COBE and global topology: an example of the application of the identified circles principle

The significance to which the cosmic microwave background (CMB) observations by the satellite COBE can be used to refute a specific observationally based hypothesis for the global topology (3-manifold) of the Universe is investigated, by a new method of applying the principle of matched circle pairs.
Moreover, it is shown that this can be done without assuming Gaussian distributions for the density perturbation spectrum.
The Universe is assumed to correspond to a flat Friedmann–Lemaître model with a zero value of the cosmological constant. The 3-manifold is hypothesized to be a 2-torus in two directions, with a third axis larger than the horizon diameter. The positions and lengths of the axes are determined by the relative positions of the galaxy clusters Coma, RX J1347.5−1145 and CL 09104+4109, assumed to be multiple topological images of a single, physical cluster.
If the following two assumptions are valid: (i) that the error estimates in the COBE DMR data are accurate estimates of the total random plus systematic error; and (ii) that the temperature fluctuations are dominated by the naı¨ve Sachs–Wolfe effect; then the distribution of the temperature differences between multiply imaged pixels is significantly wider than the uncertainty in the differences, and the candidate is rejected at the 94 per cent level.
This result is valid for either the 'subtracted' or 'combined' Analysed Science Data Sets, for either 10° or 20° smoothing, and is slightly strengthened if suspected contaminated regions from the galactic centre and the Ophiuchus and Orion complexes are removed.     

Horizon problem and inflation

We show that, the part of the universe that is observable today (in principle), could not have evolved out of a domain which was causally connected in the past. This and other issues related to horizon problem in inflationary models are discussed.     

The Lyman α forest in a truncated hierarchical structure formation

The Lyman α forest provides important constraints on the smoothness of the Universe on large scales. We calculate the flux distribution along the line of sight to quasars in a universe made of randomly distributed clumps, each of them with a Rayleigh–L'evy fractal structure with dimension D <2. We consider the probability distribution function of the normalized flux in the line of sight to quasars. We illustrate that the truncated clustering hierarchy model with D <2 shows far too many voids along the line of sight to quasars compared with the observed flux distribution and the distribution in a cold dark matter model. This supports the common view that on large scales the Universe is homogeneous, rather than fractal-like.     

The evolution of our local cosmic domain: effective causal limits

The causal limit usually considered in cosmology is the particle horizon, delimiting the possibilities of causal connection in the expanding Universe. However, it is not a realistic indicator of the effective local limits of important interactions in space–time. We consider here the matter horizon for the Solar system, i.e. the comoving region which has significantly contributed matter to our local physical environment. This lies inside the effective domain of dependence , which (assuming the universe is dominated by dark matter along with baryonic matter and vacuum-energy-like dark energy) consists of those regions that have had a significant active physical influence on this environment through effects such as matter accretion and acoustic waves. It is not determined by the velocity of light c , but by the flow of matter perturbations along their world lines and associated gravitational effects. We emphasize how small a region the perturbations which became our Galaxy occupied, relative to the observable universe – even relative to the smallest scale perturbations detectable in the cosmic microwave background radiation. Finally, looking to the future of our local cosmic domain, we suggest simple dynamical criteria for determining the present domain of influence and the future matter horizon . The former is the radial distance at which our local region is just now separating from the cosmic expansion. The latter represents the limits of growth of the matter horizon in the far future.     

Parastatistics and the equation of state for the early Universe

The equation of state for an ideal mixture of relativistic quantum gases obeying any (para-)statistics is given. Recursion formulae are obtained for the distribution function and correlations are analysed. The equation of state can be applied to the early Universe, allowing the quarks to be treated either as coloured fermions or (unequivalently) as parafermions of order 3. In the latter case, they exhibit a tendency of aggregate into triads by a mere statistical effect.     

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.     

Slow rotational perturbations of Robertson-Walker universes

A slow rotation perturbation of Robertson-Walker universes filled with perfect fluid has been investigated. It is found that the unit-four vector of perfect fluid hasno angular velocity in the perturbed cosmological models. The slow rotation which is related to the dragging of the local inertial frames, is compatible only with the cases of positive and negative curvatures of the cosmological universe. The intrinsic velocity vector field of the Universe isexpanding as well asshearing.     

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.     

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。     

The expansive nondecelerative universe

(a) Hubble's discovery of the expansion of the Universe makes it possible to choose unambiguously from the models described by Friedmann's equations of universe dynamics. (b) From the present temperature of the cosmic microwave background radiation, the specific entropy in the matter era and the model properties of the expansive nondecelerative universe, we can determine the present parameters of our Universe with deviations smaller than 2.2%.     

Cosmological parameters and cosmic topology

Geometry constrains but does not dictate the topology of the three-dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides determining the geometry, the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of setting constraints on the density parameters associated with dark matter (Ω_m) and dark energy  (Ω_Λ)  . By assuming the Poincaré dodecahedral space as the circles-in-the-sky detectable topology of the spatial sections of the Universe, we re-analyse the constraints on the density parametric plane  Ω_m–Ω_Λ  from the current Type Ia supernova plus X-ray gas mass fraction data, and show that a circles-in-the sky detection of the dodecahedral space topology gives rise to strong and complementary constraints on the region of the density parameter plane currently allowed by these observational data sets.     

