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 physical processes, still finding potentially measurable consequences for the energy spectrum and temperature anisotropies of the Cosmic Microwave Background (CMB). In this contribution we provide a short historical overview in connection with the cosmological recombination epoch and its connection to the CMB. Also we highlight some of the detailed physics that were studied over the past few years in the context of the cosmological recombination of hydrogen and helium. (abrigded)
We discuss the evolution of the ratio in number of recombinations due to 2s two photon escape and due to the escape of Lyman-$α$ photons from the resonance during the epoch of cosmological recombination, within the width of the last scattering surface and near its boundaries. We discuss how this ratio evolves in time, and how it defines the profile of the Lyman-$α$ line in the spectrum of CMB. One of the key reasons for explaining its time dependence is the strong overpopulation of the 2p level relative to the 2s level at redshifts $z \la 750$.
The redshifted 21-cm emission by neutral hydrogen offers a unique tool for mapping structure formation in the early universe in three dimensions. Here we provide the first detailed calculation of the 21-cm emission signal during and after the epoch of hydrogen recombination in the redshift range of z ~ 500-1,100, corresponding to observed wavelengths of 100-230 meters. The 21-cm line deviates from thermal equilibrium with the cosmic microwave background (CMB) due to the excess Ly-alpha radiation from hydrogen and helium recombinations. The resulting 21-cm signal reaches a brightness temperatur…
The advent of precise measurements of the cosmic microwave background (CMB) anisotropies has motivated correspondingly precise calculations of the cosmic recombination history. Cosmic recombination proceeds far out of equilibrium because of a "bottleneck" at the $n=2$ level of hydrogen: atoms can only reach the ground state via slow processes: two-photon decay or Lyman-$α$ resonance escape. However, even a small primordial abundance of molecules could have a large effect on the interline opacity in the recombination epoch and lead to an additional route for hydrogen recombination. Therefore, t…
In this paper we discuss the effect of recombinations to highly excited states (n > 100) in hydrogen during the cosmological recombination epoch. For this purpose, we developed a new ODE solver for the recombination problem, based on an implicit Gear's method. This solver allows us to include up to 350 l-resolved shells or ~61 000 separate levels in the hydrogen model and to solve the recombination problem for one cosmology in ~27 hours. This is a huge improvement in performance over our previous recombination code, for which a 100-shell computation (5050 separate states) already required ~150…
New public numerical code for fast calculations of the cosmological recombination of primordial hydrogen-helium plasma is presented. The code is based on the three-level approximation (TLA) model of recombination and allows us to take into account some fine physical effects of cosmological recombination simultaneously with using fudge factors. The code can be found at http://www.ioffe.ru/astro/QC/CMBR/atlant/atlant.html
Spectral distortions of the CMB have recently experienced an increased interest. One of the inevitable distortion signals of our cosmological concordance model is created by the cosmological recombination process, just a little before photons last scatter at redshift $z\simeq 1100$. These cosmological recombination lines, emitted by the hydrogen and helium plasma, should still be observable as tiny deviation from the CMB blackbody spectrum in the cm--dm spectral bands. In this paper, we present a forecast for the detectability of the recombination signal with future satellite experiments. We a…
An ionization front expanding into a neutral medium can be slowed-down significantly by recombinations. In cosmological numerical simulations the recombination rate is often computed using a 'clumping factor', that takes into account that not all scales in the simulated density field are resolved. Here we demonstrate that using a single value of the clumping factor significantly overestimates the recombination rate, and how a local estimate of the clumping factor is both easy to compute, and gives significantly better numerical convergence. We argue that this lower value of the recombination r…
In this paper we consider the re-processing of high frequency photons emitted by HeII and HeI during the epoch of cosmological recombination by HeI and HI. We demonstrate that, in comparison to computations which neglect all feedback processes, the number of cosmological recombination photons that are related to the presence of helium in the early Universe could be increased by ~40%-70%. Our computations imply that per helium nucleus ~3-6 additional photons could be produced. Therefore, a total of ~12-14 helium-related photons are emitted during cosmological recombination. This is an important…
We present the first fast and detailed computation of the cosmological recombination radiation released during the hydrogen (redshift z ~ 1300) and helium (z ~ 2500 and z ~ 6000) recombination epochs, introducing the code CosmoSpec. Our computations include important radiative transfer effects, 500-shell bound-bound and free-bound emission for all three species, the effects of electron scattering and free-free absorption as well as interspecies (HeII --> HeI --> HI) photon feedback. The latter effect modifies the shape and amplitude of the recombination radiation and CosmoSpec improves signifi…
Resonant conversion of high energy gravitons into photons in large scale cosmological magnetic fields at the post recombination epoch is considered. It is shown that the probability of the resonance photon production is much higher than the non-resonant one. As a result an observable isotropic background of cosmic gamma rays might be created. As shown in our previous paper, an early population of primordial black holes (PBHs) prior to big bang nucleosynthesis (BBN) could be an efficient source of high frequency gravitational waves. For the primordial black hole mass about $10^8$ g the produced…
The cosmological recombination radiation (CRR) is one of the guaranteed spectral distortion signals from the early Universe. The CRR photons from hydrogen and helium pre-date the last scattering process and as such allow probing physical phenomena in the pre-recombination era. Here we compute the modifications to the CRR caused by early dark energy models and varying fundamental constants. These new physics examples have seen increased recent activity in connection with the Hubble tension, motivating the exploratory study presented here. The associated CRR responses are spectrally-rich but the…
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 (\propto(1+z)^2 rather than (1+z)) and would have fallen to about 20mK 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.
