Stochastic density fluctuations in the radiation era of the Universe

The linear stochastic hydrodynamical equations of the radiation-matter-one-component fluid in the Universe before the recombination era are solved. The stochastic forces in the heat flux and the viscous stress tensor are described according the procedure of Landau and Lifshitz. In the case of a low density universe, where the effects of the thermal conductivity can be neglected with respect to the shear viscosity, we find analytical solutions of the dispersion relation for the different modes and of the density correlation function . At the very Jeans length, this density correlation function exhibits a linear (for very large times) or a cubic (for small times) time dependence instead of a frozen-in character of this special mode.     

The evolution of nonlinear hydrodynamical density fluctuations of the photon-plasma gas during the recombination era of the Universe

On the basis of the hydrodynamical equations of a two-component gas (photons and hydrogen with coupling via Thomson scattering) in the recombination era of the Universe (standard model), the evolution of the density perturbations up to second order are calculated. It is shown, that the generated second-order amplitudes of the density fluctuations of the matter reach values of the same order as the first-order amplitudes within only one tenth of the expansion time for fluctuations with wavelengths corresponding to 10⁷ M . Upper limits in the density fluctuations (for the gravitationally instable modes) up to which first-order calculations are valid, are given. This calculation indicates that the linear perturbation analysis is very restricted, especially at wavelengths near the lower limit of the Jeans length.The linear analysis would be a good approximation only for density fluctuations of the matter with the density contrast less than 10^–5–10^–4 at the recombination era. Therefore, a nonlinear analysis which is not based on a perturbation series is required for studying the evolution of the density perturbations, because for this we need a density contrast of 10^–2–10^–3 at the end of the recombination era.     

Quantifying dust and the ultraviolet radiation density in the local Universe

A sample of local galaxies for which far-infrared and ultraviolet fluxes are available is used to estimate the characteristic dust extinction in galaxies and to test whether standard dust properties are plausible. Assuming galaxies can be characterized by a single dust optical depth (certainly not valid for galaxies with a dominant starburst component), the infrared excess and ultraviolet colours of local galaxies are found to be consistent with normal Milky Way dust, with a mean value for   E ( B − V )  of 0.16. A significant fraction of the dust heating is caused by older, lower-mass stars, and this fraction increases towards earlier galaxy types.
Analysis of  ( F _FIR/ F _UV)  versus ultraviolet colour diagrams for starburst galaxies in terms of a simple screen dust model does not support a Calzetti (1997) rather than a Milky Way extinction law, though the absence of the expected strong 2200- Å feature in several galaxies with IUE spectra does show that more detailed radiative transfer models are needed – probably with nonspherical geometry.
A simple treatment in which the  100/60-μm  flux ratio is used to subtract the optically thick starburst contribution to the far-infrared radiation results in lower extinction estimates for the optically thin cirrus component, with a mean   E ( B − V )  of 0.10.
The ultraviolet luminosity density, corrected for dust extinction, is derived and a value for the local mean star formation rate inferred. This is consistent with previous estimates from ultraviolet surveys and from  Hα  surveys.     

Ionization feedback mechanism in the recombination era of the Universe

Within the cosmological standard models of the Universe, we inquire the 2-fluid radiation hydrodynamics during and before the recombination era. If we neglect all nonlinearities with exception of those contained in the coupling term between the two fluids via the degree of ionization, there exists a strong feedback mechanism on the instable modes which prevents them from growing if their relative amplitudes of the density contrast have values in the order of 10^–1–10^–2. The non-linear equations are numerically solved by adiabatic elimination technique used usually in self-organization problems. The effect depends very on the redshift z and become maximum atz1350. It depends also on the masses involved for the rangeM>10¹¹ M . The lowest limits in the amplitudes (10^–2) are imposed on the largest masses (10¹⁷ M ). In the range 10⁶M/M 10¹¹, the effect is independent of the mass.     

Momentum and energy transfer between plasma,hydrogen, and radiation during the recombination era of the Universe

It is assumed that during the recombination era the Universe is a fluid consisting of plasma, neutral hydrogen, and radiation interacting via the processes of photo-recombination, photo-ionization, and Thomson scattering. The corresponding mass exchanges between plasma and hydrogen and both the momentum and energy transfer are calculated near the hydrodynamical equilibrium. A perturbation in the hydrodynamical quantities is introduced and the corresponding dynamical equations are obtained as well.     

