The power spectrum of number density perturbations of free electrons is obtained for the epoch of cosmological recombination of hydrogen. It is shown that amplitude of the electron perturbations power spectrum of scales larger than acoustic horizon exceeds by factor of 17 the amplitude of baryon matter density ones (atoms and ions of hydrogen and helium). In the range of the first and second acoustic peaks such relation is 18, in the range of the third one 16. The dependence of such relations on cosmological parameters is analysed too.
The main goal of this work is to calculate the contributions to the cosmological recombination spectrum due to bound-bound transitions of helium. We show that due to the presence of helium in the early Universe unique features appear in the total cosmological recombination spectrum. These may provide a unique observational possibility to determine the relative abundance of primordial helium, well before the formation of first stars. We include the effect of the tiny fraction of neutral hydrogen atoms on the dynamics of HeII -> HeI recombination at redshifts $z\sim 2500$. As discussed recently,…
We propose a method to study the epoch of reionization based on the possible observation of 2p--2s fine structure lines from the neutral hydrogen outside the cosmological H {\sc ii} regions enveloping QSOs and other ionizing sources in the reionization era. We show that for parameters typical of luminous sources observed at $z \simeq 6.3$ the strength of this signal, which is proportional to the H {\sc i} fraction, has a brightness temperature $\simeq 20 μK$ for a fully neutral medium. The fine structure line from this redshift is observable at $ν\simeq 1 \rm GHz$ and we discuss prospects for …
A development of perturbations of number densities of ions and electrons during 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 given by Seager et al. (1999,2000). 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 perturbations from ones of baryon matter density adiabatic perturbations. …
We have developed an improved recombination calculation of H, HeI, and HeII in the early Universe which involves a line-by-line treatment of each atomic level. We find two major differences compared with previous calculations. Firstly, the ionization fraction x_e is approximately 10% smaller for redshifts <~800, due to non-equilibrium processes in the excited states of H. Secondly, HeI recombination is much slower than previously thought, and is delayed until just before H recombines. We describe the basic physics behind the new results and present a simple way to reproduce our calculation. Th…
It is argued that large scale cosmic magnetic field could be generated in the primeval plasma slightly before hydrogen recombination. Non-zero vorticity, necessary for that, might be created by the photon diffusion in the second order in the temperature fluctuations. The resulting seed fields at galactic scale would be only 4 orders of magnitude smaller than the observed ones and with a mild galactic dynamo amplifying the seed fields by the factor $\sim 10^4$ an existence of coherent magnetic fields in galaxies may be explained.
The major theoretical limitation for extracting cosmological parameters from the CMB sky lies in the precision with which we can calculate the cosmological recombination process. Uncertainty in the details of hydrogen and helium recombination could effectively increase the errors or bias the values of the cosmological parameters derived from the Planck satellite, for example. Here we modify the cosmological recombination code RECFAST by introducing one more parameter to reproduce the recent numerical results for the speed-up of the helium recombination. Together with the existing hydrogen fudg…
In this paper we compute the emission coming from the direct recombination of free electrons to a given shell (n>=2) during the epoch of cosmological hydrogen recombination. This contribution leads to a total of one photon per recombined hydrogen atom and therefore a ~30-88% increase of the recombination spectrum within the frequency range 1 GHz<=nu<=100 GHz. In particular the Balmer-continuum emission increases the distortion at nu~ 690 GHz by ~92%. With our 100 shell calculations for the hydrogen atom we find that a total of ~5 photons per hydrogen atom are emitted when including all the bou…
Induced emission due to the presence of soft CMB photons slightly increases the two-photon decay rate of the 2s level of hydrogen defining the rate of cosmological recombination. This correspondingly changes the degree of ionization, the visibility function and the resulting primordial temperature anisotropies and polarization of the CMB on the percent level. These changes exceed the precision of the widely used CMBFAST and CAMB codes by more than one order of magnitude and can be easily taken into account.
