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

Abstract

The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum field theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdorff- Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff Λ* and therefore the quantum fluctuations in the vacuum can be treated classically seriously only up to this high-energy cutoff. In this paper we argue that Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions gives high-energy cutoff on natural way. We argue that there exists hidden physical mechanism which cancel divergences in canonical QED4, QCD4, Higher-Derivative - Quantum-Gravity, etc. In fact we argue that corresponding supermassive Pauli-Villars ghost fields really exists. It means that there exists the ghost-driven acceleration of the univers hidden in cosmological constant. In order to obtain desired physical result we apply the canonical Pauli-Villars regularization up to Λ*. This would fit in the observed value of the dark energy needed to explain the accelerated expansion of the universe if we choose highly symmetric masses distribution between standard matter and ghost matter below that scale Λ*,i.e., fs.m (µ) ≈ −fg.m (µ), µ = mc, µ ⩽ µeff, µeff < Λ*/c. The small value of the cosmological constant explaned by tiny violation of the symmetry between standard matter and ghost matter. Dark matter nature also explaned using a common origin of the dark energy and dark matter phenomena.