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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 HausdorffColombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff 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 exist the ghostdriven acceleration of the univers hidden in cosmological constant. In order to obtain desired physical result we apply the canonical Pauli-Villars regularization up to .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 , i.e., fs.m fg.m , mc, eff, effc 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. Content 1.Introduction. 2.1.The formulation of the cosmological constant problem. 2.2. Zel’dovich approach by using Pauli-Villars regularization revisited. 2.3. Dark matter nature. A common origin of the dark energy and dark matter phenomena. 3.Pauli-Villars ghosts as physical dark matter. 3.1.Pauli-Villars renormalization of 4.New physical interpretation. 3.2. Pauli–Villars renormalization of QED3.New physical interpretation. 3.2.1.Pauli–Villars renormalization of QED3.What is wrong with Pauli–Villars renormalization of QED3. 3.2.2.New physical interpretation Pauli–Villars ghost fields. 3.3.High covariant derivatives renormalization as Pauli–Villars renormalization of non-Abelian gauge theories.New physical interpretation. 3.4.What is the physical significance of Pauli-Villars renormalization? 4.OFT in a ghost sector via dimensional regularization. 4.1.Dimensional renormalization via Colombeau generalized functions. 4.2.The scalar theory 4 in a ghost sector. 4.3.Quantum electrodynamics in a ghost sector. 4.4.Quantum chromodynamics in a ghost sector. 4.5.Quantum chromodynamics in a ghost sector via Colombeau generalized functions. 4.6.The general structure of the R-operation via Colombeau generalized functions. 4.7.Renormalization Group in a ghost sector. 4.8.Dimensional regularization and the MSscheme in a ghost sector. 5.Renormalizability-of-Higher-Derivative-Quantum-Gravity. 6.Hausdorff-Colombeau measure and associated negative Hausdorff-Colombeau dimensions.Fractal spacetime with negative Hausdorff-Colombeau dimension. 6.1. Fractional Integration in negative dimensions. 6.2.Hausdorff measure and associated positive Hausdorff dimension. 6.3.Hausdorff-Colombeau measure and associated negative Hausdorff dimension. 7. Scalar field theory in spacetime with negative Hausdorff-Colombeau dimension. 7.1.Equation of motion and Hamiltonian. 7.2.Propagator in spacetime with negative-dimensions. 7.3.Green’s functions in spacetime with Hausdorff-Colombeau negative dimensions. 7.4.Saddle-Point Evaluation of the Path Integral in negative dimensions. 7.5.Power-counting renormalizability of P D scalar field theory in negative dimensions D . 7.6.Power-counting renormalizability of Einstein gravity in negative dimensions. 7.7.Power-counting renormalizability of Ho rava gravity in negative dimensions. 8.The solution cosmological constant problem. 8.1.Einstein-Gliner-Zel’dovich vacuum with tiny Lorentz invariance violation. 8.2.Zeropoint energy density corresponding to Gliner non-singular cosmology. 8.3. Zeropoint energy density in models with supermassive physical ghost fields. 9. Discussion and conclusions. 10.Conclusion. 1.Introduction 1.1.The cosmological constant problem and Quantum Field Theory in fractal spacetime with negative dimension. One of the greatest challenges in modern physics is to reconcile general relativity and elementary particles physics into a unified theory. Perhaps the most dramatic clash between the two theories lies in the cosmological constant problem [1-6] and in the problem of the Dark (i.e., non-luminous and non-absorbing) Matter nature is, arguably, the most widely discussed topic in contemporary particle physics.Naive predictions of vacuum energy from canonical quantum field theory predict a magnitude so high that the expansion of the Universe should have accelerated so quickly that no any structure could have formed. The predicted rate of acceleration resulting from vacuum energy is famously 120 orders of magnitude larger than what is observed. In order to avoid these difficultnes mentioned above we assume that:(i) physics of elementary particles essentially is separated into low/high energy ones, (ii) the standard notion of smooth spacetime is assumed to be altered at a high energy cutoff scale and a new treatment based on QFT in a fractal spacetime with negative dimension is used above that scale . In this paper we argue that Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions [15] gives high-energy cutoff on natural way.No one knows what dark energy is, but we need it to explain the discovered accelerated expansion of the Universe. The most elegant and natural solution is to identify dark energy with the energy of the quantum vacuum predicted by Quantum Field Theory, but the trouble is that QFT predicts the energy density of the vacuum to be orders of magnitude larger than the observed dark energy density: de 7. 