Chicone et al [Comm Math Phys (1997)] investigated existence of fast dynamos by analyzing the spectrum kinematic magnetic dynamo. In real non-degenerate branch of the spectrum, the kinematic dynamo operator lies on a compact Riemannian 2D space of constant negative curvature. Here, generalization of Marklund and Clarkson [MNRAS (2005)], general relativistic GR-MHD dynamo equation to include mean-field dynamos is obtained. In the absence of kinetic helicity, adiabatic constant $γ={1/2}$ and gravitational colapse of negative Riemann curvature of spatial sections enhance dynamo effect $\frac{δB}{…
We use the new cosmological recombination code, CosmoRec, for parameter estimation in the context of (future) precise measurements of the CMB temperature and polarization anisotropies. We address the question of how previously neglected physical processes in the recombination model of Recfast affect the determination of key cosmological parameters, for the first time performing a model-by-model computation of the recombination problem. In particular we ask how the biases depend on different combinations of parameters, e.g. when varying the helium abundance or the effective number of neutrino s…
Photons emitted during the epochs of Hydrogen ($500 \lesssim z \lesssim 1600$) and Helium recombination ($1600 \lesssim z \lesssim 3500$ for HeII $\rightarrow$ HeI, $5000 \lesssim z \lesssim 8000$ for HeIII $\rightarrow$ HeII) are predicted to appear as broad, weak spectral distortions of the Cosmic Microwave Background. We present a feasibility study for a ground-based experimental detection of these recombination lines, which would provide an observational constraint on the thermal ionization history of the Universe, uniquely probing astrophysical cosmology beyond the last scattering surface…
In this paper we explore the potential effects of DM annihilations on the cosmological recombination spectrum. With this example we want to demonstrate that the cosmological recombination spectrum in principle is sensitive to details related to possible extra energy release during recombination. We restrict ourselves to DM models which produce a negligible primordial distortion of the CMB energy spectrum. However, since during the epoch of cosmological recombination a large fraction of the deposited energy can directly go into ionizations and excitations of neutral atoms, both the cosmological…
The cosmological recombination radiation (CRR) is one of the inevitable $Λ$CDM spectral distortions of the cosmic microwave background (CMB). While it shows a rich spectral structure across dm-mm wavelengths, it is also one of the smallest signals to target. Here we carry out a detailed forecast for the expected sensitivity levels required to not only detect but also extract cosmological information from the CRR in the presence of foregrounds. We use ${\tt CosmoSpec}$ to compute the CRR including all important radiative transfer effects and modifications to the recombination dynamics. We confi…
Calculations of cosmological hydrogen recombination are vital for the extraction of cosmological parameters from cosmic microwave background (CMB) observations, and for imposing constraints to inflation and re-ionization. The Planck} mission and future experiments will make high precision measurements of CMB anisotropies at angular scales as small as l~2500, necessitating a calculation of recombination with fractional accuracy of ~10^{-3}. Recent work on recombination includes two-photon transitions from high excitation states and many radiative transfer effects. Modern recombination calculati…
Many quintessence models possess scaling or attractor solutions where the fraction of dark energy follows the dominant component in previous epochs of the expansion, or phase transitions may happen close to matter-radiation equality time. A non-negligible early dark energy (EDE) fraction around matter-radiation equality could contribute to alleviate the $H_0$ tension. We constrain the EDE fraction using two approaches: first, we use a fluid parameterization that mimics the plateaux of the dominant components in the past. An alternative tomographic approach constrains the EDE density in binned …
[Abridged] We use our most recent training set for the RICO code to estimate the impact of recombination uncertainties on the posterior probability distributions which will be obtained from future CMB experiments, and in particular the Planck satellite. Using a MCMC analysis to sample the posterior distribution of the cosmological parameters, we find that Planck will have biases of -0.7, -0.3 and -0.4 sigmas for n_S, Omega_b h2 and log(As), respectively, in the minimal 6-parameter LCDM model, if the description of the recombination history given by RICO is not used. The remaining parameters ar…
