Gravitational wave background from neutrino-driven gamma-ray bursts

We study cosmic microwave background (CMB) secondary anisotropies produced by inhomogeneous reionization by means of cosmological simulations coupled with the radiative transfer code crash . The reionization history is consistent with the Wilkinson Microwave Anisotropy Probe Thomson optical depth determination. We find that the signal arising from this process dominates over the primary CMB component for   l ≳ 4000  and reaches a maximum amplitude of   l ( l + 1) C_l /2π≃ 1.6 × 10⁻¹³  on arcmin scales (i.e. l as large as several thousands). We then cross-correlate secondary CMB anisotropy maps with neutral hydrogen 21-cm line emission fluctuations obtained from the same simulations. The two signals are highly anticorrelated on angular scales corresponding to the typical size of H  ii regions (including overlapping) at the 21-cm map redshift. We show how the CMB/21-cm cross-correlation can be used: (i) to study the nature of the reionization sources; (ii) to reconstruct the cosmic reionization history; (iii) to infer the mean cosmic ionization level at any redshift. We discuss the feasibility of the proposed experiment with forthcoming facilities.     

Current models of the observable consequences of cosmic reionization and their detectability

A number of large current experiments aim to detect the signatures of the cosmic reionization at redshifts z > 6. Their success depends crucially on understanding the character of the reionization process and its observable consequences and designing the best strategies to use. We use large-scale simulations of cosmic reionization to evaluate the reionization signatures at redshifted 21-cm and small-scale cosmic microwave background (CMB) anisotropies in the best current model for the background universe, with fundamental cosmological parameters given by Wilkinson Microwave Anisotropy Probe three-year results. We find that the optimal frequency range for observing the 'global step' of the 21-cm emission is 120–150 MHz, while statistical studies should aim at 140–160 MHz, observable by GMRT. Some strongly non-Gaussian brightness features should be detectable at frequencies up to ∼190 MHz. In terms of sensitivity-signal trade-off relatively low resolutions, corresponding to beams of at least a few arcminutes, are preferable. The CMB anisotropy signal from the kinetic Sunyaev–Zel'dovich effect from reionized patches peaks at tens of μK at arcminute scales and has an rms of ∼1 μK, and should be observable by the Atacama Cosmology Telescope and the South Pole Telescope. We discuss the various observational issues and the uncertainties involved, mostly related to the poorly known reionization parameters and, to a lesser extend, to the uncertainties in the background cosmology.     

The effects of radiative transfer on the reionization of an inhomogeneous universe

Assuming simple dynamics for the growth of density fluctuations, we implement six-dimensional (6D) radiative transfer calculations to elucidate the effects of photon propagation during the reionization of an inhomogeneous universe. The ionizing sources are postulated to be AGN-like in this paper. The present simulations reveal that radiative transfer effects are still prominent considerably after the percolation epoch, in which patchy ionized regions connect with each other. In other words, owing to the collective opacity, the Universe does not become perfectly transparent against ionizing radiation even though strongly self-shielded regions disappear. It turns out that the inhomogeneity of the medium enhances the opacity effects and delays the end of reionization. Owing to such radiative transfer effects, the reionization in an inhomogeneous universe proceeds fairly slowly, in contrast to the prompt reionization in a homogeneous universe, and as a result the surface of reionization is not so sharply edged, but highly uneven. As a signature of the uneven surface of reionization, the cosmic IR background (CIB) radiation, which is produced by Ly photons resulting from radiative recombination, could exhibit strong anisotropies, reflecting the amplitude of density fluctuations at the reionization era. The predicted CIB intensity lies on a level of possible detection by forthcoming IR space telescope facilities.     

