The Copernican principle in compact space–times

Copernicus realized that we are not at the centre of the Universe. A universe made finite by topological identifications introduces a new Copernican consideration: while we may not be at the geometric centre of the Universe, some galaxy could be. A finite universe also picks out a preferred frame: the frame in which the universe is smallest. Although we are not likely to be at the centre of the Universe, we must live in the preferred frame (if we are at rest with respect to the cosmological expansion). We show that the preferred topological frame must also be the comoving frame in a homogeneous and isotropic cosmological space–time. Some implications of topologically identifying time are also discussed.     

On the exact solutions and invariant rays of the phase plane in Brans-Dicke theory

On the basis of the model properties of the expansive nondecelerative universe, present temperature of cosmic microwave background and specific entropy in the era of matter, the present parameters of our Universe may be exactly determined.     

The Friedmann universe and the world potential

In Section 1 of the paper the energy equation of the Friedmann universe, when matter dominates over radiation, is discussed. It is known that the value of the world potential is constant everywhere in the Universe, despite the pulsation motion of the Universe or a possible transformation of pulsation energy into matter or vice versa. The condition for the Universe being closed is deduced. Furthermore, the possibility to define the mass-energy of the Universe is discussed; and the conclusion is arrived at that the mass-energy of the Universe relative to an observer in the non-metric space outside the Universe is equal to zero; i.e. the Universe originated as a vacuum fluctuation. Finally, the view-point of an external observer is described. Such an observer can claim that our closed Universe is a black hole in a non-metric empty space. Besides, the differences between such a black hole and the astrophysical black holes are indicated.In Section 2 the origin of the gravitational force retarding the expansion is discussed, using the properties of the relativistic gravitational potential. In contradiction to Section 1, the view-point of an inner observer (inside the Universe) is used here. It is concluded that the boundary of the closed Universe is an unlocalizable potential barrier.In Section 3 of the paper the apparent discrepancy between Mach's principle and the general theory of relativity is resolved. The solution is based on the fact that, for the Euclidean open universe, the concept of mass is related to the potential of the background equal to –1, but the concept of the mass-energy is related to the zero-potential of the non-metric background. Because the universe is open and a potential barrier (a boundary of the universe) can be localized-i.e. is geometrically existing — by solution of the field equation, we have to refer to the background with zero-potential. The principal idea of the solution is then that the zero-density means the density of mass-energy, when simultaneously the mass density is equal to the critical value for which the Robertson-Walker metric becomes the Euclidean metric of the Minkowski (i.e., flat) space-time. Further a generalization of Newton's law of inertia is formulated, and the properties of nullgeodesics are touched upon. As a conclusion it is stated that this paper and the two previous ones (see Voráek, 1979a, b)de facto express Mach's principle.     

Parameters of the ultrastable expansive non-decelerative Universe and hypothetical mass of the electron neutrino

On the basis of model properties of the expansive non-decelerative universe, the temperature at the end of the radiation era and of the present temperature of cosmic microwave background spectrum, the present parameters of our Universe can be determined.From model properties of the expansive non-decelerative universe and the temperature at the end of the radiation era follow: the hypothetical mass value of electron neutrino and the hypothetical values of the final parameters of the creative-expansive evolutionary phases of ultrastable expansive non-decelerative universes.     

The Wilkinson Microwave Anisotropy Probe (WMAP) confirmed the model of our observed relativistic universe

The Wilkinson Microwave Anisotropy Probe (WMAP) confirmed the model of flat expansive homogeneous and isotropic relativistic universe, which describes the properties of our observed flat expansive homogeneous and isotropic relativistic Universe in the first (linear, Newtonian or classical-mechanical) approximation.     

Do we live in the universe successively dominated by matter and antimatter?