The estimation of the mean density in the Universe

The mean density of matter, as estimated from deep optical samples of galaxies, is too low to close the Universe. However, some additional considerations do not exclude such a possibility.     

The estimation of the mean density in the Universe

The mean density of matter, as estimated from deep optical samples of galaxies, is too low to close the Universe. However, some additional considerations do not exclude such a possibility.     

Hydrodynamical modes and gravitational instabilities in the Universe during the recombination era

We assume the Universe during the recombination era as a three-component fluid constituted by neutral hydrogen, plasma, and radiation; such fluids are coupled via the effects of photorecombination, photoionization, and Thomson scattering. The hydrodynamical modes are calculated and the relation with the gravitational instabilities is established. In addition to the well-known Jeans's instability modes two additional ones in the neighbourhood of 10¹³ M are obtained in the case of an open Universe.     

Deuterium, lithium and the density of the Universe

The main outcome of the primordial nucleosynthesis is the ability to account for the abundances of D, ³He, ⁴He and ⁷Li with the proper choice of the nuclear density parameter ω_B. The relative advantages/disadvantages of D and ⁷Li as the proper `baryometer' are discussed. In favour of D, the main arguments are the relative simplicity of the formation/destruction schema, but this is challenged by the large uncertainties on the choice of its actual `primordial' abundance and on the galactic evolution scheme. In favour of ⁷Li there are the confirmation of the so called `Spite plateau' and the observation of ⁶Li at the surface of at least one (may be two) Population II stars, but the paucity of such stars such as the possibility of scenarios in which the ⁷Li abundance could be affected even in these stars cannot be overlooked. This revised version was published online in July 2006 with corrections to the Cover Date.     

The average density of the Universe and the Regge law

We calculate the principal inertia moments of a three-dimensional mass distribution rotating with angular velocity in a self-gravitating homogeneous field with axial symmetry. We show that the angular momentumJ may, under certain conditions, be of the Regge-like type. These results are used to evaluate the mass and average density of the Universe.     

Small-scale fluctuations of relic radiation

Perturbations of the matter density in a homogeneous and isotropic cosmological model which leads to the formation of galaxies should, at later stages of evolution, cause spatial fluctuations of relic radiation. Silk assumed that an adiabatic connection existed between the density perturbations at the moment of recombination of the initial plasma and fluctuations of the observed temperature of radiation δT/T=δ _?m /3 _?m . It is shown in this article that such a simple connection is not applicable due to:

1. The long time of recombination;
2. The fact that when regions withM<10¹⁵ M _⊙ become transparent for radiation, the optical depth to the observer is still large due to Thompson scattering;
3. The spasmodic increase of δ _?m/?m in recombination.

As a result the expected temperature fluctuations of relic radiation should be smaller than adiabatic fluctuations. In this article the value of δT/T arising from scattering of radiation on moving electrons is calculated; the velocity field is generated by adiabatic or entropy density perturbations. Fluctuations of the relic radiation due to secondary heating of the intergalactic gas are also estimated. A detailed investigation of the spectrum of fluctuations may, in principle, lead to an understanding of the nature of initial density perturbations since a distinct periodic dependence of the spectral density of perturbations on wavelength (mass) is peculiar to adiabatic perturbations. Practical observations are quite difficult due to the smallness of the effects and the presence of fluctuations connected with discrete sources of radio emission.     

Relativistically induced instellar density fluctuations

The spectrum of cold electron density fluctuations induced by a relativistic electron gas is investigated and the results discussed in relation to the interstellar medium.     

Constraining the Spatial Curvature of the Local Universe with Deep Learning

We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161strong gravitational lensing systems,whose distances are calibrated from the Pantheon compilation of type Ⅰa supernovae using deep learning.To investigate the possible influence of mass model of the lens galaxy on constraining the curvature parameter Ω_k,we consider three different lens models.Results show that a flat Universe is supported in the singular isothermal sphere(S...     