Reionization and the large-scale 21-cm cosmic microwave background cross-correlation

Of the many probes of reionization, the 21-cm line and the cosmic microwave background (CMB) are among the most effective. We examine how the cross-correlation of the 21-cm brightness and the CMB Doppler fluctuations on large angular scales can be used to study this epoch. We employ a new model of the growth of large-scale fluctuations of the ionized fraction as reionization proceeds. We take into account the peculiar velocity field of baryons and show that its effect on the cross-correlation can be interpreted as a mixing of Fourier modes. We find that the cross-correlation signal is strongly peaked towards the end of reionization and that the sign of the correlation should be positive because of the inhomogeneity inherent to reionization. The signal peaks at degree scales (ℓ∼ 100) and comes almost entirely from large physical scales ( k ∼ 10⁻² Mpc). Since many of the foregrounds and noise that plague low-frequency radio observations will not correlate with CMB measurements, the cross-correlation might appear to provide a robust diagnostic of the cosmological origin of the 21-cm radiation around the epoch of reionization. Unfortunately, we show that these signals are actually only weakly correlated and that cosmic variance dominates the error budget of any attempted detection. We conclude that the detection of a cross-correlation peak at degree-size angular scales is unlikely even with ideal experiments.     

Line-of-Sight Anisotropies in the Cosmic Dawn and Epoch of Reionization 21-cm Power Spectrum

The line-of-sight direction in the redshifted 21-cm signal coming from the cosmic dawn and the epoch of reionization is quite unique in many ways compared to any other cosmological signal. Different unique effects, such as the evolution history of the signal, non-linear peculiar velocities of the matter etc. will imprint their signature along the line-of-sight axis of the observed signal. One of the major goals of the future SKA-LOW radio interferometer is to observe the cosmic dawn and the epoch of reionization through this 21-cm signal. It is thus important to understand how these various effects affect the signal for its actual detection and proper interpretation. For more than one and half decades, various groups in India have been actively trying to understand and quantify the different line-of-sight effects that are present in this signal through analytical models and simulations. In many ways the importance of this sub-field under 21-cm cosmology have been identified, highlighted and pushed forward by the Indian community. In this article, we briefly describe their contribution and implication of these effects in the context of the future surveys of the cosmic dawn and the epoch of reionization that will be conducted by the SKA-LOW.     

The cross-correlation of the CMB polarization and the 21-cm line fluctuations from cosmic reionization

The cosmic microwave background (CMB) polarization and the 21-cm line fluctuations are powerful probes of cosmological reionization. We study how the cross-correlation between the CMB polarization ( E modes) and the 21-cm line fluctuations can be used to gain further understanding of the reionization history, within the framework of inhomogeneous reionization. Since the E -mode polarization reflects the amplitude of the quadrupole component of the CMB temperature fluctuations, the angular power spectrum of the cross-correlation exhibits oscillations at all multipoles. The first peak of the power spectrum appears at the scale corresponding to the quadrupole at the redshift, which is probed by the 21-cm line fluctuations. The peak reaches its maximum value in redshift when the average ionization fraction of the universe is about half. On the other hand, on small scales, there is a damping that depends on the duration of reionization. Thus, the cross-correlation between the CMB polarization and the 21-cm line fluctuations has the potential to accurately constrain the epoch and the duration of reionization.     

How is the reionization epoch defined?

We study the effect of a prolonged epoch of reionization on the angular power spectrum of the cosmic microwave background. Typically reionization studies assume a sudden phase transition, with the intergalactic gas moving from a fully neutral to a fully ionized state at a fixed redshift. Such models are at odds, however, with detailed investigations of reionization, which favour a more extended transition. We have modified the code cmbfast to allow the treatment of more realistic reionization histories and applied it to data obtained from numerical simulations of reionization. We show that the prompt reionization assumed by cmbfast in its original form heavily contaminates any constraint derived on the reionization redshift. We find, however, that prompt reionization models give a reasonable estimate of the epoch at which the mean cosmic ionization fraction was ≈50 per cent, and provide a very good measure of the overall Thomson optical depth. The overall differences in the temperature (polarization) angular power spectra between prompt and extended models with equal optical depths are less than 1 per cent (10 per cent).     

