The next generation 21 cm surveys open a new window onto the early stages of cosmic structure formation and provide new insights about the Epoch of Reionization (EoR). However, the non-Gaussian nature of the 21 cm signal along with the huge amount of data generated from these surveys will require more advanced techniques capable to efficiently extract the necessary information to constrain the Reionization History of the Universe. In this paper we present the use of Bayesian Neural Networks (BNNs) to predict the posterior distribution for four astrophysical and cosmological parameters. Besides achieving state-of-the-art prediction performances, the proposed methods provide accurate estimation of parameters uncertainties and infer correlations among them. Additionally, we demonstrate the advantages of Normalizing Flows (NF) combined with BNNs, being able to model more complex output distributions and thus capture key information as non-Gaussianities in the parameter conditional density distribution for astrophysical and cosmological dataset. Finally, we propose novel calibration methods employing Normalizing Flows after training, to produce reliable predictions, and we demonstrate the advantages of this approach both in terms of computational cost and prediction performances.
University of California at Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Our universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work we develop Translation and Rotation Equivariant Normalizing Flow (TRENF), a generative Normalizing Flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise nonlinear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, …
Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学）
The issue of fairness in machine learning stems from the fact that historical data often displays biases against specific groups of people which have been underprivileged in the recent past, or still are. In this context, one of the possible approaches is to employ fair representation learning algorithms which are able to remove biases from data, making groups statistically indistinguishable. In this paper, we instead develop a fair representation learning algorithm which is able to map individuals belonging to different groups in a single group. This is made possible by training a pair of Nor…
The measurement of the optical depth to free electrons, tau_r, in the cosmic microwave background (CMB) provides an important constraint on reionization, but is degenerate to more complex reionization models. Small angular-scale CMB measurements of the kinetic Sunyaev-Zeldovich (kSZ) and Ostriker-Vishniac (OV) effects have the potential to break this degeneracy. We calculate the OV signal for various extended reionization histories described by a simple analytic form. These models are parametrized by dz, the duration of the reionization event. For reionization histories with identical values o…
We investigate the constraints on the reionization history of the Universe from a joint analysis of the cosmic microwave background and neutral hydrogen fraction data. The $\tanh$ parametrization and principal component analysis methods are applied to the reionization history respectively. The commonly used $\tanh$ parametrization is oversimplistic when the neutral hydrogen fraction data are taken into account. Using the principal component analysis method, the reconstructed reionization history is consistent with the neutral hydrogen fraction data. With the principal component analysis method…
Marginal Post Processing of Bayesian Inference Products with Normalizing Flows and Kernel Density Estimators
Cavendish Laboratory（卡文迪许实验室）；Kavli Institute for Cosmology, Cambridge（剑桥卡弗里宇宙学研究所）；University College London（伦敦大学学院）；University of Sussex（萨塞克斯大学）；McGill University（麦吉尔大学）；University of Cambridge（剑桥大学）；Stockholm University（斯德哥尔摩大学）
In this paper, we explore the constraints on the reionization history that are provided by current observations of the Lyman-alpha forest and the CMB. Rather than using a particular semi-analytic model, we take the novel approach of parametrizing the ionizing sources with arbitrary functions, and perform likelihood analyses to constrain possible reionization histories. We find model independent conclusions that reionization is likely to be mostly complete by z=8 and that the IGM was 50% ionized at z=9-10. Upcoming low-frequency observations of the redshifted 21 cm line of neutral hydrogen are …
Observations of the frequency dependence of the global brightness temperature of the redshifted 21 cm line of neutral hydrogen may be possible with single dipole experiments. In this paper, we develop a Fisher matrix formalism for calculating the sensitivity of such instruments to the 21 cm signal from reionization and the dark ages. We show that rapid reionization histories with duration delta z< 2 can be constrained, provided that local foregrounds can be well modelled by low order polynomials. It is then shown that observations in the range nu = 50 - 100 MHz can feasibly constrain the Lyman…
The Square Kilometre Array (SKA) will offer an unprecedented view onto the early Universe, using interferometric observations of the redshifted 21cm line. The 21cm line probes the thermal and ionization state of the cosmic gas, which is governed by the birth and evolution of the first structures in our Universe. Here we show how the evolution of the 21cm signal will allow us to study when the first generations of galaxies appeared, what were their properties, and what was the structure of the intergalactic medium. We highlight qualitative trends which will offer robust insights into the early …
