C-lab Seminar 2019 | Seminar | Nagoya University Cosmology Group (C-lab)

C-lab Seminar 2019

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Coming Seminars

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Seminars in October

Speaker
Rika Ando

Date/Place
13:00-, 9(Wed), Oct. @ES606

Title
Modeling of HI power spectrum with halo model approach

Abstract
Observations of large-scale structures (LSS) in the universe have been widely used to explore the origins of accelerated expansion of the universe, such as dark energy and modified gravity. Currently, 21-cm line emitted from neutral hydrogen (HI) is drawing attention as a probe of LSS. The 21-cm line intensity mapping can observe a wider and distant universe than conventional galaxy surveys. However, in the case of cosmological analysis by 21-cm survey, there is still no theoretical model to compare with observation, and it is necessary to construct it. Therefore it is necessary to understand the nature of the large-scale clustering of the HI. But since the complex physical processes such as UV background radiation and baryonic feedback from galaxies contribute to the ratio and spatial distribution of the HI , it is difficult to solve analytically.
Although it is necessary to model the HI power spectrum, cosmological hydrodynamical simulations with large box-size and large particle number are computationally expensive. In this study, we investigated better methods to reconstruct the HI distribution from the dark matter distribution obtained from N-body simulation.
After reionization, most of the HI is present inside the high-density regions such as dark matter halos, so a method of assigning HI on the dark matter halos has been done in several previous studies. However, we found that such a method underestimates the power spectrum. We will show the contribution to the power spectrum of HI present in the intergalactic medium (IGM) and discuss the modeling of HI in the halo and IGM.

Speaker
Shun Arai

Date/Place
15:00-, 2(Wed), Oct. @ES606

Title
Cosmological tests of scalar-tensor theories as a probe of spacetime symmetry

Abstract
In the present state of cosmology, it is believed that the accelerating expansion of the Universe called cosmic acceleration has occurred at least twice; inflation and late-time acceleration. As observations have shown, the accelerations we observed are well approximated by the de Sitter space, namely, the quasi-de Sitter phase.
The accountability for the cosmic acceleration is normally provided by a new scalar degree of freedom whose time evolution dynamically breaks the time translation symmetry of the de Sitter space. In the path of generalization of gravity theories, meanwhile, the break of the time translation symmetry is generally derived from the Effective Field Theory approach, or the analysis of the generic class of scalar-tensor theory, such as Horndeski, GLPV, and DHOST theories. In the last decade, the application of the EFT or scalar-tensor theories for cosmic acceleration has drawn the attention of the cosmological community as an alternative explanation for cosmic acceleration.
In this seminar, we shed the light to spot the nature of late time acceleration through the tests of scalar-tensor theories. We specifically argue how significantly the scalar-tensor theories are inspected by forthcoming observations such as galaxy surveys, cosmic shear, and gravitational wave observations. We show that the most promising cases enable us to reach the accuracy at 1% for testing any departure from the Lambda-CDM concordance cosmology.

Seminars in July

Speaker
Shin’ichi Hirano

Date/Place
15:00-, 24(Wed), July. @ES606

Title
Constraining Degenerate Higher-Order Scalar-Tensor (DHOST) theories with matter density fluctuations

Abstract
We consider the constraints on Degenerate Higher-Order Scalar-Tensor (DHOST) theories with matter density fluctuations. The DHOST theory is one of the most interesting model of modified gravity which is an origin of the late-time acceleration. Its equations of motion has higher derivatives more than second order, but there is no ghost modes due to its degeneracy. These derivative interactions are imprinted on the growth of density fluctuations at both linear and non-linear levels. At a linear level, the effect of these interactions appears as the new friction term on the evolution equation of linear density fluctuations. Then, we derive the growth index of the linear growth rate in the DHOST theories and can constrain it from LSS observations. At a non-linear level, the second-order kernel is modified from that of GR and the shape dependence of matter bispectrum is peaked at the folded triangle in the DHOST theories.