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially flat cosmologies, varying the matter density Ω₀ (the flatness being restored by a cosmological constant), the Hubble parameter h and the spectral index n of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently favoured low-density model with Ω₀=0.3 and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits that we quote.     

Cosmic microwave background anisotropies resulting from feedback-regulated inhomogeneous reionization

We calculate the secondary anisotropies in the cosmic microwave background (CMB) produced by inhomogeneous reionization from simulations in which the effects of radiative and stellar feedback effects on galaxy formation have been included. This allows us to determine self-consistently the beginning ( z _i≈30), the duration ( δz ≈20) and the (non-linear) evolution of the reionization process for a critical density cold dark matter (CDM) model. In addition, from the simulated spatial distribution of ionized regions, we are able to calculate the evolution of the two-point ionization correlation function, C _χ , and obtain the power spectrum of the anisotropies, C _ℓ, in the range 5000<ℓ<10⁶. The power spectrum has a broad maximum around ℓ≈30 000, where it reaches the value 2×10⁻¹². We also show that the ionization correlation function C _χ is not Gaussian, but at separation angles θ ≲10⁻⁴ rad it can be approximated by a modified Lorentzian shape; at larger separations an anticorrelation signal is predicted for both C _χ and C ( θ ). Detection of signals as above will be possible with future millimetre-wavelength interferometers like the Atacama Large Millimeter Array (ALMA) , which appears as an optimum instrument to search for signatures of inhomogeneous reionization.     

The effect of reionization on the cosmic microwave background–density correlation

In this paper, we show how the rescattering of cosmic microwave background photons after cosmic reionization can give a significant linear contribution to the temperature–matter cross-correlation measurements. These anisotropies, which arise via a late-time Doppler effect, are on scales much larger than the typical scale of non-linear effects at reionization; they can contribute to degree scale cross-correlations and could affect the interpretation of similar correlations resulting from the integrated Sachs–Wolfe effect. While expected to be small at low redshifts, these correlations can be large given a probe of the density at high redshift, and so could be a useful probe of the cosmic reionization history.     

Inhomogeneous reionization of the intergalactic medium regulated by radiative and stellar feedbacks

We study the inhomogeneous reionization in a critical density CDM universe resulting from stellar sources, including Population III objects. The spatial distribution of the sources is obtained from high-resolution numerical N -body simulations. We calculate the source properties, taking into account a self-consistent treatment of both radiative (i.e. ionizing and H₂-photodissociating photons) and stellar (i.e. SN explosions) feedbacks regulated by massive stars. This allows us to describe the topology of the ionized and dissociated regions at various cosmic epochs, and to derive the evolution of H, He and H₂ filling factors, soft UV background, cosmic star formation rate and the final fate of ionizing objects. The main results are: (i) galaxies reionize the intergalactic medium by z ≈10 (with some uncertainty related to the gas clumping factor), whereas H₂ is completely dissociated already by z ≈25; (ii) reionization is mostly caused by the relatively massive objects which collapse via H line cooling, while objects the formation of which relies on H₂ cooling alone are insufficient for this purpose; (iii) the diffuse soft UV background is the major source of radiative feedback effects for z ≤15; at higher z direct flux from neighbouring objects dominates; (iv) the match of the calculated cosmic star formation history with that observed at lower redshifts suggests that the conversion efficiency of baryons into stars is ≈1 per cent; (v) we find that a very large population of dark objects which failed to form stars is present by z ≈8. We discuss and compare our results with similar previous studies.     

Modelling the 21-cm Signal from the Epoch of Reionization and Cosmic Dawn

Studying the cosmic dawn and the epoch of reionization through the redshifted 21-cm line are among the major science goals of the SKA1. Their significance lies in the fact that they are closely related to the very first stars in the Universe. Interpreting the upcoming data would require detailed modelling of the relevant physical processes. In this article, we focus on the theoretical models of reionization that have been worked out by various groups working in India with the upcoming SKA in mind. These models include purely analytical and semi-numerical calculations as well as fully numerical radiative transfer simulations. The predictions of the 21-cm signal from these models would be useful in constraining the properties of the early galaxies using the SKA data.     