We present proof of principle for a two way interplay between physics at very early Universe and late time observations. We find a relation between primordial mechanisms responsible for large scale power suppression in the primordial power spectrum and the value of reionization optical depth $τ$. Such mechanisms can affect the estimation of $τ$. We show that using future measurements of $τ$, one can obtain constraints on the pre-inflationary dynamics, providing a new window on the physics of the very early Universe. Furthermore, the new, re-estimated $τ$ can potentially resolve moderate discre…
We present an analysis of the evolution of the Lyman-series forest into the epoch of reionization using cosmological radiative transfer simulations in a scenario where reionization ends late. We explore models with different midpoints of reionization and gas temperatures. We find that once the simulations have been calibrated to match the mean flux of the observed Lyman-$α$ forest at $4 < z < 6$, they also naturally reproduce the distribution of effective optical depths of the Lyman-$β$ forest in this redshift range. We note that the tail of the largest optical depths that is most challenging …
The discovery of fast radio bursts (FRBs) about a decade ago opened up new possibilities for probing the ionization history of the Intergalactic Medium (IGM). In this paper we study the use of FRBs for tracing the epoch of HeII reionization, using simulations of their dispersion measures. We model dispersion measure contributions from the Milky Way, the IGM (homogeneous and inhomogeneous) and a possible host galaxy as a function of redshift and star formation rate. We estimate the number of FRBs required to distinguish between a model of the Universe in which helium reionization occurred at z …
The period in which hydrogen in the intergalactic medium (IGM) is ionized, known as the Epoch of Reionization (EoR) is still poorly understood. The timing and duration of the EoR is expected to be governed by the underlying astrophysics. Furthermore, most models of reionization predict a correlation between the density and ionization field. Here we consider using the mean dispersion measure (DM) of high redshift Fast Radio Bursts (FRBs) as a probe of the underlying astrophysics and morphology of the EoR. To do this, we forecast observational scenarios by building mock data sets of non-repeatin…
We investigate the cosmic reionization history by comparing semi-analytical models of the Lya forest with observations of high-z quasars and gamma ray bursts absorption spectra. In order to constrain the reionization epoch z_rei, we consider two physically motivated scenarios in which reionization ends either early (ERM, z_rei>= 7) or late (LRM, z_rei~6). We analyze the transmitted flux in a sample of 17 quasars spectra at 5.7<z<6.4 and in the spectrum of the gamma ray burst 050904 at z=6.3, studying the wide dark portions (gaps) in the observed absorption spectra. By comparing the statistics …
A number of independent observations suggest that the intergalactic medium was significantly neutral at $z=7$ and that reionization was, perhaps, still in progress at $z=5.7$. The narrowband survey, SILVERRUSH, has mapped over $2,000$ Lyman-$α$ emitters (LAEs) at these redshifts. Previous analyses have assumed that reionization was over by $z=5.7$, but this data may actually sample the final stages of reionization when the last neutral islands were relegated to the cosmic voids. Motivated by these developments, we reexamine LAE void and peak statistics and their ability to constrain reionizati…
Neutral diffuse intergalactic gas that existed during the Epoch of Reionization (EoR) suppresses Lyman Alpha (Lya) flux emitted by background galaxies. In this chapter I summarise the increasing observational support for the claim that Lya photons emitted by galaxies at z>6 are suppressed by intervening HI gas. I describe key physical processes that affect Lya transfer during the EoR. I argue that in spite of the uncertainties associated with this complex multiscale problem, the data on Lya emitting galaxies at z=0-6 strongly suggests that the observed reduction in Lya flux from galaxies at z>…
Given that the reionization history of cosmic hydrogen is yet to be stringently constrained, it is worth checking the prospects of doing so using physically motivated models and available observational data. For this purpose, we use an extended version of the explicitly photon-conserving semi-numerical model of reionization, $\texttt{SCRIPT}$, which also includes thermal evolution of the intergalactic medium (IGM). The model incorporates the effects of inhomogeneous recombination and radiative feedback self-consistently and is characterized by five free parameters (two for the redshift-depende…
We combine available constraints on the local CII 158 $μ$m line luminosity function from galaxy observations (Hemmati et al. 2017), with the evolution of the star-formation rate density and the recent CII intensity mapping measurement in Pullen et al. (2018, assuming detection), to derive the evolution of the CII luminosity - halo mass relation over $z \sim 0-6$. We develop convenient fitting forms for the evolution of the CII luminosity - halo mass relation, and forecast constraints on the CII intensity mapping power spectrum and its associated uncertainty across redshifts. We predict the sen…