The inhibition of the total HI $n\leftrightarrow 1$ transition rate by delayed resonant reabsorption of HI $(n+1)\to 1$ photons by HI $n\to 1$ line which is possible due to cosmological redshift is considered semi-analytically. The method taking into account this effect in the frame of simple three-level approximation model of recombination is suggested. It is confirmed that the resonant feedbacks affect ionization fraction at the level about 0.2% for the epoch of last scattering. Similar consideration of HeI $2^1P\leftrightarrow 1^1S$ $\Rightarrow$ HeI $2^3P\leftrightarrow 1^1S$ feedback for …
Precision measurement of the cosmological recombination spectrum can provide an entire new window to look at the early universe. We aim to quantify the information hidden in the cosmological recombination spectrum and for this purpose we have developed a new code following the algorithm proposed in Ali-Haimoud and Hirata (2010), Ali-Haimoud (2013). Our code is closely based on the COSMOSPEC code [Chluba and Ali-Haimoud (2016)]. We find, using Fisher information matrix and assuming that the foregrounds can be subtracted by using higher or lower frequency channels and spatial information, that g…
The origin of cosmic magnetic fields is an unsolved problem and magnetogenesis could have occurred in the early Universe. We study the evolution of such primordial magnetic fields across the cosmological recombination epoch via 3D magnetohydrodynamic numerical simulations. We compute the effective or net heating rate of baryons due to decaying magnetic fields and its dependence on the magnetic field strength and spectral index. In the drag-dominated regime ($z \gtrsim 1500$), prior to recombination, we find no real heating is produced. Our simulations allow us to smoothly trace a new transitio…
In this paper we consider the effects of resonance and electron scattering on the escape of Lyman alpha photons during cosmological hydrogen recombination. We pay particular attention to the influence of atomic recoil, Doppler boosting and Doppler broadening using a Fokker-Planck approximation of the redistribution function describing the scattering of photons on the Lyman alpha resonance of moving hydrogen atoms. We extend the computations of our recent paper on the influence of the 3d/3s-1s two-photon channels on the dynamics of hydrogen recombination, simultaneously including the full time-…
In this paper, we study small-scale fluctuations (baryon pressure sound waves) in the baryon fluid during recombination. In particular, we look at their evolution in the presence of relative velocities between baryons and photons on large scales ($k \sim 10^{-1} \ {\rm Mpc}^{-1}$), which are naturally present during the era of decoupling. Previous work concluded that the fluctuations grow due to an instability of sound waves in a recombining plasma, but that the growth factor is small for typical cosmological models. These analyses model recombination in an inhomogenous universe as a perturbat…
In some instances, e.g. near phase transitions, thermodynamic fluctuations become macroscopically relevant, and relative amplitudes grow far above the standard $N^{-1/2}$ scale, with $N$ the number of particles. Such large fluctuations are characterised by a scale invariant Gaussian power spectrum. In this letter I show that the abrupt drop in the baryonic sound speed across recombination leads to conditions resulting in such large thermodynamic Gaussian fluctuations in the ionisation fraction of the baryons. Under pressure equilibrium, this will result in a mechanism for generating scale inva…
We present the new recombination code HYREC-2, holding the same accuracy as the state-of-the-art codes HYREC and COSMOREC and, at the same time, surpassing the computational speed of the code RECFAST commonly used for CMB-anisotropy data analyses. HYREC-2 is based on an effective 4-level atom model, accounting exactly for the non-equilibrium of highly excited states of hydrogen, and very accurately for radiative transfer effects with a correction to the Lyman-$α$ escape rate. The latter is computed with the original HYREC, and tabulated, as a function of temperature, along with its derivatives…
Density inhomogeneity in the intergalactic medium (IGM) can boost the recombination rate of ionized gas substantially, affecting the growth of HII regions during reionization. Previous attempts to quantify this effect typically failed to resolve down to the Jeans scale in the pre-ionization IGM, which is important in establishing this effect, along with the hydrodynamical back-reaction of reionization on it. Towards that end, we perform a set of fully-coupled, radiation-hydrodynamics simulations from cosmological initial conditions, extending the mass resolution of previous work to the scale o…