Speaker
Kunihiko Furugori

Date/Place
13:00-, 24(Wed), July. @ES606

Title
21-cm線を用いた小スケールの初期パワースペクトルへの制限

Abstract
ビッグバン理論の宇宙初期に関する諸問題の解決策としてインフレーション理論がある。インフレーションモデルは無数に存在するため、そのモデルを制限する必要がある。その方法の一つに初期パワースペクトルによる制限がある。初期パワースペクトルの制限は宇宙マイクロ波背景放射の観測などから得られてきたが、小スケール側 ($波数 k \ge 1Mpc^{-1}$) は不定性が大きい。近年注目されている Ultracompact minihalo (UCMH) という天体を用いることで小スケール側に制限を課せる可能性がある。 UCMH は、赤方偏移 z=1000 に形成される高密度天体であり、密度揺らぎの大きさが $10^{-3} \le \delta \le 0.3$ を 満たす時に構造形成されうる。高赤方偏移において形成される UCMH は、空間的にコンパクトであり、初期パワースペクトルの短波長側の波数範囲に制限をつけることが期待される。
本研究では、21-cm 線を用いて UCMH の存在量に制限を課し、小スケール側の初期パワースペクトルに制限をつけることを目的とする。21-cm 線とは、中性水素の超微細構造由来の電磁波である。2020 年代前半に観測を開始する Square Kilometre Array(SKA) によって z =30 程度までの観測が期待される見込みである。宇宙再電離より十分以前であるから、 UCMH も中性水素ガスを持つと考えられる。そのため UCMH 内部の中性水素に由来する 21cm 線が観測できると期待される。
本講演では、UCMH の中性水素密度分布および温度分布をモデル化することで、個別の UCMH の 21-cm 線シグナル分布 を導出する手法を紹介する。そして、SKA の感度を考慮することにより、UCMH の存在量に制限を与える可能性につい て議論する。また、その結果から、$k \ge 1Mpc^{-1}$ の小スケール 側の初期パワースペクトルの制限について議論する。

Speaker
Koya Murakami

Date/Place
13:00-, 24(Wed), July. @ES606

Title
Non Bunch-Davies真空における単一スカラー場インフレーションモデルの観測量の推定

Abstract
インフレーション理論はビッグバン理論の抱える問題を解決するために生まれた理論であり、多様なモデルが存在する。その中でも最も単純なモデルとして、単一スカラー場インフレーションモデルがある。インフレーションモデルを特徴付ける観測量として、テンソル・スカラー比 r と非ガウス性パラメータ fNL に着目する。ここでテンソル・スカラー比とは、テンソル型の揺らぎ (初期重力波を生む時空の揺らぎ) とスカラー型の揺らぎ (曲率揺らぎと呼ばれる揺らぎで、密度揺らぎの起源となる) それぞれの二点相関関数の大きさの比に対応する量で、非ガウス性パラメータ fNL はインフレーション期につくられる初期揺らぎの三点相関の大きさを表す量である。このモデルでは r はスローロールパラメーター ε を用いて理論的に r = 16ε で表され、実際の CMB 観測では、その値は r < 0.07(⇒ ε < 0.07/16) に制限されている。また、fNL は無視できるほど小さな値となる。
上述のテンソル・スカラー比とスローロールパラメーターの関係や fNL の大きさを求める際には、曲がった時空において不定性を持つ真空について、Bunch-Davies 真空と呼ばれる小スケール極限で平坦時空の真空と一致するよう定義された真空が仮定されているが、今回はそれとは異なった真空を考える. 本発表では参考文献 Brahma, & Hossain(2019) 及び Ashoorioon(2019) のレビューとして、真空の変更がテンソル・スカラー比や fNL に与える影響について議論する。さらに近年の Planck による制限との比較を行い、string swampland conjecture と呼ばれる弦理論の予言との整合性についても紹介する。