We build a physical model for high-redshift Lyman Alpha emitters (LAEs) by coupling state of the art cosmological simulations (GADGET-2) with a dust model and a radiative transfer code (pCRASH). We post-process the cosmological simulation with pCRASH using five different values of the escape fraction of hydrogen ionizing photons (f_esc=0.05,0.25,0.5,0.75,0.95) until reionization is complete, i.e. the average neutral hydrogen fraction drops to <X_HI>~10^-4. Then, the only free-parameter left to match model results to the observed Lya and UV luminosity functions of LAEs at z~6.6 is the relative …
We combine observational data on a dozen independent cosmic properties at high-$z$ with the information on reionization drawn from the spectra of distant luminous sources and the cosmic microwave background (CMB) to constrain the interconnected evolution of galaxies and the intergalactic medium since the dark ages. The only acceptable solutions are concentrated in two narrow sets. In one of them reionization proceeds in two phases: a first one driven by Population III stars, completed at $z\sim 10$, and after a short recombination period a second one driven by normal galaxies, completed at $z\…
We present a new semi-analytical model of the population of satellite galaxies of the Milky Way, aimed at estimating the effect of the geometry of reionization at galaxy scale on the properties of the satellites. In this model reionization can be either: (A) externally-driven and uniform, or (B) internally-driven, by the most massive progenitor of the Milky Way. In the latter scenario the propagation of the ionisation front and photon dilution introduce a delay in the photo-evaporation of the outer satellites' gas with respect to the inner satellites. As a consequence, outer satellites experie…
High-signal to noise observations of the Ly$α$ forest transmissivity in the z = 7.085 QSO ULAS J1120+0641 show seven narrow transmission spikes followed by a long 240 cMpc/h trough. Here we use radiative transfer simulations of cosmic reionization previously calibrated to match a wider range of Ly$α$ forest data to show that the occurrence of seven transmission spikes in the narrow redshift range z = 5.85 - 6.1 is very sensitive to the exact timing of reionization. Occurrence of the spikes requires the most under dense regions of the IGM to be already fully ionised. The rapid onset of a long t…
The latest measurements of CMB electron scattering optical depth reported by Planck significantly reduces the allowed space of HI reionization models, pointing toward a later ending and/or less extended phase transition than previously believed. Reionization impulsively heats the intergalactic medium (IGM) to $\sim10^4$ K, and owing to long cooling and dynamical times in the diffuse gas, comparable to the Hubble time, memory of reionization heating is retained. Therefore, a late ending reionization has significant implications for the structure of the $z\sim5-6$ Lyman-$α$ (ly$α$) forest. Using…
A possible way to study the reionization of cosmic hydrogen is by observing the large ionized regions (bubbles) around bright individual sources, e.g., quasars, using the redshifted 21 cm signal. It has already been shown that matched filter-based methods are not only able to detect the weak 21 cm signal from these bubbles but also aid in constraining their properties. In this work, we extend the previous studies to develop a rigorous Bayesian framework to explore the possibility of constraining the parameters that characterize the bubbles. To check the accuracy with which we can recover the b…
We investigate Lyman-$α$ transmission spikes at $z > 5$ in synthetic quasar spectra, and discuss their connection to the properties of the intergalactic medium and their ability to constrain reionization models. We use state-of-the-art radiation-hydrodynamic simulations from the Cosmic Reionization On Computers series to predict the number of transmission spikes as a function of redshift, both in the ideal case of infinite spectral resolution and in a realistic observational setting. Transmission spikes are produced in highly-ionized underdense regions located in the vicinity of UV sources. We…
Understanding the detailed process of cosmic reionization is one of the remaining problems in astrophysics and cosmology. Here we construct a model of cosmic reionization that includes contribution from high-$z$ galaxies and active galactic nuclei (AGNs), and calculate the reionization and thermal histories with the model. To keep the model to be general and realistic, we vary the escape fraction of ionizing photons, $f_{\rm esc}$, and the faint-end slope of the AGN luminosity function at high redshifts, $α_{\rm hz}$, within the constraints from the observed cosmic star formation history and t…
One of the most promising probes to constrain the reionization history of the universe is the power spectrum of neutral hydrogen 21 cm emission fluctuations. The corresponding analyses require computationally efficient modelling of reionization, usually achieved through semi-numerical simulations. We investigate the capability of one such semi-numerical code, SCRIPT, to constrain the reionization parameters. Our study involves creating a mock data set corresponding to the upcoming SKA-Low, followed by a Bayesian inference method to constrain the model parameters. In particular, we explore in d…