Bianchi model CMB polarization and its implications for CMB anomalies

We derive the cosmic microwave background (CMB) radiative transfer equation in the form of a multipole hierarchy in the nearly Friedmann–Robertson–Walker limit of homogeneous, but anisotropic, universes classified via their Bianchi type. Compared with previous calculations, this allows a more sophisticated treatment of recombination, produces predictions for the polarization of the radiation and allows for reionization. Our derivation is independent of any assumptions about the dynamical behaviour of the field equations, except that it requires anisotropies to be small back to recombination; this is already demanded by observations.
We calculate the polarization signal in the Bianchi VII _h case, with the parameters recently advocated to mimic the several large-angle anomalous features observed in the CMB. We find that the peak polarization signal is  ∼1.2 μK  for the best-fitting model to the temperature anisotropies, and is mostly confined to multipoles   l < 10  . Remarkably, the predicted large-angle EE and TE power spectra in the Bianchi model are consistent with Wilkinson Microwave Anisotropy Probe ( WMAP ) observations that are usually interpreted as evidence of early reionization. However, the power in B-mode polarization is predicted to be similar to the E-mode power and parity-violating correlations are also predicted by the model; the WMAP non-detection of either of these signals casts further strong doubts on the veracity of attempts to explain the large-angle anomalies with global anisotropy. On the other hand, given that there exist further dynamical degrees of freedom in the VII _h universes that are yet to be compared with CMB observations, we cannot at this time definitively reject the anisotropy explanation.     

Studying the sources of cosmic reionization with 21-cm fluctuations

We explore the ability of measurements of the 21-cm power spectrum during reionization to enable the simultaneous reconstruction of the reionization history and the properties of the ionizing sources. For various sets of simulated 21-cm observations, we perform maximum likelihood fits in order to constrain the reionization and galaxy formation histories. We employ a flexible six-parameter model that parametrizes the uncertainties in the properties of high-redshift galaxies. The computational speed needed is attained through the use of an analytical model that is in reasonable agreement with numerical simulations of reionization. We find that one-year observations, with the Murchison Widefield Array, should measure the cosmic ionized fraction to  ∼1 per cent  accuracy at the very end of reionization, and a few per cent accuracy around the mid-point of reionization. The mean halo mass of the ionizing sources should be measurable to 10 per cent accuracy when reionization is 2/3 of the way through, and to 20 per cent accuracy throughout the central stage of reionization, if this mass is anywhere in the range 1/3 to 100 billion solar masses.     

Probing the dark ages with the Square Kilometer Array

The epoch of reionization (EoR) sets a fundamental benchmark in cosmic structure formation, corresponding to the formation of the first luminous objects that act to ionize the neutral intergalactic medium (IGM). Recent observations at near-IR and radio wavelengths imply that we are finally probing into this key epoch of galaxy formation at z 6. The Square Kilometer Array (SKA) will provide critical insight into the EoR, in a number of ways. First, the ability of the SKA to image the neutral IGM in 21-cm emission is a truly unique probe of the process of reionization, and is recognized as the next necessary and fundamental step in our study of the evolution of large scale structure and cosmic reionization. Second, study of HI 21-cm absorption toward the first radio loud objects probes small to intermediate scale structure in the neutral ‘cosmic web’, as well as HI in the first collapsed structures (proto-disks and mini-halos). And third, the incomparable sensitivity of the SKA allows for the study of the molecular gas, dust, and star formation activity in the first galaxies, as well as the radio continuum emission from the first accreting massive black holes. Such objects will be obscured at optical wavelengths due to absorption by the neutral IGM.     