Speaker
Ikumi Ueda

Date/Place
13:00-, 17(Wed), July. @ES606

Title
クォーク・ハドロン相転移による背景重力波への影響

Abstract
宇宙が誕生して間もない頃にクォーク・ハドロン相転移(QCD相転移)が起きたであろうことは広く受け入れられている。QCD相転移とは、それまで自由粒子として存在していたクォークとグルーオンが、宇宙が冷えていくにつれて陽子などのハドロンを形成し始めることである。しかし、宇宙の進化の過程で相転移が起きたことを示す直接的な証拠は未だ得られておらず、その詳細も十分に理解されていない。QCD相転移が起きたのは宇宙の晴れ上がり以前なので、重力波でのみ直接観測することができる。そのため、QCD相転移期間に生み出される重力波を観測することは宇宙の進化の過程で相転移が生じた証拠になるとともに、基礎物理学に対する理解を深める上で重要である。
格子QCDを用いた相転移の非摂動的な解析により、QCD相転移中では状態方程式パラメータが時間とともに変化することが明らかになっている。この状態方程式パラメータの時間変化は重力ポテンシャルの振る舞いを変化させる。その結果、重力ポテンシャルの空間的な揺らぎによって生み出される重力波もその影響を受けるため、QCD相転移が生じた痕跡を求めることができる。そこで、本研究では状態方程式パラメータの時間変化が重力波のシグナルに与える影響を計算する。これにより将来的な観測に対する制限をつけるとともに、QCD相転移に対する検証可能性を与えることが期待される。
本発表では、今回行なった重力波の数値計算の結果を報告し、将来的な検出可能性について議論する。

Speaker
Kouki Sakoda

Date/Place
13:00-, 17(Wed), July. @ES606

Title
21cm線とCMB弱重力レンズ効果の相互相関による中性水素存在量の推定

Abstract
宇宙の再電離以降、宇宙空間に存在する水素のほとんどは電離されており、残された中性水素(HI)の大部分は銀河などの高密度領域に存在する。従ってHIを探ることは銀河などの高密度領域の中を見るということに他ならない。高密度領域では星形成が行われており、HIはその苗床である。したがってHIの存在量の時間変化を探ることは宇宙論的な星形成の理解につながる。
HIは波長21cmの電磁波(21cm線)を放出する。従って21cm線を観測すば、HIの存在量の時間発展を得ることができる。しかし、21cm線のシグナルは前景放射によって汚染されてしまう。この問題を解決するために、21cm線と、大規模構造がCMBに及ぼす重力レンズ効果による収束場との相互相関をとるという手法を採用する。[Tanaka et al 2019]では、今後観測が始まる望遠鏡であるSKA(Square Kilometre Array)を想定した場合に、HIの存在量の推定精度をFisher解析により予測している。その結果、SKA観測による、相互相関を用いたHIの存在量の推定は、従来の望遠鏡による他の手法を用いた制限よりも、高赤方偏移まで精度よくHIの存在量を推定できる可能性を示している。
本発表では、21cm線とCMB弱重力レンズ効果の相互相関によるHI存在量推定の妥当性をシミュレーションにより検証し、その結果について議論を行う。

Speaker
Nanaka Yamamoto

Date/Place
13:00-, 17(Wed), July. @ES606

Title
CMBレンジングを用いた銀河団の質量推

Abstract
銀河団は宇宙の中で最も大きな質量を持つ天体であり、銀河団の質量と数の関係は、原始密度揺らぎや暗黒 エネルギーの性質に強く依存する。そのため、観測によって多くの銀河団を発見し、その質量を正しく推定 する事は、宇宙論モデルの制限において非常に重要である。近年すばる望遠鏡 Hyper Suprime-Cam (HSC)などの観測により z ∼ 1 程度の遠方銀河団が数多く見つかっており、銀河団を用いた精密宇宙論が期待され る。また、質量の大部分を暗黒エネルギーが占める銀河団に対し、弱重力レンズ効果を用いることで高精度の質量推定が可能となる。特に、z ∼ 1100 の最終散乱面から放射される宇宙マイクロ波背景放射 (CMB) を背 景光とする弱重力レンズ効果を用いると、遠方宇宙における質量分布の情報を手に入れることが出来る。
本発表では、質量推定のための準備としてPlanckのCMB レンズマップとSDSS のredMaPPerカタログ、 HSC のCAMIRA カタログ を組み合わせて銀河団 の周囲 における CMB レンズ信号のスタッキング解析を行った結果を報告す。