In the absence of complex astrophysical processes that characterize the reionization era, the 21-cm emission from neutral hydrogen (HI) in the post-reionization epoch is believed to be an excellent tracer of the underlying dark matter distribution. Assuming a background cosmology, it is modelled through (i) a bias function b(k,z), which relates HI to the dark matter distribution and (ii) a mean neutral fraction (x_{HI}) which sets its amplitude. In this paper, we investigate the nature of large scale HI bias. The post-reionization HI is modelled using gravity only N-Body simulations and a suit…
The neutral intergalactic medium in the post reionization epoch allows us to study cosmological structure formation through the observation of the redshifted 21 cm signal and the Lyman-alpha forest. We investigate the possibility of measuring the total neutrino mass through the suppression of power in the matter power spectrum. We investigate the possibility of measuring the neutrino mass through its imprint on the cross-correlation power spectrum of the 21-cm signal and the Lyman-alpha forest. We consider a radio-interferometric measurement of the 21 cm signal with a SKA1-mid like radio teles…
Upcoming 21cm surveys with the SKA1-LOW telescope will enable imaging of the neutral hydrogen distribution on cosmological scales in the early Universe. These surveys are expected to generate huge imaging datasets that will encode more information than the power spectrum. This provides an alternative unique way to constrain the reionization history, which might break the degeneracy in the power spectral analysis. Using Convolutional Neural Networks (CNN), we create a fast estimator of the neutral fraction from the 21cm maps that are produced by our large semi-numerical simulation. Our estimato…
Several experiments are underway to detect the cosmic redshifted 21-cm signal from neutral hydrogen from the Epoch of Reionization (EoR). Due to their very low signal-to-noise ratio, these observations aim for a statistical detection of the signal by measuring its power spectrum. We investigate the extraction of the variance of the signal as a first step towards detecting and constraining the global history of the EoR. Signal variance is the integral of the signal's power spectrum, and it is expected to be measured with a high significance. We demonstrate this through results from a simulation…
We use the Fisher matrix formalism and semi-numerical simulations to derive quantitative predictions of the constraints that power spectrum measurements on next-generation interferometers, such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA), will place on the characteristics of the X-ray sources that heated the high redshift intergalactic medium. Incorporating observations between $z=5$ and $z=25$, we find that the proposed 331 element HERA and SKA phase 1 will be capable of placing $\lesssim 10\%$ constraints on the spectral properties of these first X…
The Murchison Widefield Array (MWA) team has derived new upper limits on the spherically averaged power spectrum of the 21-cm signal at six redshifts in the range $z \approx 6.5-8.7$. We use these upper limits and a Bayesian inference framework to derive constraints on the ionization and thermal state of the intergalactic medium (IGM) as well as on the strength of a possible additional radio background. We do not find any constraints on the state of the IGM for $z\gtrsim 7.8$ if no additional radio background is present. In the presence of such a radio background, the 95 per cent credible inte…
We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, $δτ$, and the Compton $y$-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the $y$-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic SZ effect can not. We measure this new observable using a Planck…
We investigate the effect of primordial non-Gaussianity on the cross-correlation between the CMB anisotropies and the 21 cm fluctuations from the epoch of reionization. We assume an analytic reionization model and an ionization fraction with $f_{\rm NL}$ induced scale dependent bias. We estimate the angular power spectrum of the cross-correlation of the CMB and 21 cm. In order to evaluate the detectability, the signal-to-noise (S/N) ratio for only a single redshift slice is also calculated for current and future observations, such as CMB observations by Planck satellite and 21 cm observations …
We explore the possibility of constraining model parameters of the Epoch of Reionization (EoR) from 21cm brightness temperature maps, using a combination of morphological descriptors constructed from the eigenvalues of the Contour Minkowski Tensor (CMT), Betti numbers (count of connected regions $n_{con}$ and holes $n_{hole}$) and the area of structures in the excursion set of the field. We use a three parameter model of EoR simulated using 21\textrm{cmFAST}, namely the ionizing efficiency of sources $ζ$, the minimum virial temperature $T_{vir}$ required for collapse into a halo and the maximu…
We investigate the prospects of detecting the cross correlation of CMBR weak-lensing convergence field with the large scale tracers of the underlying dark matter distribution in the post-reionization epoch. The cross-correlation is then used to make error projections for dark energy equation of state (EoS)for models with a time evolving dark energy. We study the cross-correlation angular power spectrum of the weak-lensing field with the Lyman-$α$ forest and the redshifted HI 21 cm signal from the post reionization epoch. The angular power spectra is expressed as a line of sight average over th…