The effect of reionization on the COBE normalization

We point out that the effect of reionization on the microwave anisotropy power spectrum is not necessarily negligible on the scales probed by COBE . It can lead to an upward shift of the COBE normalization by more than the 1 σ error quoted, ignoring reionization. We provide a fitting function to incorporate reionization into the normalization of the matter power spectrum.     

Lyα damping wing constraints on inhomogeneous reionization

One well-known way to constrain the hydrogen neutral fraction,     , of the high-redshift intergalactic medium (IGM) is through the shape of the red damping wing of the Lyα absorption line. We examine this method's effectiveness in light of recent models showing that the IGM neutral fraction is highly inhomogeneous on large scales during reionization. Using both analytic models and 'seminumeric' simulations, we show that the 'picket-fence' absorption typical in reionization models introduces both scatter and a systematic bias to the measurement of     . In particular, we show that simple fits to the damping wing tend to overestimate the true neutral fraction in a partially ionized universe, with a fractional error of ∼30 per cent near the middle of reionization. This bias is generic to any inhomogeneous model. However, the bias is reduced and can even underestimate     if the observational sample only probes a subset of the entire halo population, such as quasars with large H  ii regions. We also find that the damping wing absorption profile is generally steeper than one would naively expect in a homogeneously ionized universe. The profile steepens and the sightline-to-sightline scatter increases as reionization progresses. Of course, the bias and scatter also depend on     and so can, at least in principle, be used to constrain it. Damping wing constraints must therefore be interpreted by comparison to theoretical models of inhomogeneous reionization.     

Cosmic microwave background constraints on the tensor-to-scalar ratio

One of the main goals of modern cosmic microwave background(CMB)missions is to measure the tensor-to-scalar ratio r accurately to constrain inflation models. Due to ignorance about the reionization history Xe(z), this analysis is usually done by assuming an instantaneous reionization Xe(z) which, however, can bias the best-fit value of r. Moreover, due to the strong mixing of B-mode and E-mode polarizations in cut-sky measurements, multiplying the sky coverage fraction fskyby the full-sky likelihood would not give satisfactory results. In this work, we forecast constraints on r for the Planck mission taking into account the general reionization scenario and cut-sky effects. Our results show that by applying an N-point interpolation analysis to the reionization history, the bias induced by the assumption of instantaneous reionization is removed and the value of r is constrained within 5% error level, if the true value of r is greater than about 0.1.     

The impact of H i in galaxies on 21-cm intensity fluctuations during the reionization epoch

We investigate the impact of neutral hydrogen (H  i ) in galaxies on the statistics of 21-cm fluctuations using seminumerical modelling. Following the reionization of hydrogen, the H  i content of the Universe is dominated by damped absorption systems (DLAs), with a cosmic density in H  i that is observed to be constant at a level equal to ∼2 per cent of the cosmic baryon density from   z ∼ 1  to   z ∼ 5  . We show that extrapolation of this constant fraction into the reionization epoch results in a reduction in the amplitude of 21-cm fluctuations over a range of spatial scales. We further find that consideration of H  i in galaxies/DLAs reduces the prominence of the H  ii region induced shoulder in the 21-cm power spectrum (PS), and hence modifies the scale dependence of 21-cm fluctuations. We also estimate the 21-cm–galaxy cross PS and show that the cross PS changes sign on scales corresponding to the H  ii regions. From consideration of the sensitivity for forthcoming low-frequency arrays, we find that the effects of H  i in galaxies/DLAs on the statistics of 21-cm fluctuations will be significant with respect to the precision of a PS or cross PS measurement. In addition, since overdense regions are reionized first we demonstrate that the cross-correlation between galaxies and 21-cm emission changes sign at the end of the reionization era, providing an alternative avenue to pinpoint the end of reionization. The sum of our analysis indicates that the H  i content of the galaxies that reionize the universe will need to be considered in detailed modelling of the 21-cm intensity PS in order to correctly interpret measurements from forthcoming low-frequency arrays.