A generation of magnetic fields from cosmological density perturbations is investigated. In the primordial plasma before cosmological recombination, all of the materials except dark matter in the universe exist in the form of photons, electrons, and protons (and a small number of light elements). Due to the different scattering nature of photons off electrons and protons, electric currents and electric fields are inevitably induced, and thus magnetic fields are generated. We present a detailed formalism of the generation of cosmological magnetic fields based on the framework of the well-establ…
We present Rico, a code designed to compute the ionization fraction of the Universe during the epoch of hydrogen and helium recombination with an unprecedented combination of speed and accuracy. This is accomplished by training the machine learning code Pico on the calculations of a multi-level cosmological recombination code which self-consistently includes several physical processes that were neglected previously. After training, Rico is used to fit the free electron fraction as a function of the cosmological parameters. While, for example at low redshifts (z<~900), much of the net change in…
In this thesis we focus on studying the physics of cosmological recombination and how the details of recombination affect the Cosmic Microwave Background (CMB) anisotropies. We present a detailed calculation of the spectral line distortions on the CMB spectrum arising from the Lyman-alpha and the lowest two-photon transitions in the recombination of hydrogen (H), and the corresponding lines from helium (He). The peak of these distortions mainly comes from the Lyman-alpha transition and occurs at about 170 microns, which is the Wien part of the CMB. The major theoretical limitation for extracti…
We derive the full set of second-order equations governing the evolution of cosmological perturbations, including the effects of the first-order electron number density perturbations, δ_e. We provide a detailed analysis of the perturbations to the recombination history of the universe and show that a perturbed version of the Peebles effective 3-level atom is sufficient for obtaining the evolution of δ_e for comoving wavenumbers smaller than 1Mpc^{-1}. We calculate rigorously the perturbations to the Lyαescape probability and show that to a good approximation it is governed by the local baryon …
After cosmological recombination, the primordial hydrogen gas decoupled from the cosmic microwave background (CMB) and fell into the gravitational potential wells of the dark matter. The neutral hydrogen imprinted acoustic oscillations on the pattern of brightness fluctuations due to its redshifted 21cm absorption of the CMB. Unlike CMB temperature fluctuations which probe the power spectrum at cosmic recombination, we show that observations of the 21cm fluctuations at z ~ 20-200 can measure four separate fluctuation modes (with a fifth mode requiring very high precision), thus providing a uni…
The cosmological recombination history of lithium, produced during Big--Bang nucleosynthesis, is presented using updated chemistry and cosmological parameters consistent with recent cosmic microwave background (CMB) measurements. For the popular set of cosmological parameters, about a fifth of the lithium ions recombine into neutral atoms by a redshift $z\sim 400$. The neutral lithium atoms scatter resonantly the CMB at 6708 Åand distort its intensity and polarization anisotropies at observed wavelengths around $\sim 300 μ$m, as originally suggested by Loeb (2001). The modified anistropies res…
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 GHz-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 $500\leq z\leq 3500$. All angular momentum sub-states 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 HeII…
A number of recent works in astronomy and cosmology have relied upon theoretical He I emissivities, but we know of no effort to quantify the uncertainties in the atomic data. We analyze and assign uncertainties to all relevant atomic data, perform Monte Carlo analyses, and report standard deviations in the line emissivities. We consider two sets of errors, which we call "optimistic" and "pessimistic." We also consider three different conditions, corresponding to prototypical Galactic and extragalactic H II regions and the epoch of cosmological recombination. In the extragalactic H II case, the…
The physical ingredients to describe the epoch of cosmological recombination are amazingly simple and well-understood. This fact allows us to take into account a very large variety of processes, still finding potentially measurable consequences. In this contribution we highlight some of the detailed physics that were recently studied in connection with cosmological hydrogen and helium recombination. The impact of these considerations is two-fold: (i) the associated release of photons during this epoch leads to interesting and unique deviations of the Cosmic Microwave Background (CMB) energy sp…
The physical ingredients to describe the epoch of cosmological recombination are amazingly simple and well-understood. This fact allows us to take into account a very large variety of processes, still finding potentially measurable consequences. In this contribution we highlight some of the detailed physics that were recently studied in connection with cosmological hydrogen recombination. The impact of these considerations is two-fold: (i) the associated release of photons during this epoch leads to interesting and unique deviations of the Cosmic Microwave Background (CMB) energy spectrum from…
CMBR distortion concerned with recombination of the primordial plasma is calculated in frequency band from 1 GHz to 100 GHz in the frame of the standard cosmological model for different values of cosmological density parameters: nonrelativistic matter density $Ω_m$ and baryonic matter density $Ω_b$. Comparison of these results with observational data which will be obtained from planned experiments may be used for independent determination of the cosmological parameters $Ω_m$ and $Ω_b$.
