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Dark Energy in the Universe


Field Models of Dark Energy in the Universe

Tech Area / Field

  • PHY-PFA/Particles, Fields and Accelerator Physics/Physics
  • SAT-AST/Astronomy/Space, Aircraft and Surface Transportation

3 Approved without Funding

Registration date

Leading Institute
Kyrgyz-Russian Slavonic University, Kyrgyzstan, Bishkek


  • Waseda University, Japan, Tokyo\nTufts University, USA, MA, Medford\nFreie Universität Berlin / Institut fuer Theoretische Physik, Germany, Berlin\nUniversity of Toronto / Canadian Institute for Theoretical Astrophysics, Canada, ON, Toronto\nInternational Center for Relativistic Astrophysics (ICRA), Italy, Rome

Project summary

Recent observations of Type Ia supernovae indicating an accelerating Universe at the present epoch. Such accelerated expansion is caused by presence of some antigravitating substance which acts as repulsive force in the Universe. The immediate observation of this substance is sufficiently hard due to its weak interaction with electromagnetic radiation. In this connection this substance was called dark energy. The true nature of dark energy remains a puzzle till now.

For description of dark energy, it seems natural to consider the models which were used at examination of the early Universe. In fact, during that epoch the Universe also passed through the stage of accelerated expansion (inflation). The simplest method of getting such type of accelerated expansion consists in introduction into gravitational equations of a constant cosmological lambda-term. The well-known problem of an initial cosmological singularity and mysterious unique properties of our Universe - homogeneity and isotropy, causal connectedness of the Universe - were solved actually with use of the cosmological lambda-term which has near Planck value in the models of the very early Universe.

At the subsequent evolution of the early Universe, this value decreases fast and the model transferred into the classical solution for the hot Friedmann model. This implies that the constant lambda-term for such evolution of the Universe is not suitable - it has non-constant values.

An achievement of the theory of the early Universe consists in physical substantiation of occurrence of such a lambda-term. The possible mechanism of liquidation of the singularity and realization of inflationary expansion of the Universe can be fulfilled by introduction of polarization effects of quantized fields in strongly curved space-time of the very early Universe. The mentioned investigations have shown that polarization effects for a cosmological model could be taken into account by introduction of corresponding nonlinear components into Einstein’s gravitational lagrangian. These components depended on invariants of Riemann and Ricci curvature and created the dynamical lambda-term which varied from the Planck value up to the extremely small value.

Consideration of semiclassical scalar fields on a background of the expanding Friedmann universe was also successful. The initial near Planck value of the energy density of these fields, concentrated mainly in the potential part, ensured inflationary expansion. The gradual transition of the energy into the kinetic part of these fields liquidated the dynamical lambda-term and filled the Universe by hot plasma.

These two directions could supplement each other and solved the basic problems of the theory of the very early Universe. One more direction of the account of polarization effects of quantized fields in strongly curved space-time of the very early Universe consists in introduction into Einstein's equations of the additional terms ensuring an invariance of the generalized equations relative to conformal transformations. This direction is intensively developing last years and is called conformal geometrodynamics.

Unexpected discovery of the accelerated expansion of the present Universe initiated searching the mechanisms of the current inflation. For its description, a number of terms are used: quintessence, dark energy, etc. At present there is no standard theory for explanation of this phenomenon. In the simplest theory, the whole set of observations (in the judgment of a number of experts) is described rather well by the simplest flat Friedmann cosmological model with cold dark matter Ωc≈0.3 and the constant lambda-term ΩΛ≈0.7. But the origin of the constant lambda-term has no substantiation still. The deep analysis of the observational data shows an existence of the dynamical lambda-term. It is natural that at the present stage the ideas from the known models in the theory of the early Universe are used for construction of corresponding cosmological models. It is necessary to speak here about the hypotheses of existence in the present Universe of different forms of fields which energy is capable to model the dynamical lambda-term.

Another phenomenological direction is related to modeling of quasihydrodynamical energy-momentum tensor. This direction is capable to explain the dynamics of the Universe after recombination and till now.

As independent direction at description of the quintessence in the present Universe, its modeling with use of different forms of nonlinear additional terms to Einstein’s lagrangian is picked out. Though in some cases such approach is mathematically equivalent to introduction of the scalar fields into classical gravitation, it is considered as independent and uses wide experience of mathematical analysis of the similar models in the theory of the very early Universe. In this direction a series of important results was obtained but there is no detailed comparison with the observations till now.

In this connection the aim of the present project consists in carrying out of investigations of the cosmological models within the framework of higher-order gravitational theories and the generalized gravitational equations invariant with respect to conformal transformations. At the present stage of examinations, these models are phenomenological and contain parameters which value should be chosen by comparison to one group of the observational data.

During realization of the project, it is supposed carrying out a detailed examination of the cosmological models within the framework of the higher-order gravitational theories. These models are obtained from consideration of the Einstein’s equations with the nonlinear terms depending on scalar curvature and Riemann invariants. Also, it is supposed to prolong the examinations of the conformal geometrodynamics which have been begun during realization of the ISTC Projects #KR-154 and #KR-677.

The Project meets the ISTC requirements as it:

  1. promotes the fundamental science development in countries of transitional economy;
  2. meets the principal ISTC goals, i.e. reorientation of weapons scientists to civil activities;
  3. this subject scope resolves the problem of integration of the Republic scientists into the international scientific community through cooperation with collaborators, attendance of international conferences, and participation in international research projects.

All the Project collaborators are worldwide leading specialists in the area of the Project research. So their consultations will be extremely important during the Project. For this purpose the following is suggested: exchange of information during the Project; assistance and financial support of the Project participants in attendance of international meetings (as it took place repeatedly during the previous Projects #KR-154 and #KR-677); joint symposiums and workshops.

The analytical and numerical methods for studying of the nonlinear and self-consistent problems will be used at realization of the Project. The scientific group has a long-term work experience both in the field of classical gravitation and at its modification with account of quantum effects in the early Universe. The group consists from researchers with wide work experience which participated in development of this direction since 1960th, and also from young researchers performing their scientific work in mentioned directions recently.


The International Science and Technology Center (ISTC) is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.


ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

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