We compute in detail the rate at which energy injected by dark matter annihilation heats and ionizes the photon-baryon plasma at z ~ 1000, and provide accurate fitting functions over the relevant redshift range for a broad array of annihilation channels and DM masses. The resulting perturbations to the ionization history can be constrained by measurements of the CMB temperature and polarization angular power spectra. We show that models which fit recently measured excesses in 10-1000 GeV electron and positron cosmic rays are already close to the 95% confidence limits from WMAP. The recently la…
The calculation of a highly accurate cosmological recombination history has been the object of particular attention recently, as it constitutes the major theoretical uncertainty when predicting the angular power spectrum of Cosmic Microwave Background anisotropies. Lyman transitions, in particular the Lyman-alpha line, have long been recognized as one of the bottlenecks of recombination, due to their very low escape probabilities. The Sobolev approximation does not describe radiative transfer in the vicinity of Lyman lines to a sufficient degree of accuracy, and several corrections have alread…
A new approach to the cosmological recombination problem is presented, which completes our previous analysis on the effects of two-photon processes during the epoch of cosmological hydrogen recombination, accounting for ns-1s and nd-1s Raman events and two-photon transitions from levels with n>=2. The recombination problem for hydrogen is described using an effective 400-shell multi-level approach, to which we subsequently add all important recombination corrections discussed in the literature thus far. We explicitly solve the radiative transfer equation of the Lyman-series photon field to obt…
Decaying cold dark matter (CDM) has been considered as a mechanism to tackle the tensions in the Hubble expansion rate and the clustering of matter. However, polarization measurements of the cosmic microwave background (CMB) severely constrain the fraction of dark matter decaying before recombination, and lensing of the CMB anisotropies by large-scale structure set strong constraints on dark matter decaying after recombination. Together, these constraints make an explanation of the Hubble tension in terms of decaying dark matter unlikely. In response to this situation, we investigate whether a…
Investigation of the cosmic microwave background formation processes is one of the most actual problem at present time. In this paper we analyze the response of the hydrogen atom to the external photon fields. Field characteristics are defined via conditions corresponding to the recombination era of universe. Approximation of three-level atom is used to describe the "atom - fields" interaction. It is found that the phenomena of the electromagnetically induced transparancy takes place in this case. Consideration of EIT phenomena makes it necessary to update astrophysical description of the proc…
Cosmological hydrogen recombination has recently been the subject of renewed attention because of its importance for predicting the power spectrum of cosmic microwave background anisotropies. It has become clear that it is necessary to account for a large number n >~ 100 of energy shells of the hydrogen atom, separately following the angular momentum substates in order to obtain sufficiently accurate recombination histories. However, the multi-level atom codes that follow the populations of all these levels are computationally expensive, limiting recent analyses to only a few points in paramet…
Cosmic evolution in the hydrogen content of the Universe through recombination and up to the end of reionization is expected to be revealed as subtle spectral features in the uniform extragalactic cosmic radio background. The redshift evolution in the excitation temperature of the 21-cm spin flip transition of neutral hydrogen appears as redshifted emission and absorption against the cosmic microwave background. The precise signature of the spectral trace from cosmic dawn and the epoch of reionization are dependent on the spectral radiance, abundance and distribution of the first bound systems…
One of the strongest arguments against the cosmological constant as an explanation of the current epoch of accelerated cosmic expansion is the existence of an earlier, dynamical acceleration, i.e. inflation. We examine the likelihood that acceleration is an occasional phenomenon, putting stringent limits on the length of any accelerating epoch between recombination and the recent acceleration; such an epoch must last less than 0.05 e-fold (at z>2) or the matter power spectrum is modified by more than 20%.