We wonder if a cyclic universe may be dominated alternatively by matter and antimatter. Such a scenario demands a mechanism for transformation of matter to antimatter (or antimatter to matter) during the final stage of a big crunch. By giving an example, we have shown that in principle such a mechanism is possible. Our mechanism is based on a hypothetical repulsion between matter and antimatter, existing at least deep inside the horizon of a black hole. When universe is reduced to a supermassive black hole of a small size, a very strong field of the conjectured force might create (through a Schwinger type mechanism) particle-antiparticle pairs from the quantum vacuum. The amount of antimatter created from the vacuum is equal to the decrease of mass of the black hole and violently repelled from it. When the size of the black hole is sufficiently small, the creation of antimatter may become so fast, that matter of our Universe might be transformed to antimatter in a fraction of second. Such a fast conversion of matter into antimatter may look as a Big Bang. Our mechanism prevents a singularity; a new cycle might start with an initial size more than 30 orders of magnitude greater than the Planck length, suggesting that there is no need for inflationary scenario in Cosmology. In addition, there is no need to invoke CP violation for explanation of matter-antimatter asymmetry. Simply, our present day Universe is dominated by matter, because the previous universe was dominated by antimatter.     

The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic Universe in the light of the Wilkinson Microwave Anisotropy Probe (WMAP) observations

The Wilkinson Microwave Anisotropy Probe (WMAP) confirmed the model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe with the total zero mass (energy), which describes the properties of our observed expansive homogeneous and isotropic relativistic Universe in the first (linear, Newtonian or classical-mechanical) approximation.     

A hypothetical end of creative-expansive evolution phase of the expansive non-decelerative universe

The hypothetical final parameters of the Universe result from the model properties of the expansive non-decelerative universe and properties of the hypothetical primordial black holes.     

Light propagation in a universe with spatial inhomogeneities

A light propagation in a universe which is homogeneous only in average systematically differs from a light propagation in a strictly homogeneous Universe. We demonstrate a link between this effect and the general theory of transport phenomenon in random media. The effective spatial curvature of a universe which is homogeneous only in average is introduced. This curvature is governing a light propagation in such universe. We show that the effective spatial curvature is lower than the average curvature. It implies that a universe with critical mean density looks like a space with negative curvature.     

Boltzmann constant in the model of expansive non-decelerative universe

From the observed present parameters of the Universe and the model properties of an expansive non-decelerative universe it results that the value of Boltzmann's constant (coefficient)k does not change only before the end of radiation era, but also in the matter era; with the increase of gauge factora, it decreases as (a ^–1)^1/4.     

A note on the problem of choosing a model of the Universe,I

The author considers the possibility of transition of the current universe expansion to contraction. The considerations are based on the fact that a homogeneous Universe is structured into non-homogeneous units, the latter expanding as a whole. An analysis of the effects of these wholes on further development shows that in the future contractions may occur only locally; however, the current spatial expansion of the Universe cannot be replaced by a global contraction.     

宇宙在大尺度上是均匀的吗?

宇宙中的物质在大尺度上是均匀分布的,还是保持着分形分布的特点,成为近年来观测宇宙学中争论的一个热点。Ｐｉｅｔｒｏｎｅｒｏ等人认为直到目前观测到的最大尺度（≈１０００ｈ＾－１Ｍｐｃ）星系的分布仍保持Ｄ≈２的分形结构,而大多数坚持标准模型的宇宙学家都认为宇宙在大尺度上是均匀分布的。宇宙物质在大尺度上是否均匀分布,将由下一代的红移巡天的结果来判断。     

Dynamics of viscous universe

The dynamics of the viscous Robertson-Walker universe is presented using the phase variables method. Connection between violence of the strong energy condition and the behaviour of the Universe near the singularity is discussed.     

The number of photons for tolman-type metric

A Tolman-like Scenario is described in which due to the direct coupling of electromagnetic fields to space-time curvature, the total number of photons comprised in the universe at a given epoch changes as the Universe expands.     

Constraints on cosmological parameters from recent measurements of cosmic microwave background anisotropy

A key prediction of cosmological theories for the origin and evolution of structure in the Universe is the existence of a 'Doppler peak' in the angular power spectrum of cosmic microwave background (CMB) fluctuations. We present new results from a study of recent CMB observations which provide the first strong evidence for the existence of a 'Doppler peak' localized in both angular scale and amplitude. This first estimate of the angular position of the peak is used to place a new direct limit on the curvature of the Universe, corresponding to a density of Ω = 0.7^+0.8_−0.5, consistent with a flat universe. Very low-density 'open' universe models are inconsistent with this limit unless there is a significant contribution from a cosmological constant. For a flat standard cold dark matter dominated universe we use our results in conjunction with big bang nucleosynthesis constraints to determine the value of the Hubble constant as H ₀ = 30 − 70 km s⁻¹ Mpc⁻¹ for baryon fractions Ω_b = 0.05 to 0.2. For H ₀ = 50 km s⁻¹ Mpc⁻¹ we find the primordial spectral index of the fluctuations to be n  = 1.1 ± 0.1, in close agreement with the inflationary prediction of n  ≃ 1.0.     