We compute the corrections to the cosmological hydrogen recombination history due to delayed feedback of Lyman-series photons and the escape in the Lyman-continuum. The former process is expected to slightly delay recombination, while the latter should allow the medium to recombine a bit faster. It is shown that the subsequent feedback of released Lyman-n photons on the lower lying Lyman-(n-1) transitions yields a maximal correction of DN_e/N_e 0.22% at z~ 1050. Including only Lyman-βfeedback onto the Lyman-αtransition, accounts for most of the effect. We find corrections to the cosmic microwa…
We present results for the spectral distortions of the Cosmic Microwave Background (CMB) arising due to bound-bound transitions during the epoch of cosmological hydrogen recombination at frequencies down to nu~100MHz. We extend our previous treatment of the recombination problem now including the main collisional processes and following the evolution of all the hydrogen angular momentum sub-states for up to 100 shells. We show that, due to the low baryon density of the Universe, even within the highest considered shell full statistical equilibrium (SE) is not reached and that at low frequencie…
The HeII->HeI recombination of primordial helium plasma (z = 1500 - 3000) is considered in terms of the standard cosmological model. This process affects the formation of cosmic microwave background anisotropy and spectral distortions. We investigate the effect of neutral hydrogen on the HeII->HeI recombination kinetics with partial and complete redistributions of radiation in frequency in the HeI resonance lines. It is shown that to properly compute the HeII->HeI recombination kinetics, one should take into account not only the wings in the absorption and emission profiles of the HeI resonanc…
We consider the effects connected with the detailed radiative transfer during the epoch of cosmological recombination on the ionization history of our Universe. We focus on the escape of photons from the hydrogen Lyman-alpha resonance at redshifts 600<~ z <~ 2000, one of two key mechanisms defining the rate of cosmological recombination. We approach this problem within the standard formulation, and corrections due to two-photon interactions are deferred to another paper. As a main result we show here that within a non-stationary approach to the escape problem, the resulting correction in the f…
We study the possibility of generating magnetic fields during the evolution of electron, proton, and photon plasma in the pre-recombination era. We show that a small magnetic field can be generated in the second order of perturbation theory for scalar modes with adiabatic initial conditions. The amplitude of the field is $\la 10^{-30} \rm G$ at the present epoch for scales from sub-kpc to $\ga 100 \rm Mpc$.