Current models of the observable consequences of cosmic reionization and their detectability

A number of large current experiments aim to detect the signatures of the cosmic reionization at redshifts z > 6. Their success depends crucially on understanding the character of the reionization process and its observable consequences and designing the best strategies to use. We use large-scale simulations of cosmic reionization to evaluate the reionization signatures at redshifted 21-cm and small-scale cosmic microwave background (CMB) anisotropies in the best current model for the background universe, with fundamental cosmological parameters given by Wilkinson Microwave Anisotropy Probe three-year results. We find that the optimal frequency range for observing the 'global step' of the 21-cm emission is 120–150 MHz, while statistical studies should aim at 140–160 MHz, observable by GMRT. Some strongly non-Gaussian brightness features should be detectable at frequencies up to ∼190 MHz. In terms of sensitivity-signal trade-off relatively low resolutions, corresponding to beams of at least a few arcminutes, are preferable. The CMB anisotropy signal from the kinetic Sunyaev–Zel'dovich effect from reionized patches peaks at tens of μK at arcminute scales and has an rms of ∼1 μK, and should be observable by the Atacama Cosmology Telescope and the South Pole Telescope. We discuss the various observational issues and the uncertainties involved, mostly related to the poorly known reionization parameters and, to a lesser extend, to the uncertainties in the background cosmology.     

The statistics of weak lensing at small angular scales: probability distribution function

Weak gravitational lensing surveys have the potential to probe mass density fluctuation in the Universe directly. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by modelling the statistics of the underlying density field in the highly non-linear regime. We propose a new method to model the complete probability distribution function of the convergence field as a function of smoothing angle and source redshift. The model relies on a hierarchical ansatz for the behaviour of higher order correlations of the density field. We compare our results with ray-tracing simulations and find very good agreement over a range of smoothing angles. Whereas the density probability distribution function is not sensitive to the cosmological model, the probability distribution function for the convergence can be used to constrain both the power spectrum and cosmological parameters.     

Radiocarbon evidence of the global stochasticity of solar activity

An estimate of the dimension of the attractor of the dynamic system responsible for solar activity is obtained from the time series of carbon 14 experimental data (4300 BC to 1950 AD). According to this estimate the attractor is a fractal, in shape close to a 3-torus. The attractor's trajectories characterizing the evolution of the magnetic field exhibit irregular long-term behaviour.     

Topology and geometry of the CfA2 redshift survey

We analyse the redshift space topology and geometry of the nearby Universe by computing the Minkowski functionals of the Updated Zwicky Catalogue (UZC). The UZC contains the redshifts of almost 20 000 galaxies, is 96 per cent complete to the limiting magnitude m _Zw=15.5, and includes the Center for Astrophysics (CfA) Redshift Survey (CfA2). From the UZC we can extract volume-limited samples reaching a depth of 70  h ⁻¹ Mpc before sparse sampling dominates. We quantify the shape of the large-scale galaxy distribution by deriving measures of planarity and filamentarity from the Minkowski functionals. The nearby Universe shows a large degree of planarity and a small degree of filamentarity. This quantifies the sheet-like structure of the Great Wall, which dominates the northern region (CfA2N) of the UZC. We compare these results with redshift space mock catalogues constructed from high-resolution N -body simulations of two cold dark matter (CDM) models with either a decaying massive neutrino ( τ CDM) or a non-zero cosmological constant (ΛCDM). We use semi-analytic modelling to form and evolve galaxies in these dark matter‐only simulations. We are thus able, for the first time, to compile redshift space mock catalogues which contain galaxies, along with their observable properties, rather than dark matter particles alone. In both models the large-scale galaxy distribution is less coherent than the observed distribution, especially with regard to the large degree of planarity of the real survey. However, given the small volume of the region studied, this disagreement can still be a result of cosmic variance, as shown by the agreement between the ΛCDM model and the southern region of CfA2.     

Non-random phases in non-trivial topologies

We present a new technique for constraining the topology of the Universe. The method exploits the existence of correlations in the phases of the spherical harmonic coefficients of the cosmic microwave background (CMB) temperature pattern associated with matched pairs of circles seen in the sky in universes with non-trivial topology. The method is computationally faster than all other statistics developed to hunt for these matched circles. We applied the method to a range of simulations with topologies of various forms and on different scales. A characteristic form of phase correlation is found in the simulations. We also applied the method to preliminary CMB maps derived from WMAP , but the separation of topological effects from e.g. foregrounds is not straightforward.     

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.     

Signatures for a cosmic flux of magnetic monopoles

Any early Universe phase transition occurring after inflation has the potential to populate the Universe with relic magnetic monopoles. Observations of galactic magnetic fields, as well as observations matched with models for extragalactic magnetic fields, lead to the conclusion that monopoles of mass 10¹⁵ GeV are accelerated in these fields to relativistic velocities. We explore the possible signatures of a cosmic flux of relativistic monopoles impinging on the Earth. The electromagnetically induced signatures of monopoles are reliable. The hadronically induced signatures are highly model-dependent. Among our findings are (i) the electromagnetic energy losses of monopoles continuously initiate a protracted shower of small intensity; (ii) monopoles may traverse the Earth’s diameter, making them a probe of the Earth’s interior structure; (iii) in addition to the direct monopole Cherenkov signal presently employed, a very attractive search strategy for monopoles is detection of their coherent radio-Cherenkov signal produced by the charge-excess in the e⁺–e⁻ shower––in fact, Cherenkov-detectors have the potential to discover a monopole flux (or limit it) several orders of magnitude below the theoretical Parker limit of 10⁻¹⁵ cm⁻² s⁻¹ sr⁻¹; (iv) it is conceivable (but not compelling) that bound states of colored monopoles may be the primary particles initiating the air showers observed above the GZK cutoff.     

Reionization: characteristic scales, topology and observability

Recently the numerical simulations of the process of reionization of the universe at z>6 have made a qualitative leap forward, reaching sufficient sizes and dynamic range to determine the characteristic scales of this process. This allowed making the first realistic predictions for a variety of observational signatures. We discuss recent results from large-scale radiative transfer and structure formation simulations on the observability of high-redshift Ly-α sources. We also briefly discuss the dependence of the characteristic scales and topology of the ionized and neutral patches on the reionization parameters.     

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.