Speaker
Toshiyuki Tanaka

Date/Place
13:00-, 10(Wed), July. @ES606

Title
Sub-grid model of escape fraction for cosmological 21-cm signal simulation

Abstract
Based on the standard model of structure formation, the first stars have formed at around redshift 20-30 in mini-haloes. They play important roles in the history of the universe such as emitting ionizing photons and providing metals into intergalactic medium. Although resent theoretical studies remarkably improve our understanding on the stellar mass function (SMF) of the first stars, these studies have not reached consensus on the SMF. On the other hand, forthcoming 21-cm observation by SKA is expected to obtain 21-cm signal, originated from neutral hydrogen, from the first stars’ era, which would enables us to approach the SMF observationally. However, the relation between the SMF and cosmological 21-cm signal is poorly understood. Therefore, we model the relation focusing on the escape fraction of the ionizing photons for mini-haloes hosing the first stars. In this talk, I will explain, in detail, the model of escape fraction dependent on the SMF, background density, and redshift. Finally, I will show the results from test calculations of cosmological 21-cm signal with 21cmFAST in order to demonstrate how important the escape fraction is on the large scale 21-cm signal distribution.

Speaker
Mutsumi Minoguchi

Date/Place
13:00-, 3(Wed), July. @ES606

Title
Dynamical Evolution of Voids with Surrounding Gravitational Tidal Field

Abstract
The underdense regions of the Universe are called voids. While they are promising probe of gravity and cosmology on a larger scale than the galaxy, there is not enough agreement on what is the appropriate model for individual voids' evolution. It is known that the underdense region itself tends to grow to be spherical (V. Icke 1984), but the voids in cosmic web rather distort as it grows (e.g. E.G.P. Bos et al. 2012). Though there are some possibilities to cause this, here I follow the description that voids are distorted by the tidal field on their effective radii, and examine the correlation between time derivative of void shape and the tidal field. In this talk, I will first briefly introduce some previous works on the nature of void and related topics, and discuss the main cause of void shape evolution.

Seminars in June

Speaker
Teppei Minoda

Date/Place
13:00-, 26(Wed), June. @ES606

Title
CMB constraint on primordial magnetic fields

Abstract
Large-scale structure (e.g., voids and galaxy clusters) is magnetized. The primordial magnetic fields (PMFs) are expected to explain the origin of these magnetic fields. If the PMFs exist, they possibly create remarkable effects on some cosmological observables, including the cosmic microwave background (CMB) anisotropy. PMFs create additional metric perturbations in the early universe, and induce the CMB temperature and polarization anisotropy. As these effects should include the information about the epoch or mechanisms of the primordial magnetogenesis, we can put a constraint on the PMF model parameters by analyzing the CMB data from Planck satellite and South Pole Telescope. In this seminar, I mainly review the effect of PMFs on the CMB anisotropy, and show the constraint on PMFs that we obtained.

Speaker
Alexis Boudon

Date/Place
13:00-, 26(Wed), June. @ES606

Title
Non-minimally coupled quintessence and the evolution of the present day equation of state

Abstract
Quintessence, a canonical scalar tensor theory, is one of the simplest candidates to explain dark energy. During this presentation, we will look at the different changes that a non-minimally coupled theory of the quintessence can bring to the cosmological equation of state and to the gravitational "constant". In the first part, I will present the modifications on the Friedmann and Klein-Gordon equations as well as important formulas. In a second part, I will explain the approach used to build a code capable of numerically solving these equations according to different parameters. Finally, I will show that the equation of state and the gravitational "constant" depend a lot of these parameters but that within the limits of current observations, these differences are minimal.

Speaker
Yuichiro Tada

Date/Place
13:00-, 19(Wed), June. @ES606

Title
Aspects of primordial black holes and implication to multi-phase inflation

Abstract
As proposed by Hawking and Carr more than four decades ago, black holes can be formed even during the early radiation-dominated era in advance of the ordinary star formation, called “primordial black hole (PBH)”. The possible mass of PBHs covers a very wide range, and the extremely light one (~10^-12 M_\odot) attracts attention as a candidate of the main component of dark matters. Moreover recent LIGO/VIRGO’s gravitational wave detections have revealed the ubiquitous existence of slightly massive and less spinning BHs, which also can be explained by the primordial ones. I first briefly review such astrophysical motivations of PBHs and current constraints on those. Then I show that PBHs can be easily realized if inflation is not a single continuous phase but can be divided into multiple phases. Interestingly recently proposed “dS conjecture” in the context of string theory may also support such a multi-phase inflation scenario.

