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Relevance of vacuum energy or quintessence in astrophysics and cosmology

Present level of knowledge and research activity

(at the beginning of the project)

Observations:
Recent cosmological tests give strong arguments for the presence of a non-zero repulsive cosmological constant, L>0. The „concordance“ models of the observations of the fluctuations of the microwave cosmic background and the measurements of the Hubble constant favor the parabolic model of the Universe, deserved by the inflationary paradigm [1, 2]. The parabolic model with a zero cosmological constant remains strongly disfavored in comparison with the parabolic model including a repulsive cosmological constant, according to an analysis of the new globular cluster dating and baryon abundance constraints [3].  Direct geometrical tests treating statistics of gravitational lensing, measurements of the angular size of some standard objects, and galaxy number counts, can put strong limits on the allowed value of the cosmological constant. Results from the statistics of the gravitational lensing of quasars and active galactic nuclei limit the contribution of the vacuum energy density, i.e., the repulsive cosmological constant, up to 66% of the critical energy density characterizing the parabolic Universe which causes a negative pressure of vacuum leading to acceleration of the Universe. The data of the high-redshift supernovae indicate a negative decceleration parametr, giving a direct evidence for the accelerating recent Universe. The most recent results from the Wilkinson Microwave Anisotropy Probe confirm all the previous results [4].

It is very important to understand the role of the effective repulsive cosmological constant in the Universe, i.e., in the cosmological models, and in astrophysical situations. On the other hand, in the framework of superstring theories, anti-de Sitter spacetimes play an important role [5]. Therefore, it is also interesting to obtain information on the influence of an attractive cosmological constant (L < 0) in astrophysical situations, especially on the structure of black-hole backgrounds, and on properties of other compact objects.

Theory:
Inflationary cosmology has become the crucial cornerstone of modern cosmology. It is the first theory enabling predictions about the structure of the Universe on large scales, based on causal physics. Developments of the inflationary cosmology opened up an  extremely promising way for connecting fundamentals particle physics with experiment and observation. There is a wide variety of different scenarios of the inflationary Universe ranging from the basic Guth’s model through Linde’s chaotic inflation to the string inflationary models. The crucial ingredient of the inflation cosmology is the presence of an inflation field with properties similar to those of vacuum energy, or, equivalently, to an effective cosmological constant. Recent cosmological tests indicate that a nonzero repulsive cosmological constant, or an analogous notion of a quintessence, has to be invoked in order to explain the present Universe. Therefore, the recent state of the Universe is dominated by a dark energy with properties very similar to the inflation field relevant at the very early stages of the expansion of the Universe, although they differ significantly by energy-density scales.

The vacuum energy is not the only possibility to obtain a negative pressure and accelerating Universe. In fact, there is a plenty of possibilities of generating negative pressure, called quintessence (fifth element) [6, 7], giving accelerating Universe at its present state. The quintessence models are inspired by the ideas of the chaotic inflation [8], and they use fields that behave similar to vacuum energy, having negative pressure, but their energy density is not fixed, as in the case of vacuum energy. Moreover, quantum approach to superstring M-theory could even lead to an idea of “evolving” vacuum energy (cosmological constant) [9, 10].

Therefore, it is worthwhile to consider also astrophysical relevance of quintessence fields or “evolving” vacuum energy and make studies of the influence of the non-zero cosmological constant in astrophysical and cosmological models, and compare them with the influence of various kinds of quintessence, or a “evolving” vacuum energy.

The standard cosmological models with a nonzero cosmological constant were extensively discussed from the theoretical point of view by Tolman [11], and in connection to observational cosmological parameters in [12], and recently in [13]. An Einstein-Straus-de Sitter model, representing a spherically symmetric mass condensation immersed in an expanding Friedman Universe with an effective cosmological constant has been constructed in [14, 15].

