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We introduce Hausdorff-Colombeau measure in respect with negative fractaldimensions. Axiomatic quantum field theory in spacetime with negative fractaldimensions is proposed.Spacetime is modelled as a multifractal subset of$R^{4}$ with positive and negative fractal dimensions.The cosmological constantproblem arises because the magnitude of vacuum energy density predicted byquantum field theory is about 120 orders of magnitude larger than the valueimplied by cosmological observations of accelerating cosmic expansion. Wepointed out that the fractal nature of the quantum space-time with negativeHausdorff-Colombeau dimensions can resolve this tension. The canonical QuantumField Theory is widely believed to break down at some fundamental high-energycutoff $E$ and therefore the quantum fluctuations in the vacuum can be treatedclassically seriously only up to this high-energy cutoff. In this paper weargue that Quantum Field Theory in fractal space-time with negativeHausdorff-Colombeau dimensions gives high-energy cutoff on natural way. Inorder to obtain disered physical result we apply the canonical Pauli-Villarsregularization up to $E$. It means that there exist the ghost-drivenacceleration of the univers hidden in cosmological constant.

Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions.The solution cosmological constant problem