On the effect of collisional transitions on the cosmological hydrogen recombination spectrum

We study the effect of collisional 2s ? 2p transitions on the populations of the 2s and 2p states at the cosmological hydrogen recombination epoch and on the intensity of the recombination Hα line. Our calculations are based on a simple model hydrogen atom with four bound states (1s, 2s, 2p, and the n = 3 level with an equilibrium distribution in sublevels with different orbital quantum numbers l). We show that collisions do not lead to an equilibrium distribution in sublevels of the n = 2 level. The relative change in the cosmological Hα line intensity due to collisional transitions does not exceed 10^?3.     

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

We compute the spectral distortions of the cosmic microwave background (CMB) arising during the epoch of cosmological hydrogen recombination within the standard cosmological (concordance) model for frequencies in the range 1–3500 GHz. We follow the evolution of the populations of the hydrogen levels including states up to principle quantum number   n = 30  in the redshift range  500 ≤ z ≤ 3500  . All angular momentum substates are treated individually, resulting in a total number of 465 hydrogen levels. The evolution of the matter temperature and the fraction of electrons coming from He  ii are also included. We present a detailed discussion of the distortions arising from the main dipolar transitions, for example Lyman and Balmer series, as well as the emission due to the two-photon decay of the hydrogen 2s level. Furthermore, we investigate the robusteness of the results against changes in the number of shells considered. The resulting spectral distortions have a characteristic oscillatory behaviour, which might allow experimentalists to separate them from other backgrounds. The relative distortion of the spectrum exceeds a value of 10⁻⁷ at wavelengths longer than 21 cm. Our results also show the importance of detailed follow-up of the angular momentum substates, and their effect on the amplitude of the lines. The effect on the residual electron fraction is only moderate, and mainly occurs at low redshifts. The CMB angular power spectrum is changed by less than 1 per cent. Finally, our computations show that if the primordial radiation field is described by a pure blackbody, then there is no significant emission from any hydrogen transition at redshifts greater than   z ∼ 2000  . This is in contrast to some earlier works, where the existence of a 'pre-recombination' peak was claimed.     

Matter temperature during cosmological recombination

The temperature of the atomic matter in the Universe is held to that of the cosmic background radiation until decoupling at   z ∼ 100  . After this, it cools faster than the radiation [  ∝ (1 + z )²  rather than  (1 + z )  ] and would have fallen to about 20 mK today if astrophysical feedback processes had not heated up the interglactic medium. We show how the derivative of the Compton coupling equation helps numerically to follow the decoupling process.     

Nonresonant effects and hydrogen transition line shape in cosmological recombination problems

Data on the fluctuations in cosmic microwave background (CMB) radiation, whose accuracy is expected to increase in the immediate future, allow the cosmological recombination of atomic hydrogen and its interaction with the CMB radiation to be studied. Nonresonant effects play an important role in these recombination processes. We consider the quantum-mechanical foundations of the nonresonant processes and present our calculations for the differential two-photon decay rates of the 3s and 3d levels in the hydrogen atom. This article was submitted by the authors in English.     

CMB recombination lines of hydrogen: The differential spectrum

We have calculated the distortions of the cosmic microwave background (CMB) spectrum in the wavelength range 2–50 cm due to the superposition of the CMB hydrogen recombination radiation in subordinate lines. The level populations were determined by numerically solving the equation of recombination kinetics together with the statistical equilibrium equations for a 60-level model hydrogen atom. The relative distortions are ≈10^?7–10^?6, with their wavelength dependence having a low-contrast, wavy pattern. However, the contrast increases severalfold and becomes pronounced when passing to the differential distortion spectrum. We study the dependence of the distortions on cosmological parameters.     

Phase information and the evolution of cosmological density perturbations

The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical techniques. Using a toy model of one-dimensional perturbations evolving under the Zel'dovich approximation as an initial motivation, we develop a statistic that quantifies the information content of the distribution of phases. Using numerical simulations beginning with more realistic Gaussian random-phase initial conditions, we show that the information content of the phases grows from zero in the initial conditions, first slowly and then rapidly when structures become non-linear. This growth of phase information can be expressed in terms of an effective entropy. Gaussian initial conditions are a maximum entropy realization of the initial power spectrum; gravitational evolution decreases the phase entropy. We show that our definition of phase entropy results in a statistic that explicitly quantifies the information stored in the phases of density perturbations (rather than their amplitudes), and that this statistic displays interesting scaling behaviour for self-similar initial conditions.     

Spherically symmetric cosmological perturbations in the de Donder gauge

Cosmological perturbations on a F-R-W background are considered in a modified de Donder gauge. To guarantee the energy-momentum conservation for the perturbations in the de Donder gauge a compatibility condition is obtained. Finally we present the basic equations for the propagation of spherically symmetric perturbations. These equations are the basis for investigating the influence of cosmological epoches on the growing of density contrasts.     

Validity of the 'conservation law' in the evolution of cosmological perturbations

It is shown that the 'conservation law' for metric fluctuations with long wavelengths is indeed applicable for growing modes of perturbations, which are of interest in cosmology, in spite of recent criticism. This is demonstrated both by general arguments and by presenting an explicitly solvable toy model for the evolution of metric perturbations during inflation.     