I show that neutral lithium couples strongly to the cosmic microwave background (CMB) through its 6708A resonant transition after it recombines at z~500. At observed wavelengths of <335 micron, the CMB anisotropies are significantly altered since the optical depth for resonant scattering by neutral lithium is substantial, of order 0.5. The scattering would suppress the original anisotropies, but will generate strong new anisotropies in the CMB temperature and polarization on sub-degree scales (l>100). Observations at different wavelengths in this spectral regime can probe different thin slices…
We discuss the hypotheses that cosmological baryon asymmetry and entropy were produced in the early Universe by phase transition of the scalar fields in the framework of spontaneous baryogenesis scenario. We show that annihilation of the matter-antimatter clouds during the cosmological hydrogen recombination could distort of the CMB anisotropies and polarization by delay of the recombination. After recombination the annihilation of the antibaryonic clouds (ABC) and baryonic matter can produce peak-like reionization at the high redshifts before formation of quasars and early galaxy formation. W…
We explore the imprint of the cosmological hydrogen recombination lines on the power spectrum of the cosmic microwave background (CMB). In particular, we focus our analysis in the three strongest lines for the Balmer, Paschen and Brackett series of hydrogen. We expect changes in the angular power spectrum due to these lines on the level of $0.3 μK$ for the H$α$ line, being maximum at small angular scales ($\ell \approx 870$). The morphology of the signal is very rich. It leads to relatively narrow spectral features ($Δν/ ν\sim 10^{-1}$), with several regions in the power spectrum showing a cha…
Gravitational interaction of cosmic microwave background (CMB) photons with matter perturbations present along the line-of-sight to the surface of last scattering modifies the shape of the CMB anisotropy power spectrum. Here I focus on (linear) integrated Sachs-Wolfe and (non-linear) gravitational lensing effects and discuss the detectability of the resulting distortions and their possible consequences for the CMB-based estimation of cosmological parameters. Specifically, I discuss if any of those effects may allow us to use CMB experiments to put independent constraints on the curvature of th…
Based on the standard cosmological model, we calculate the correction to the rate of two-photon 2s<->1s transitions in the hydrogen atom under primordial hydrogen plasma recombination conditions that arises when the induced transitions under equilibrium background radiation with a blackbody spectrum and plasma recombination radiation are taken into account.
We approximately compute the bispectrum induced on the CMB temperature by fluctuations in the standard recombination epoch. Of all the second order sources that can induce non-Gaussianity during recombination, we concentrate on those proportional to the perturbation in the free electron density, which is about a factor of 5 larger than the other first order perturbations. This term induces some non-Gaussianity by delaying the time of recombination and by changing the photon diffusion scale. We find that the signal is not scale invariant, peaked on squeezed triangles with the smaller multipole …
Current cosmological constraints from Cosmic Microwave Background (CMB) anisotropies are typically derived assuming a standard recombination scheme, however additional resonance and ionizing radiation sources can delay recombination, altering the cosmic ionization history and the cosmological inferences drawn from CMB data. We show that for recent observations of CMB anisotropy, from the Wilkinson Microwave Anisotropy Probe satellite mission 5-year survey (WMAP5) and from the ACBAR experiment, additional resonance radiation is nearly degenerate with variations in the spectral index, n_s, and h…
With the recent measurement of full sky cosmic microwave background polarization from WMAP, key cosmological degeneracies have been broken, allowing tighter constraints to be placed on cosmological parameters inferred assuming a standard recombination scenario. Here we consider the effect on cosmological constraints if additional ionizing and resonance radiation sources are present at recombination. We find that the new CMB data significantly improve the constraints on the additional radiation sources, with $\log_{10}[ε_α] < -0.5$ and $\log_{10}[ε_{i}] <-2.4$ at 95% c.l. for resonance and ioni…
We solve the recombination equation by taking into account the induced recombinations and a physical cut off in the hydrogen spectrum. The effective recombination coefficient is parametrized as a function of temperature and free electron density and is about a factor of four larger than without the induced recombination. This accelerates the last stage of the recombination processes and diminishes the residual ionization by a factor of about 2.6. The number and energy distribution of photons issuing from the hydrogen recombination are calculated. The distortion of the cosmic microwave backgrou…