One of the important light elements created during the big bang nucleosynthesis is Be-7 which then decays to Li-7 by electron capture when recombination becomes effective but well before the Saha equilibrium recombination is reached. This means that Be-7 should wait until its recombination epoch even though the half-life of the hydrogenic beryllium atom is only 106.4 days. We calculate when the conversion from primordial Be-7 to Li-7 occurs taking into account the population of the hyperfine structure sublevels and solving the kinetic equations for recombination, photoionization and conversion…
Tomographic intensity mapping of the HI using the redshifted 21 cm observations opens up a new window towards our understanding of cosmological background evolution and structure formation. This is a key science goal of several upcoming radio telescopes including the Square Kilometer Array (SKA). In this article we focus on the post-reionization signal and investigate the of cross correlating the 21 cm signal with other tracers of the large scale structure. We consider the cross-correlation of the post-reionization 21 cm signal with the Lyman-alpha forest, Lyman-break galaxies and late time an…
The cosmic microwave background (CMB) temperature, $T$, surely the most precisely measured cosmological parameter, has been inferred from {\it local} measurements of the blackbody spectrum to an exquisite precision of 1 part in $\sim 4700$. On the other hand, current precision allows inference of other basic cosmological parameters at the $\sim 1\%$ level from CMB power spectra, galaxy correlation and lensing, luminosity distance measurements of supernovae, as well as other cosmological probes. A basic consistency check of the standard cosmological model is an independent inference of $T$ at r…
The electromagnetically induced transparency (EIT) phenomenon in earlier universe is considered. We evaluated the elementary processes of the single scattering of photon on the hydrogen atom with the purpose of their use in the tasks of the radiation transfer theory. The additional function $f$, which depends on external conditions, is found. This function can be considered as an adjustment of the optical depth that leads to the necessity of modernization of the escape probability $p_{ij}(τ_S)\rightarrow p_{ij}(τ_S(1+f))$. The numerical values of $f$ for the different schemes of atom in three-…
If vector type perturbations are present in the primordial plasma before recombination, the generation of magnetic fields is known to be inevitable through the Harrison mechanism. In the context of the standard cosmological perturbation theory, non-linear couplings of first-order scalar perturbations create second-order vector perturbations, which generate magnetic fields. Here we reinvestigate the generation of magnetic fields at second-order in cosmological perturbations on the basis of our previous study, and extend it by newly taking into account the time evolution of purely second-order v…
We study inhomogeneous magnetised cosmologies through the post-recombination era in the framework of Newtonian gravity and the ideal-magnetohydrodynamic limit. The nonlinear kinematic and dynamic equations are derived and linearised around the Newtonian counterpart of the Einstein-de Sitter universe. This allows for a direct comparison with the earlier relativistic treatments of the issue. Focusing on the evolution of linear density perturbations, we provide new analytic solutions which include the effects of the magnetic pressure as well as those of the field's tension. We confirm that the pr…
The cosmological coincidences between the matter and radiation energy densities at recombination as well as between the densities of matter and the cosmological constant at present time are well known. We point out that moreover the third intersection between the energy densities of radiation and the cosmological constant coincides with the reionization epoch. To quantify the statistical relevance of this concurrence, we compute the Bayes factor between the concordance cosmology with free Thomson scattering optical depth and a model for which this parameter is inferred from imposing a match be…
We present a multi-epoch analysis of the galaxy populations formed within the cosmological hydrodynamical simulations presented in Vogelsberger et al. (2013). These simulations explore the performance of a recently implemented feedback model which includes primordial and metal line radiative cooling with self-shielding corrections; stellar evolution with associated mass loss and chemical enrichment; feedback by stellar winds; black hole seeding, growth and merging; and AGN quasar- and radio-mode heating with a phenomenological prescription for AGN electro-magnetic feedback. We illustrate the i…
In the pre-recombination era, cosmological density fluctuations can naturally generate magnetic fields through Thomson scatterings. In previous studies, only the magnetic field generation from the initially-adiabatic fluctuations has been considered. Here we investigate the generation of cosmological magnetic fields sourced by the primordial non-adiabatic fluctuations based on the cosmological perturbation theory, using the tight-coupling approximations between photon and baryon fluids. It is found that the magnetic fields from the non-adiabatic fluctuations can arise at the first-order expans…
We give a formulation of the radiative transfer equation for Lyman alpha photons which allows us to include the two-photon corrections for the 3s-1s and 3d-1s decay channels during cosmological hydrogen recombination. We use this equation to compute the corrections to the Sobolev escape probability for Lyman alpha photons during hydrogen recombination, which then allow us to calculate the changes in the free electron fraction and CMB temperature and polarization power spectra. We show that the effective escape probability changes by DP/P ~+ 11% at z~1400 in comparison with the one obtained usi…
We discuss the phenomenological imprints of modifications to gravity in the early universe with a specific focus on the time of recombination. We derive several interesting results regarding the effect that such modifications have on cosmological observables, especially on the driving and phasing of acoustic oscillations, observed in the CMB and BAO, as well as the weak gravitational lensing of the CMB and of galaxy shapes. This widens the pool of measurements that can be used to test gravity with present and future surveys, in particular realizing the full constraining power of the structure …
Injection of high energy electromagnetic particles around the recombination epoch can modify the standard recombination history and therefore the CMB anisotropy power spectrum. Previous studies have put strong constraints on the amount of electromagnetic energy injection around the recombination era (redshifts $z\lesssim 4500$). However, energy injected in the form of energetic ($>$ keV) visible standard model particles is not deposited instantaneously. The considerable delay between the time of energy injection and the time when all energy is deposited to background baryonic gas and CMB photo…