Speaker
Kenji Hasegawa

Date/Place
13:00-, 12(Wed), June. @ES606

Title
Where are metals originated in massive Population III stars?

Abstract
Theoretical studies have shown that Population III stars are massive. Since massive metal-free stars are expected to eject metals with a characteristic pattern when the stars explode, detecting such a characteristic abundance pattern would be direct evidence for massive Pop III stars. In this study, by using numerical simulation data, we explore the distribution of metals ejected by Pop III stars, and compare it to that by Pop I (or II) galaxies. As a result, we find that metals originated in Pop III stars are dominant in low-density regions in the Universe. The absorption feature imprinted on QSO spectra could be detected by spectroscopic observations with Subaru PFS.

Speaker
Atsushi J. Nishizawa

Date/Place
13:00-, 5(Wed), June. @ES606

Title
Photometric Redshift for Hyper Suprime Cam Survey

Abstract
Photometric redshift (photo-z) is a method to measure the distance to galaxies. Although the photo-z measurement is a crude estimate, particularly for the photometric surveys where no spectrograph is available, the photo-z is the only tool to measure the distance. To alleviate the uncertainty of the photo-z, various approaches have been established. In this seminar, we will review the methods based on the traditional template fitting and empirical method including machine learning. Moreover, the image based analysis using deep neural network is recently proposed and approved by the practical data of BOSS survey. Finally, as an alternative approach, clustering redshift method is introduced where no photometric information is used. As an application of the clustering-z, we will also discuss how we quantify the effect of cosmic variance due to the limited region of the calibration sample, by use of Illustris TNG simulation with super survey modes.

Seminars in May

Speaker
Shuichiro Yokoyama

Date/Place
13:00-, 29(Wed), May. @ES606

Title
Clustering of PBHs

Abstract
We formulate two-point correlation function of primordial black holes (PBHs) at the formation, based on the functional integration approach which has been often used in the context of clustering of the halos. We found that the PBH clustering on large scales could be never induced in the case where the initial smoothed density fluctuations are Gaussian, while it can be enhanced by the so-called local-type trispectrum (4-point correlation function) of the primordial curvature perturbations.

Speaker
Hiroyuki Tashiro

Date/Place
13:00-, 22(Wed), May. @ES606

Title
Charge excess in the Universe

Abstract
It is widely accepted that the Universe is electrically neutral. So far, cosmological analysis are almost performed, based on the charge neutrality, and there are no observational results which is conflict with this assumption. However no one knows that the universe is perfectly neutral. In this seminar, we discuss the observational constraint on the charge excess in the Universe.

Speaker
Kiyotomo Ichiki

Date/Place
13:00-, 15(Wed), May. @ES606

Title
Future 21cm Forest Constraints on the Nature of Dark Matter

Abstract
Although the CDM paradigm is consistent with a wide variety of existing observations, it has yet to be sufficiently tested on scales smaller than those of massive galaxies. Here we show that the future 21cm forest observations may offer a powerful test for various alternative dark matter models such as WDM, ULA and PBHs.

Speaker
Hironao Miyatake

Date/Place
13:00-, 8(Wed), May. @ES606

Title
Weak lensing cosmology with ongoing and upcoming imaging surveys

Abstract
Weak gravitational lensing is one of the most powerful cosmological probes because of its direct sensitivity to dark matter distribution, and thus quite a few galaxy imaging surveys are carried out and being planned. In this talk, I will give a broad overview of ongoing and upcoming weak lensing surveys, including the Subaru Hyper Suprime-Cam survey, and major challenges towards high-precision weak lensing measurement. I will also present the current status of cosmological analysis I am recently working on, especially about the combined galaxy-galaxy clustering and lensing analysis.