It is shown that the standard cosmological model predicts {\it ab initio} generation of large-scale but very small-amplitude cosmic magnetic fields at the epoch of recombination of the primeval plasma. Matter velocities dominated by coherent flows on a scale $L\approx 50h^{-1}(1+z)^{-1}$ Mpc lead to a dipole of radiation flux in the frame of the moving matter. Thomson scattering of the radiation differentially accelerates the electrons and ions, creating large-scale coherent electric currents and magnetic fields. This process is analyzed using magnetohydrodynamic equations which include a modi…
More than half of the atoms in the Universe recombined via forbidden transitions, so that accurate treatment of the forbidden channels is important in order to follow the cosmological recombination process with the level of precision required by future microwave anisotropy experiments. We perform a multi-level calculation of the recombination of hydrogen (H) and helium (He) with the addition of the triplet 2P to singlet 1S spin-forbidden transition for neutral helium (He I), plus the nS--1S and nD--1S two-photon transitions for H (up to n=40) and among singlet states of He I (n<=10 and l<=7). …
Recombination of the primordial helium plasma (HeII->HeI, $z \simeq 1500 - 3000$) is considered. This process has an effect on the CMBR anisotropy and CMBR spectrum distortion. In this work an influence of neutral hydrogen on kinetics of HeII->HeI recombination is investigated in the frame of the standard cosmological model. It is shown that small amount of neutral hydrogen ($10^{-5} - 10^{-2}$ of total number of hydrogen ions and atoms) leads to acceleration of HeII->HeI recombination at $z\lesssim 2000$ and at $z\lesssim 1600$ quasi-equilibrium HeII->HeI recombination (according to the Saha …
The evolution of baryon density perturbations on very small scales is investigated. In particular, the nonlinear growth induced by the radiation drag force from the shear velocity field on larger scales during the recombination epoch, which is originally proposed by Shaviv in 1998, is studied in detail. It is found that inclusion of the diffusion term which Shaviv neglected in his analysis results in rather mild growth whose growth rate is $\ll 100$ instead of enormous amplification $\sim 10^4$ of Shaviv's original claim since the diffusion suppresses the growth. The growth factor strongly dep…
Using the values of the cosmological parameters obtained from Wilkinson Microwave Anisotropy Probe (WMAP) and the cosmological chemical clock observed by high-redshift quasars, it is shown that star formation should have started by the redshift $z_F > 9.5$, and that $z_F$ is sensitive only to $\omegamz h^2$ in flat $Λ$CDM cosmology.
The subject of cosmological hydrogen recombination has received much attention recently because of its importance to predictions for and cosmological constraints from CMB observations. While the central role of the two-photon decay 2s->1s has been recognized for many decades, high-precision calculations require us to consider two-photon decays from the higher states ns,nd->1s (n>=3). Simple attempts to include these processes in recombination calculations have suffered from physical problems associated with sequences of one-photon decays, e.g. 3d->2p->1s, that technically also produce two phot…
The non-linear effects operating at the recombination epoch generate a non-Gaussian signal in the CMB anisotropies. Such a contribution is relevant because it represents a major part of the second-order radiation transfer function which must be determined in order to have a complete control of both the primordial and non-primordial part of non-Gaussianity in the CMB anisotropies. We provide an estimate of the level of non-Gaussianity in the CMB arising from the recombination epoch which shows up mainly in the equilateral configuration. We find that it causes a contamination to the possible mea…
The structures produced during the epoch of reionization by the action of radiation on neutral hydrogen are in principle different to those that arise through gravitational growth of initially small perturbations. We explore the difference between the two mechanisms using high resolution cosmological radiative transfer. Our computations use a Monte Carlo code which raytraces directly through SPH kernels without a grid, preserving the high spatial resolution of the underlying hydrodynamic simulation. Because the properties of the first sources of radiation are uncertain, we simulate a range of …
The emission from neutral hydrogen (HI) clouds in the post-reionization era (z < 6), too faint to be individually detected, is present as a diffuse background in all low frequency radio observations below 1420 MHz. The angular and frequency fluctuations of this radiation (~ 1 mK) is an important future probe of the large scale structures in the Universe. We show that such observations are a very effective probe of the background cosmological model and the perturbed Universe. In our study we focus on the possibility of determining the redshift space distortion parameter, coordinate distance and…
The recombination history of the Universe depends exponentially on the temperature, T_0, of the cosmic microwave background. Therefore tiny changes of T_0 are expected to lead to significant changes in the free electron fraction. Here we show that even the current 1sigma-uncertainty in the value of T_0 results in more than half a percent ambiguity in the ionization history, and more than 0.1% uncertainty in the TT and EE power spectra at small angular scales. We discuss how the value of T_0 affects the highly redshifted cosmological hydrogen recombination spectrum and demonstrate that T_0 coul…