5 10 27kg/m3. 1. 1. 1 Recall that it was stressed by Zeldovich [1] that quantum field theory generically demands that cosmological constant or, let us repeat, what is the same, vacuum energy is non-vanishing.Summing the zero-point energies of all normal modes of some quantum field of mass m up to a wave number cut-off /c2 m, QFT yields [1],[5] a vacuum energy density vac 0 p d3p p2 m2 p 4 . 1. 1. 2 1.2. Sources of Vacuum Energy It is not excluded experimentally that the number of fermionic and bosonic species in Nature are the same. Moreover it is practically a necessity, because otherwise vacuum energy density would be infinite. Still the masses of bosons and corresponding fermions are different and, with arbitrary relations between their masses, only the leading term, which diverges as the fourth power of the integration limit, would be canceled out. However in some supersymmetric theories with spontaneous symmetry breaking there may be specific relations between masses of different fields which ensure the compensation not only of the leading term but also quadratically and logarithmically divergent terms. This looks as a very strong argument in favor of such models. However the finite terms are not compensated. Moreover in global supersymmetric theories finite contributions into ρvac must be nonzero and by the order of magnitude they are equal to vac susy msusy 4 1. 2. 1 where msusy is the scale of supersymmetry breaking. It is known from experiment that msusy 100 GeV. Correspondingly vac susy 108 GeV, i.e. 55 orders of magnitude larger than the permitted upper bound. In more advanced supersymmetric theories which include gravity (the so called supergravity or local supersymmetry) the condition of non-vanishing vacuum energy in the broken symmetry phase is not obligatory. However, if one does not take a special care, the value of vacuum energy in unbroken supergravity models is typically about mPl 4 1076 GeV. One can choose in principle the parameters in such a way that this contribution into ρvac is compensated down to zero with the accuracy 10 123 but this demands a fantastic fine-tuning. One more source of vacuum energy is the energy of the scalar (Higgs) field in the theories with spontaneous symmetry breaking. 1.3.New Model of ”Nullification” of Vacuum Energy Several possible approaches to the problem of vacuum energy have been discussed in the contemporary literature, for the review see ref. [5]. They can be roughly devided into four different groups: (1) Modification of gravity on large scales. (2) Anthropic principle. (3) Symmetry leading to ρvac 0. (4) Adjustment mechanism. (5) Hidden nonstandard matter sector and corresponding symmetry leading to ρvac 0. 1.A modification of gravity at large scales should be done in such a way that the general covariance, which ensures vanishing of the graviton mass, is preserved, energy momentum tensor is covariantly conserved, and simultaneously the vacuum part of this tensor, which is proportional to gμ ,does not gravitate. This is definitely not an easy thing to do. Possibly due to this reasons there is no satisfactory model of this kind at the present time. 2.Anthropic principle states that the conditions in the universe must be suitable for life, otherwise there would be no observer that could put a question why the universe is such and not another. With cosmological constant which is as large as predicted by natural estimates in quantum theory, life of our type is definitely impossible. Still this point of view does not look very appealing. The situation is similar to the one that existed in the Friedmann cosmology before inflationary resolution of the fundamental cosmological problems has been proposed. There is one more difficulty in the implimenttion of the anthropic principle. Even if we assume that it is effective, there are n

journal of physics. conference series

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