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.
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…
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 …
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 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 $z \la 750$.
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…
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…
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 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…
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…
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…
[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…
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…
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…
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…
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-…
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…
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…
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 …
We study cosmological perturbation theory in the cosmology associated with conformal gravity, establish the validity of the decomposition theorem for it, and then use the theorem to provide an exact solution to the theory in the recombination era. Central to our approach is the use of a fully gauge invariant formulation of the cosmological fluctuations equations. In the recombination era not only is perturbation theory applicable, because of its specific structure in the conformal case the fluctuation equations are found to greatly simplify. Using a master equation for scalar, vector and tenso…
Combining pre- and post-recombination new physics to address cosmological tensions: case study with varying electron mass and sign-switching cosmological constant
In the studies on pre-recombination early dark energy (EDE), the evolution of Universe after recombination is usually regarded as $ΛCDM$-like, which corresponds that the equation of state of dark energy responsible for current accelerated expansion is $w=-1$. However, in realistic models, $w$ might be evolving. We consider the parametrizations of $w$ with respect to the redshift $z$ in Axion-like EDE and AdS-EDE models, respectively. We performed the Monte Carlo Markov chain analysis with recent cosmological data, and found that the bestfit $w(z)$ is compatible with $w_0=-1,w_a=0$ (the cosmolo…
We consider scenario of the dark matter consisting of two fractions, stable part being dominant and a smaller unstable fraction, which has decayed after the recombination epoch. It has been suggested in Ref. [arxiv:1505.03644] that the above scenario may alleviate tension between high-redshift (CMB anisotropy) and low-redshift (cepheid variables and SNe Ia, cluster counts) cosmological measurements. We derive constraints on the heavy relics branching to $q\bar{q}$, $e^+e^-$, $μ^+μ^-$, $τ^+τ^-$, $ν_e\bar{ν_e}$, $ν_μ\bar{ν_μ}$, $W^+W^-$ and $γγ$ in the above scenario by comparison of the seconda…
We study the formation of first molecules, negative Hydrogen ions and molecular ions in model of the Universe with cosmological constant and cold dark matter. The cosmological recombination is described in the framework of modified model of the effective 3-level atom, while the kinetics of chemical reactions in the framework of the minimal model for Hydrogen, Deuterium and Helium. It is found that the uncertainties of molecular abundances caused by the inaccuracies of computation of cosmological recombination are about 2-3%. The uncertainties of values of cosmological parameters affect the abu…
Pushing the Limits of Atomic Dark Matter: First-Principles Recombination Rates and Cosmological Constraints
C.N. Yang Institute for Theoretical Physics, Stony Brook University（纽约州立大学石溪分校杨振宁理论物理研究所）；Physics and Astronomy Department, Stony Brook University（纽约州立大学石溪分校物理与天文系）
It has been recently suggested~\cite{Berezhiani:2015yta} that emerging tension between cosmological parameter values derived in high-redshift (CMB anisotropy) and low-redshift (cluster counts, Hubble constant) measurements can be reconciled in a model which contains subdominant fraction of dark matter decaying after recombination. We check the model against the CMB Planck data. We find that lensing of the CMB anisotropies by the large-scale structure gives strong extra constraints on this model, limiting the fraction as $F<8\%$ at 2\,$σ$ confidence level. However, investigating the combined da…
We consider the propagation and energy losses of protons and anti-protons produced by dark matter annihilation at redshifts 100<z<~2000. In the case of dark matter annihilations into quarks, gluons and weak gauge bosons, protons and anti-protons carry about 20% of the energy injected into e^\pm and γ's, but their interactions are normally neglected when deriving cosmic microwave background bounds from altered recombination histories. Here, we follow numerically the energy-loss history of typical protons/antiprotons in the cosmological medium. We show that about half of their energy is channele…
In our recent papers (Kereslidze et all 2019a, 2021) a non-standard quasi-molecular mechanism was suggested and applied to treat the cosmological recombination. It was assumed that in the pre-recombination stage of evolution of the Universe an electron combined with two neighbouring protons and created the hydrogen molecular ion, $H_2^+$ in highly excited states, which then descended into the lower-lying states or dissociated. In this work, we elaborate the scheme of calculation for free-bound radiative transitions into attractive states of $H_2^+$ as functions of redshift $z$. Together with t…
The possible variation of the fine structure constant may be due to the non-minimal coupling of the electromagnetic field to a light scalar field which can be the candidate of dark energy. Its dynamical nature renders the fine structure constant varies with time as well as space. In this paper we point out the spatial fluctuation of the fine structure will modify the power spectra of the temperature and the polarization of the cosmic microwave background. We show explicitly that the fluctuations of the coupled scalar field generate new temperature anisotropies at the linear order and induce a …
It has been recently suggested~\cite{Berezhiani:2015yta} that a subdominant fraction of dark matter decaying after recombination may alleviate tension between high-redshift (CMB anisotropy) and low-redshift (Hubble constant, cluster counts) measurements. In this report, we continue our previous study~\cite{Chudaykin:2016yfk} of the decaying dark matter (DDM) model adding all available recent baryon acoustic oscillation (BAO) and redshift space distortions (RSD) measurements. We find, that the BAO/RSD measurements generically prefer the standard $Λ$CDM and combined with other cosmological measu…
We show that dark matter annihilation around the time of recombination can lead to growing ionization fraction perturbations, that track the linear collapse of matter over-densities. This amplifies small scale cosmological perturbations to the free electron density by a significant amount compared to the usual acoustic oscillations. Electron density perturbations distort the CMB, inducing secondary non-gaussianity. We calculate the CMB bispectrum from recombination, that is marginally observable by Planck. Even though electron perturbations can be markedly boosted compared with the Standard Mo…
Dissipative dark matter predicts rich observable phenomena that can be tested with future large-scale structure surveys. As a specific example, we study atomic dark matter, consisting of a heavy particle and a light particle charged under a dark electromagnetism. In particular, we calculate the cosmological evolution of atomic dark matter focusing on dark recombination and dark-molecule formation. We have obtained the relevant interaction-rate coefficients by re-scaling the rates for normal hydrogen, and evolved the abundances for ionized, atomic, and molecular states using a modified version …