A number of radio interferometers are currently being planned or constructed to observe 21 cm emission from reionization. Not only will such measurements provide a detailed view of that epoch, but, since the 21 cm emission also traces the distribution of matter in the Universe, this signal can be used to constrain cosmological parameters at 6 < z < 20. The sensitivity of an interferometer to the cosmological information in the signal may depend on how precisely the angular dependence of the 21 cm 3-D power spectrum can be measured. Utilizing an analytic model for reionization, we quantify all …
We investigate the dependence of the epoch of reionization on the properties of cosmological perturbations, in the context of cosmologies permitted by WMAP. We compute the redshift of reionization using a simple model based on the Press-Schechter approximation. For a power-law initial spectrum we estimate that reionization is likely to occur at a redshift $z_{reion} = 17^{+10}_{-7}$, consistent with the WMAP determination based on the temperature-polarization cross power spectrum. We estimate the delay in reionization if there is a negative running of the spectral index, as weakly indicated by…
We present a study of open inflation cosmological scenarios in which cosmic strings form betwen the two inflationary epochs. It is shown that in these models strings are stretched outside the horizon due to the inflationary expansion but must necessarily re-enter the horizon before the epoch of equal matter and radiation densities. We determine the power spectrum of cold dark matter perturbations in these hybrid models, finding good agreement with observations for values of $Γ=Ω_0h\sim0.3$ and comparable contributions from the active and passive sources to the CMB. Finally, we briefly discuss …
We consider class of modified $f(R)$ gravities with the effective cosmological constant epoch at the early and late universe. Such models pass most of solar system tests as well they satisfy to cosmological bounds. Despite their very attractive properties, it is shown that one realistic class of such models may lead to significant Newton law corrections which become small at the future universe only. The model with acceptable Newton law regime shows the matter instability. This suggests that more complicated version of such theory (or extended parameters space) should be investigated.
The universe is found to have undergone several phases in which the gravitational constant had different behaviors. During some epochs the energy density of the universe remained constant and the universe remained static. In the radiation dominated epoch the radiation field satisfies Stefan's formula while the scale factor varies linearly with time. The model enhances the formation of the structure in the universe as observed today.
We study the two-photon process for the transitions ns --> 1s and nd --> 1s in hydrogen up to large n. For n<=20 we provide simple analytic fitting formulae to describe the non-resonant part of the two-photon emission profiles. Combining these with the analytic form of the cascade-term yields a simple and accurate description of the full two-photon decay spectrum, which only involves a sum over a few intermediate states. We demonstrate that the cascade term naturally leads to a nearly Lorentzian shape of the two-photon profiles in the vicinity of the resonances. However, due to quantum-electro…
In the scalar tensor gravitational theories Newton's constant G_N evolves in the expanding universe. Likewise, it has been speculated that the acceleration scale a_0 in Milgrom's modified Newtonian dynamics (MOND) is tied to the scale of the cosmos, and must thus evolve. With the advent of relativistic implementations of the modified dynamics, one can address the issue of variability of the two gravitational ''constants'' with some confidence. Using TeVeS, the Tensor-Vector-Scalar gravitational theory, as an implementation of MOND, we calculate the dependence of G_N and a_0 on the TeVeS parame…
We explore the possibility of generating large-scale magnetic fields from second-order cosmological perturbations during the pre-recombination era. The key process for this is Thomson scattering between the photons and the charged particles within the cosmic plasma. To tame the multi-component interacting fluid system, we employ the tight coupling approximation. It is shown that the source term for the magnetic field is given by the vorticity, which signals the intrinsically second-order quantities, and the product of the first order perturbations. The vorticity itself is sourced by the produc…
We suggest two realistic f(R) and one F(G) modified gravities which are consistent with local tests and cosmological bounds. The typical property of such theories is the presence of the effective cosmological constant epochs in such a way that early-time inflation and late-time cosmic acceleration are naturally unified within single model. It is shown that classical instability does not appear here and Newton law is respected. Some discussion of possible anti-gravity regime appearence and related modification of the theory is done.
Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be ``predictive'', in the sense that once somea priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a retrodictive approach might usefully take observational dataconcerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of…