We constrain the warm dark matter (WDM) particle mass with the observations of cosmic reionization and CMB optical depth. We suggest that the GWs from stellar mass black holes (BHs) could give a further constraint on WDM particle mass for future observations. The star formation rates (SFRs) of Population I/II (Pop I/II) and Population III (Pop III) stars are also derived. If the metallicity of the universe have been enriched beyond the critical value of $Z_{\rm crit}=10^{-3.5}Z_{\odot}$, the star formation shift from Pop III to Pop I/II stars. Our results show that the SFRs are quite dependent…
Shanghai Jiao Tong University（上海交通大学）；King’s College London（伦敦国王学院）；University of Sheffield（谢菲尔德大学）；Harvard University（哈佛大学）；Università degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）
Dark matter constitutes the great majority of the matter content in the Universe, but its microscopic nature remains an intriguing mystery, with profound implications for particle physics, astrophysics and cosmology. Here we shed light on the longstanding issue of whether the dark matter is warm or cold by combining the measurements of the galaxy luminosity functions out to high redshifts z~10 from the Hubble Space Telescope with the recent cosmological data on the reionization history of the Universe from the Planck mission. We derive robust and tight bounds on the mass of warm dark matter pa…
The epoch of reionization (6 < z < 10) marks the period in our universe when the first large galaxies grew to fruition, and began to affect the universe around them. Massive stars, and potentially accreting supermassive black holes, filled the universe with ionizing radiation, burning off the haze of neutral gas that had filled the intergalactic medium (IGM) since recombination (z~1000). The evolution of this process constrains key properties of these earliest luminous sources, thus observationally constraining reionization is a key science goal for the next decade. The measurement of Lyman-al…
Constraining reionization with persistent homology: a novel summary statistic for wide-field Lyman-$α$ emitter observations
University of California, Los Angeles（加州大学洛杉矶分校）；Scuola Normale Superiore（比萨高等师范学院）；University of Tsukuba（筑波大学）；The University of Tokyo（东京大学）；Institute for Cosmic Ray Research, The University of Tokyo（东京大学宇宙射线研究所）；University of Catania（卡塔尼亚大学）；National Astronomical Observatory of Japan, National Institutes of Natural Sciences（日本国立天文台，国立自然科学研究院）；SOKENDAI (The Graduate University for Advanced Studies)（综合研究大学院大学）；Kavli Institute for the Physics and Mathematics of the Universe (WPI)（宇宙物质与物理学 Kavli 研究所）
Redshifted 21cm-line signal from neutral hydrogens in the intergalactic medium (IGM) gives a direct probe of the epoch of reionization (EoR). In this paper, we investigate the potential of the variance and skewness of the probability distribution function of the 21cm brightness temperature for constraining EoR models. These statistical quantities are simple, easy to calculate from the observed visibility and thus suitable for the early exploration of the EoR with ongoing telescopes such as the Murchison Widefield Array (MWA) and LOw Frequency ARray (LOFAR). We show, by performing Fisher analys…
The 21cm line probes the evolution of matter perturbations over a wide range of redshifts, from the dark ages down to the completion of reionization. Observing the 21cm cosmological signal will extend our understanding of the evolution of the Universe and it is thus important to investigate the predictions of different cosmological models. In this paper we focus on the prospect of constraining coupled quintessence models during the Epoch of Reionization both for global signal experiments and for intensity mapping surveys. To derive the all-sky 21cm signal and fluctuations in coupled quintessen…
We explore the ability of observations of the global brightness temperature of the 21-cm signal to constrain the reionization history and the properties of the ionizing sources. In order to describe the reionization signal, we employ either a commonly-used toy model or a structure formation model that parameterizes the properties of the ionizing sources. If the structure formation model captures the actual evolution of the reionization signal, then detecting the signal is somewhat easier than it would be for the toy model; using the toy model in this case also leads to systematic errors in rec…
The dispersion measure of extragalactic radio transients, such as of recently discovered Fast Radio Burst FRB150418, can be used to measure the column density of free electrons in the intergalactic medium. The same electrons also scatter the Cosmic Microwave Background (CMB) photons, affecting precision measurements of cosmological parameters. We explore the connection between the dispersion measure of radio transients existing during the Epoch of Reionization (EoR) and the total optical depth for the CMB, $τ_{CMB}$, showing that the existence of such transients would provide a new sensitive p…
We derive constraints on the thermal and ionization states of the intergalactic medium (IGM) at redshift $\approx$ 9.1 using new upper limits on the 21-cm power spectrum measured by the LOFAR radio-telescope and a prior on the ionized fraction at that redshift estimated from recent cosmic microwave background (CMB) observations. We have used results from the reionization simulation code GRIZZLY and a Bayesian inference framework to constrain the parameters which describe the physical state of the IGM. We find that, if the gas heating remains negligible, an IGM with ionized fraction $\gtrsim 0.…