Perturbations of ionization fractions at the cosmological recombination epoch

The development of perturbations of number densities of ions and electrons during the recombination epoch is analysed. The equations for relative perturbations of ionization fractions were derived from the system of equations for accurate computation of the ionization history of the early Universe. It is shown that strong dependence of ionization and recombination rates on the density and temperature of plasma provides the significant deviations of amplitudes of ionization fractions relative to perturbations from those of baryon matter density adiabatic perturbations. Such deviations are most prominent for cosmological adiabatic perturbations of scales larger than the sound horizon at the recombination epoch. The amplitudes of relative perturbations of number densities of electrons and protons at the last scattering surface exceed by a factor of ≃5 the amplitude of the relative perturbation of baryons total number density: for helium ions this ratio reaches a value of ≃18. For subhorizon cosmological perturbations, these ratios appear to be essentially smaller and depend on oscillation phase at the moment of decoupling. These perturbations of number densities of ions and electrons at the recombination epoch do not contribute to the intrinsic plasma temperature fluctuations but cause the 'corrugation' of the last scattering surface in optical depth,  δ z _dec/( z _dec+ 1) ≈−δ_b/3  , at scales larger than the sound horizon. It may result in notable changes of pre-calculated values of the cosmic microwave background polarization pattern at several degrees of angular scales.     

Mond,dark matter and the cosmological constant

A possible connection between MOND (Modification of Newtonian Dynamics) proposed as an alternative hypothesis to dark matter in galaxies and clusters and a residual cosmological constant term dominating cosmological dynamics in a = 1 universe is explored.     

Rotational perturbations of cosmological viscous-fluid Universe with zero-mass scalar field

Certain new analytic solutions for the rotational perturbations of the Robertson-Walker universe are found out to substantiate the possibility of the existence of a rotating viscous universe with zero-mass scalar field. The values for (r, t) which is related to the local dragging of inertial frames are investigated. In all the cases the rotational velocity is found to decay with time. Except for perfect dragging the scalar field is found to have a damping effect on the rotation of matter. The damping effect is found to be roughly analogous to viscosity. In some solutions it is found that the scalar field may exist only during a time period in the course of evolution of the Universe.     

Spherically symmetric cosmological perturbations in flat space-time theory of gravitation

The previously developed equations for the propagation of perturbations in a homogeneous, isotropic cosmological model are studied. At the beginning of the universe spherically symmetric inhomogeneities can arise. In the dust dominated universe the growth of spherically symmetric perturbations is given in form of infinite series. The increase of the inhomogeneity is faster than in general relativity.     

Spherically symmetric cosmological perturbations in the de Donder gauge (III)

The evolution of a perfect fluid perturbation is considered in the radiation dominated period and in the dust epoch. In the investigation we make use of the general formalism developed in previous papers.It turns out that the evolution tendency is predicted by the state of the cosmic background. The radiation dominated universe does not stimulate growing processes of the perturbation, whereas the dust dominated universe causes a growing tendency of small perfect fluid formations. The results of this work are in accordance with these obtained by the present writers in a previous work.     

Spherically symmetric cosmological perturbations in the de Donder gauge (II)

In the framework of a previously developed procedure the evolution of small spherically symmetric perturbations in a homogeneous R-W-F universe is analyzed. It turns out that the evolution tendency is mainly predicted by the state of the cosmic background. In the radiation dominated period the universe does not stimulate growing processes, a perturbation will be in a frozen state or it will diffuse. It is found that a dust dominated universe stimulates the perturbation masses to grow. The rate of this cosmic affected growing process is proportional to (R)^–1/2 (R being the scale factor). Consequently almost all galaxies were formed at the beginning of the dust dominated era.     

Theory of linear cosmological perturbations in flat space-time theory of gravitation

Covariant linear cosmological perturbations are considered in flat space-time theory of gravitation. The background metric is not altered. The perturbed energy-momentum is given. The basic equations for the propagation of the perturbations are presented. The perturbed equations for a homogeneous, isotropic universe are stated.     

Implications of a cosmological term coupled to matter

The possibility that the cosmological term is proportional toGU, whereG is the gravitational coupling andU is the mass density of the universe is proposed and discussed. WithG = constant, a cosmological model is obtained, which avoids the flatness and horizon problems and does not affect the well known predictions on the cosmic helium abundance which come from standard big bang cosmology. In such model, the deceleration parameter is a null constant, there is matter creation process throughout the universe at the rate 10^–47 g cm^–3 s^–1 and the cosmological term varies asH ² =t ^–2, whereH is the Hubble constant andt is the cosmic time.The possibility of a time-dependentG is then considered. The main consequence of this is that there is a mass creation process on the local scale; the rate of mass creation inside a body of massM is dM/dt =M H. In Section 6 it is suggested that the new matter might be in the form of neutrinos. This suggestion leads to an interesting consequence in celestial mechanics: the radius of a binary system should depend on time according to the nature of the components (the radius of a binary star should decrease, the radius of a planet-moon system should expand, and the orbital radius of a planet should stay constant).