The effects of radiative transfer on the reionization of an inhomogeneous universe

Assuming simple dynamics for the growth of density fluctuations, we implement six-dimensional (6D) radiative transfer calculations to elucidate the effects of photon propagation during the reionization of an inhomogeneous universe. The ionizing sources are postulated to be AGN-like in this paper. The present simulations reveal that radiative transfer effects are still prominent considerably after the percolation epoch, in which patchy ionized regions connect with each other. In other words, owing to the collective opacity, the Universe does not become perfectly transparent against ionizing radiation even though strongly self-shielded regions disappear. It turns out that the inhomogeneity of the medium enhances the opacity effects and delays the end of reionization. Owing to such radiative transfer effects, the reionization in an inhomogeneous universe proceeds fairly slowly, in contrast to the prompt reionization in a homogeneous universe, and as a result the surface of reionization is not so sharply edged, but highly uneven. As a signature of the uneven surface of reionization, the cosmic IR background (CIB) radiation, which is produced by Ly photons resulting from radiative recombination, could exhibit strong anisotropies, reflecting the amplitude of density fluctuations at the reionization era. The predicted CIB intensity lies on a level of possible detection by forthcoming IR space telescope facilities.     

The study of topology of the Universe using multipole vectors

We study a multipole vector-based decomposition of cosmic microwave background data in order to search for signatures of a multiconnected topology of the universe. Using 10⁶ simulated maps, we analyse the multipole vector distribution on the sky for the lowest order multipoles together with the probability distribution function of statistics based on the sum of the dot products of the multipole vectors for both the simply connected flat universe and universes with the topology of a 3 torus. The estimated probabilities of obtaining lower values for these statistics as compared to the 5-yr Wilkinson Microwave Anisotropy Probe data indicate that the observed alignment of the quadrupole and octopole is statistically favoured in a 3-torus topology where at least one dimension of the fundamental domain is significantly shorter than the diameter of the observable Universe, as compared to the usual standard simply connected universe. However, none of the obtained results is able to clearly rule out the latter (at more than 97 per cent confidence level). Multipole vector statistics do not appear to be very sensitive to the signatures of a 3-torus topology if the shorter dimension of the domain becomes comparable to the diameter of the observable Universe. Unfortunately, the signatures are also significantly diluted by the integrated Sachs–Wolfe effect.     

Global momentum loss in a non-expanding Universe

Applying the basic concepts of general relativity to the global motion of a particle in a mass-filled universe leads to a loss of momentum relative to the rest frame of the Universe. This loss is caused by the different running times of the gravitational interaction quanta exchanged with masses in front and behind the moving particle, if the signal velocity is limited to the speed of light. Due to this gravitational viscosity of space, the energy of photons will be reduced with the time, and thus with the distance of the emitting source. This red shift is superimposed on the Doppler shift in an expanding universe. A discussion of the limiting case of vanishing expansion leads to predictions about mass and radius of the Universe. The value of the mass density in such a steady-state universe must be about three times the closing density discussed in Big-Bang theories. The existence of the gravitational viscosity casts severe doubts on all estimations of the age of the Universe derived from the red-shift data.     

Formation of a void and galaxies in a neutrino-dominated universe

The recent discovery of the large honeycomb structure of the Universe has triggered many models of the Universe dominated by dark matter. The neutrino-dominated universe is a favorable model for explaining the size of the large-scale structure and the dark matter of the larger scale than the galactic one. Our calculations on the evolution of density perturbations in a two-component universe composed of neutrinos and dissipative gas on a spherically-symmetric model have shown that the galactic scale does correlate the scale of a void of galaxies: if a neutrino has the mass of some tens eV, galaxies of the typical size form surrounding a typical void.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.