From beyond the Big Bang to the end of the Planck era of the Universe

The state ante beyond the Big Bang is described as a non-metrical space devoid of time, and some circumstances are discussed. It is also concluded that the non-metrical space outside our closed Universe is identical with the stateante.Further, the conclusion is made that the virtual pairs production cannot occur in a space without any metric; then, the virtual pairs (the matter) and space had to arise together within the Planck era of the Universe, where it was not possible to arrange events in order of time. Consequently, the origin of the virtual pairs and of space could be mutually determined and synchronous. The sum of binding energies of the pairs at the same time both already were and only were becoming the binding gravitational energy of the closed Universe. The non-locality phenomenon (the Einstein-Rosen-Podolski paradox) is then considered as a possible explanation for the causal interconnection of the Universe.Another possible mechanism is proposed, namely the quantum tunneling effect, this is but combined with the special conditions existing during the Planck era. Moreover, the creational process is assumed to be an optimal quantum phenomenon possibly governed by as yet unknown laws. The role of the Planck density is analyzed and the conclusion is made that probably only one option exists for the results of the creational process: the closed quasi-Euclidean universe. The causal interconnection of our Universe would then only be apparent.In the final section a philosophical problem is found: in the stateante the law of probability was valid without the existence of the objects necessary in order for the law to actually exist; thus, it would be a law of divine character.     

Quantum fluctuations in radiation dominated anisotropic cosmology

Using the metric conformal transformation and simple path integral, Feynman propagator method, for computing its quantum fluctuations, we analyse the radiation dominated anisotropic Bianchi Type I cosmology. We proceed to show that the quantum conformal fluctuations diverge at the classical spacetime singularity, suggesting that a singularity free solution can exist in anisotropic cosmology in the quantum regime. Since the December 1998 issue of this journal was delayed, we were able to include this paper in this issue.     

Nonconformal fluctuations in radiation dominated anisotropic cosmology

Using simple path integral, Feynman propagator method and the relation between conformal timeη and scale factor Τ, we investigate the non-conformal quantum fluctuations (of expansion and shear) and axisymmetric singularity case in radiation dominated anisotropic cosmology. We show that near the classical singularity the quantum fluctuations tend to diverge. Since the December 1998 issue of this journal was delayed, we were able to include this paper in this issue.     

Small scale entropy and adiabatic density perturbations — Antimatter in the Universe

Fluctuations of all scales are equally interesting from the point of view of the characteristics of the singular state and not only those which led to the formation of astronomical objects such as clusters of galaxies, separate galaxies, globular clusters and quasars. In this article estimates are given of the homogeneity of the overall density of hot plasma and the relation between the quantity of baryons and antibaryons at early stages of evolution of the Universe. These estimates are made for small scales, considerably smaller than the scale of the astronomical objects enumerated above. Considerations about the energy balance of hot plasma and distortions of the spectrum of relic radiation due to dissipation of density fluctuations of matter are used for these estimates. The corrected upper limit to early energy injection is given. In our preceding paper (Sunyaev and Zeldovich, 1970) this upper limit was underestimated. Difficulties with a model of the Universe which is symmetric in baryon charge are noted.     

Bianchi type-I Universe filled with disordered radiation in self-creation cosmology

A spatially homogeneous and anisotropic cosmological model in self-creation theory of gravitation proposed by Barber is obtained when the source of the gravitational field is a perfect fluid with disordered radiation and the metric is of Bianchi type-I. Some physical properties of the model are discussed.     

Time evolution of the unstable two-fluid density fluctuations in Robertson-Walker Universes

We consider density fluctuations of a two-fluid model consisting of hydrogen plasma and radiation prior to the cosmic hydrogen recombination. As investigation method that of the dispersion relations is applied, which have been derived from the general-relativistic sound-wave equations taking into account the coupling between plasma and radiation carefully. We obtain growing unstable acoustic modes within the mass range 2 · 10⁶ M _⊙ < M < 6 · 10 ¹² M _⊙. In a second step the coupled differential equations for the amplitudes of the unstable modes are integrated numerically with respect to time where the integration extends from the initial time prior to the hydrogen recombination up to the present time. We find a significant increase of the amplitudes up to 4 orders of magnitude, if the Universe is described by a cosmological model with a positive cosmological constant (Λ ? 2,2 · 10^-56 cm^-2) and a positive curvature (Lemaître-Universe) without an essential amount of cold dark matter. We conclude that the existence of galaxies confirm these statements.