The role of a non-zero cosmological constant in astrophysical situations can be conveniently estimated by investigating its influence on black-hole (naked-singularity) spacetimes. For these purposes, the analysis of test-particle and photon motion is among the most fundamental techniques. Such motion is fully governed by the geodesics structure of the spacetime under consideration. Further, the curvature of the spacetime can be demonstrated conveniently by using embedding diagrams of 2-dimensional, appropriately chosen, spacelike surfaces into 3-dimensional Euclidean space ¾ a very well known example is the Schwarzschild „throat“ [12]. In order to understand astrophysical phenomena present in extremely strong gravitational fields of black holes, and other extremely compact objects, it can be useful to study embedding diagrams of both the ordinary space geometry and the optical reference geometry, which enables a natural „Newtonian“ concept of gravitational and inertial forces, and reflects some hidden properties of the test-particle motion [16].

In the Czech Republic, such studies were extensively realized by our group in Opava, and by complementary studies of the Prague group of Prof. J. Bičák, concentrated on radiative spacetimes with nonzero cosmological constant.


[1] J. P. Ostriker and P. J. Steinhart. Nature, 377:600, 1995.
[2] L. M. Krauss and M. S. Turner. General Relativity Gravitation, 27:1137, 1995.
[3] L. M. Krauss, Astrophys. J., 501(2):461-466, 1998.
[4] D. N. Spergel et. al. First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. 2003. arXiv:astro-ph/0302209v3, accepted by the ApJ.
[5] A. Sen. Developments in superstring theory. In A. Astbury, D. Axen, and J. Robinson, editors, 29th International Conference on High Energy Physics, Vancouver, 23-29 July 1998, Singapore, 1999. World Scientific.
[6] R. R. Caldwell et al. Cosmological imprint of an energy component with general equation of state. Phys. Rev. Lett., 80(8):1582, 1998.
[7] L. Wang et al. Cosmic concordance and quintesence. Astrophys. J., 530(1):17-35, 2000.
[8] A. D. Linde. Particle Physics and Inflationary Cosmology. Gordon and Breach, New York, 1990.
[9] J. Ellis et al. Time-Dependent Vacuum Energy Induced by D-Particle Recoil. Gen. Relativity Gravitation, 32(5):943, 2000. arXiv: gr-gc/9810086.
[10] J. Ellis et al. "Is Nothing Sacred? Vacuum Energy, Supersymmetry and Lorentz Breaking from Recoiling D branes". arXiv: gr-gc/0005100, May 2000.
[11] R. C. Tolman. Relativity, Thermodynamics, and Cosmology. The Clarendon Press, Oxford, 1969.
[12] C. W. Misner et al. Gravitation. Freeman, San Francisco 1973.
[13] G. Börner. The Early Universe. Springer-Verlag, Berlin-Heidelberg-New York, 1993.
[14] Z. Stuchlík. Bull. Astronom. Inst. Czechoslovakia, 34(3):129-149, 1983.
[15] Z. Stuchlík. Bull. Astronom. Inst. Czechoslovakia, 35(4):205-215, 1984.
[16] M. A. Abramowicz. Monthly Notices Roy. Astronom. Soc., 256(4):710-718, 1992.

Basic ideas of our research plan in the proposed area

Inflationary cosmology has become the crucial cornerstone of modern cosmology. It is the first theory enabling predictions about the structure of the Universe on large scales, based on causal physics. Developments of the inflationary cosmology opened up an extremely promising way for connecting fundamental physics with experiment and observation. There is a wide variety of different scenarios of the inflationary Universe ranging from the basic Guth’s model through Linde’s chaotic to the string inflationary models. The crucial ingredient of the inflationary cosmology is the presence of an inflation field with properties similar to those of vacuum energy, or, equivalently, to an effective cosmological constant. Recent observational data indicate that the Universe at the present time entered an accelerated expansion induced by an effective repulsive cosmological constant that can be explain by a positive vacuum energy, or by slowly rolling, quintessential scalar field. The acceleration mechanism is the same for both inflation field in the very beginning of the Universe and a quintessential field in the current Universe. The inflation fields decay is giving rise to the standard decelerated expansion of the Universe described by the Big Bang model. The behavior of the quintessential fields is the key to the fate of our Universe. Therefore, the most important question of present physics is: what is the driving force of our accelerating Universe and what are its properties. We want to understand manifestations of the effective repulsive cosmological constant in astrophysically relevant situations, its influence on black holes (naked singularities), mass configurations, cosmic microwave radiation, etc., thus helping to find answers to the fundamental questions of the properties of the driving force of our accelerating Universe.