Abstract
We introduce Hausdorff-Colombeau measure in respect with negative fractal dimensions. Axiomatic quantum field theory in spacetime with negative fractal dimensions is proposed.Spacetime is modelled as a multifractal subset of $R^{4}$ with positive and negative fractal dimensions.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 $E$ 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. In order to obtain disered physical result we apply the canonical Pauli-Villars regularization up to $E$. It means that there exist the ghost-driven acceleration of the univers hidden in cosmological constant.
Highlights
The cosmological constant problem arises because the magnitude of vacuum energy density predicted by the Quantum Field Theory is about 120 orders of magnitude larger the value implied by cosmological observations of accelerating cosmic expansion
In this paper we argue that the Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions gives high-energy cutoff on natural way
In order to obtain the 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 the scale Λ∗, i.e., fs.m ( μ ) − fg.m ( μ= ), μ mc, μ ≤ μeff, μeff c < Λ∗ The small value of the cosmological constant is explained by tiny violation of the symmetry between standard matter and ghost matter
Summary
The cosmological constant problem arises at the intersection between general relativity and quantum field theory, and is regarded as a fundamental unsolved problem in modern physics. In this paper the ghost sector is considered as physical mechanism which acts only on a function f (μ ) in Equations (43) It means that there exists the ghost-driven acceleration of the universe hidden in cosmological constant Λ. The requirement that the graviton propagator behaves like p−4 for large momenta makes it necessary to choose the indefinite-metric vector space over the negative-energy states These negative-norm states cannot be excluded from the physical sector of the vector space without destroying the unitarity of the S matrix, for their unphysical behavior may be restricted to arbitrarily large energy scales Λ∗ by an appropriate limitation on the renormalized masses m2 and m0. 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
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