Quantum gravity in Heisenberg representation and self-consistent theory of gravitons in macroscopic spacetime

The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically equivalent to the operator equations of quantum theory of gravity with canonical rules of quantization of the gravitational and ghost fields. In its operator formulation, the theory can be used to calculate the graviton S-matrix as well as to describe the quantum evolution of macroscopic system of gravitons in the non-stationary Universe or in the vicinity of relativistic objects. In the S-matrix case, the standard results are obtained. For problems of the second type, the original Heisenberg equations of quantum gravity are converted to a self-consistent system of equations for the metric of the macroscopic spacetime and Heisenberg operators of quantum fields. It is shown that conditions of the compatibility and internal consistency of this system of equations are performed without restrictions on the amplitude and wavelength of gravitons and ghosts. The status of ghost fields in the various formulations of quantum theory of gravity is discussed.Comment: 15 pages; v2: Expanded explanation of the reasons why the vast majority of papers on the quantum theory of gravitons published in 1977-2008 is erroneou

Dark Energy from graviton-mediated interactions in the QCD vacuum

Adopting the hypothesis about the exact cancellation of vacuum condensates contributions to the ground state energy in particle physics to the leading order in graviton-mediated interactions, we argue that the observable cosmological constant can be dynamically induced by an uncompensated quantum gravity correction to them after the QCD phase transition epoch. To start with, we demonstrate a possible cancellation of the quark-gluon condensate contribution to the total vacuum energy density of the Universe at temperatures $T<100$ MeV without taking into account the graviton-mediated effects. In order to incorporate the latter, we then calculate the leading-order quantum correction to the classical Einstein equations due to metric fluctuations induced by the non-perturbative vacuum fluctuations of the gluon and quark fields in the quasiclassical approximation. It has been demonstrated that such a correction to the vacuum energy density has a form $\varepsilon_{\Lambda}\sim G \Lambda_{\rm QCD}^6$, where $G$ is the gravitational constant, and $\Lambda_{\rm QCD}$ is the QCD scale parameter. We analyze capabilities of this approach based on the synthesis between quantum gravity in quasiclassical approximation and theory of non-perturbative QCD vacuum for quantitative explanation of the observed Dark Energy density.Comment: 21 pages, a discussion of cosmological evolution of the \Lambda-term has been added; published versio

On a possible compensation of the QCD vacuum contribution to the Dark Energy

We suggest one of the possible ways to compensate the large negative quantum-topological QCD contribution to the vacuum energy density of the Universe by means of a positive constant contribution from a cosmological Yang-Mills field. An important role of the exact particular solution for the Yang-Mills field corresponding to the finite-time instantons is discussed. An interesting connection of the compensation mechanism to the color confinement in the framework of instanton models has been pointed out. Besides the $\Lambda_{\rm QCD}$ scale, this proposal relies on one yet free dimensionless normalisation constant which cannot be fixed by the perturbative QCD theory, and thus should be fine-tuned for the exact compensation to hold.Comment: 10 pages, typos corrected, comments on fine-tuning and QCD confinement added; published versio

Composite scalar Dark Matter from vector-like SU(2)SU(2) confinement

A toy-model with $SU(2)_{\rm TC}$ dynamics confined at high scales $\Lambda_{\rm TC}\gg 100$ GeV enables to construct Dirac UV completion from the original chiral multiplets predicting a vector-like nature of their weak interactions consistent with electroweak precision tests. In this work, we investigate a potential of the lightest scalar baryon-like (T-baryon) state $B^0=UD$ with mass $m_B\gtrsim 1$ TeV predicted by the simplest two-flavor vector-like confinement model as a Dark Matter (DM) candidate. We show that two different scenarios with the T-baryon relic abundance formation before and after the electroweak (EW) phase transition epoch lead to symmetric (or mixed) and asymmetric DM, respectively. Such a DM candidate evades existing direct DM detection constraints since its vector coupling to $Z$ boson absents at tree level, while one-loop gauge boson mediated contribution is shown to be vanishingly small close to the threshold. The dominating spin-independent (SI) T-baryon--nucleon scattering goes via tree-level Higgs boson exchange in the $t$-channel. The corresponding bound on the effective T-baryon--Higgs coupling has been extracted from the recent LUX data and turns out to be consistent with naive expectations from the light technipion case $m_{\tilde \pi}\ll \Lambda_{\rm TC}$. The latter provides the most stringent phenomenological constraint on strongly-coupled $SU(2)_{\rm TC}$ dynamics so far. Future prospects for direct and indirect scalar T-baryon DM searches in astrophysics as well as in collider measurements have been discussed.Comment: 17 pages, 14 figures; an extra figure added, discussion of mass splitting improved, minor corrections, conclusions unchange

Vector-like technineutron Dark Matter: is a QCD-type Technicolor ruled out by XENON100?

We continue to explore a question about the existence of a new strongly coupled dynamics above the electroweak scale. The latter has been recently realized in the simplest consistent scenario, the vector-like (or chiral-symmetric) Technicolor model based upon the gauged linear sigma-model. One of the predictions of a new strong dynamics in this model, the existence of stable vector-like technibaryon states at a TeV scale, such that the lightest neutral one could serve as a Dark Matter candidate. Here, we consider the QCD-type Technicolor with SU(3)_TC confined group and one SU(2)_W doublet of vector-like techniquarks and test this model against existing Dark Matter astrophysics data. We show that the spin-independent Dirac technineutron-nucleon cross section is by far too large and ruled out by XENON100 data. We conclude that vector-like techniquark sectors with an odd group of confinement SU(2n+1)_TC, n=1,2,... and with ordinary vector-like weak SU(2)_W interactions are excluded if the technibaryon number is conserved. We discuss a possible generic TC scenario with a technibaryon sector interacting via an extra vector SU(2)_V other than the standard weak SU(2)_W and consider immediate implications for the cosmological evolution and freeze out of heavy relic technineutrons.Comment: 30 pages, 4 figures; extra clarification and motivation for the VLTC scenario has been made; minor correction

Chiral-Symmetric Technicolor with Standard Model Higgs boson

Most of the traditional Technicolor-based models are known to be in a strong tension with the electroweak precision tests. We show that this serious issue is naturally cured in strongly coupled sectors with chiral-symmetric vector-like gauge interactions in the framework of gauged linear \sigma-model. We discuss possible phenomenological implications of such non-standard chiral-symmetric Technicolor scenario in its simplest formulation preserving the Standard Model (SM) Higgs mechanism. For this purpose, we assume the existence of an extra technifermion sector confined under extra SU(3)_TC at the energy scales reachable at the LHC, \Lambda_TC ~ 0.1-1 TeV, and interacting with the SM gauge bosons in a chiral-symmetric (vector-like) way. In the framework of this scenario, the SM Higgs vev acquires natural interpretation in terms of the condensate of technifermions in confinement in the nearly conformal limit. We study the influence of the lowest lying composite physical states, namely, technipions, technisigma and constituent technifermions, on the Higgs sector properties in the SM and other observables at the LHC. We found out that the predicted Higgs boson signal strengths in \gamma\gamma, vector-boson VV* and fermion ffbar decay channels can be sensitive to the new strongly-coupled dynamics and are consistent with the current SM-like Higgs boson observations in the limit of relatively small Higgs-technisigma mixing. At the same time, the chiral-symmetric Technicolor provides us with rich technipion phenomenology at the LHC, and its major implications are discussed in detail.Comment: 47 pages, 28 figures; a discussion of naturalness and quartic Higgs-TC coupling in the suggested model has been added; the version accepted to Phys. Rev.

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.Comment: 6 pages, REVTeX