langle\rho\rangle$ has to take a large negative value. The spacetime dynamics sourced by this large negative $\lambda_{\mathrm{eff}}$ would be similar to the cyclic model of the universe in the sense that at small scales every point in space is a "micro-cyclic universe" which is following an eternal series of oscillations between expansions and contractions. Moreover, if the bare cosmological constant $\lambda_B$ is dominant, the size of each "micro-universe" would increase a tiny bit at a slowly accelerating rate during each micro-cycle of the oscillation due to the weak parametric resonance effect produced by the fluctuations of the quantum vacuum stress energy tensor. In this way, the large cosmological constant generated at small scales is hidden at observable scale and no fine-tuning of $\lambda_B$ to the accuracy of $10^{-122}$ is needed. This at least resolves the old cosmological constant problem and suggests that it is the quantum vacuum fluctuations serve as the dark energy which is accelerating the expansion of our Universe.