Seminars in April

Speaker
Ikumi Ueda

Date/Place
13:00-, 24(Wed), Apr. @ES606

Title
Self Introduction

Abstract
Self Introduction

Speaker
Kouki Sakoda

Date/Place
13:00-, 24(Wed), Apr. @ES606

Title
Verify the Inhomogeneity of Universe using the kinematic Sunyaev-Zel’dovich effect

Abstract
The cosmological principle is the Cosmology’s standard assumption. The cosmological principle is the idea that the Universe is isotropic and homogeneous. Isotropy of the universe is supported by some direct evidence. (CMB, Galaxy, etc. ). But homogeneity of the universe is NOT supported by any direct evidence. It is announced that distant Supernovae are darker than expected by matter dominated epoch in the universe under cosmological principle. The homogenous universe is necessary a dark energy to explain it. (Perlmutter(1998)) But the inhomogeneous universe causes it without a dark energy. I think the constrained (LTB) spacetime as the inhomogeneous universe. I verified that constrained LTB spacetime satisfied both SN-Ia and kinematic Sunyaev Zel’dovich effect, So the constrained LTB metric was excluded. I review the paper “Looking the void in the eyes – the kSZ effect in LTB models”(Garcia, Haugboelle(2008).

Speaker
Kunihiko Furugori

Date/Place
13:00-, 24(Wed), Apr. @ES606

Title
Pt/TiO2のCOガス導入によるTEM観察

Abstract
TiO2に担持されたPtナノ粒子触媒(以下Pt/TiO2と略記)は、CO酸化反応に高い活性を示し、COガスによって強い金属担体間相互作用(SMSI)を引き起こす。SMSIは、加熱処理や反応ガスの導入によって著しい活性の促進や劣化が起きる現象である。O2とCO導入におけるPt/TiO2のSMSI効果は報告されていないため、本研究では、Pt/TiO2触媒のCO,O2ガス導入による構造変化をTEMで観察した。その結果、O2ガス導入で、Pt/TiO2界面のピラー成長が見られた。

Speaker
Koya Murakami

Date/Place
13:00-, 17(Wed), Apr. @ES606

Title
Cosmological model classification with machine learning

Abstract
The analysis of large-scale structure is performed by calculating two-point correlation function, and most of the information on density fluctuations known to be approximately Gaussian can be obtained from the two-point correlation function. However, in order to further restrict the cosmological model, it is necessary to investigate non-Gaussianity contained in density fluctuation, and in order to extract this information, it is necessary to investigate the correlation of three or more points. The problem is that we need to increase the number of points in order to obtain sufficient information, but the information doesn’t increase greatly even if we increase the point which is calculated. On the other hand, it is difficult to calculate multi-point correlation. In this study, we focused on the analysis of the image of density distribution using machine learning. In the Convolutional Neural Network (CNN) method used in this research, the image is filtered and analyzed to extract the information of multi-point correlation at a small computational cost and classify the image. In this study, images of density distribution are created from simulations of the universe with cold dark matter (cdm), and with warm dark matter (wdm), and CNN is trained to use classification of cdm model and wdm model, or the estimation of mass of warm dark matter. In addition, the difference of results of the classification between when the value of density is converted and when it is not is examined. As a result of learning, the classifications of cdm and wdm of all the masses examined in this study can be correctly classified with probability of 80% or more, and the mass estimation of wdm is also much more accurate than randomly classifying.

Speaker
Nanaka Yamamoto

Date/Place
13:00-, 17(Wed), Apr. @ES606

Title
The curvature perturbations for the model which changes from slow-roll to ultra slow-roll inflation

Abstract
In order to solve the problem of pure big bang theory, it is thought that inflation is necessary. In particular, slow-roll inflation (SR), which is one of the inflation models, is widely accepted. SR is characterized by the fact that initial perturbations, which are the seeds of large-scale structures, are preserved after horizon cross. However, in recent years, an inflation model with potential with an inflection point has been considered. Inflation with a flat potential is called ultra slow-roll inflation (USR). USR has the feature that the perturbation grows after the horizon cross. Therefore, it has recently been attracting attention as a theory for forming initial black holes. In this study, first, we explain the characteristics of the power spectrum in each model, and show that USR cannot end inflation. Next, we connect two models to solve this problem, and show the result of analytically investigating the influence of the connection on the power spectrum for the curvature perturbation.

Speaker
Naoshi Sugiyama

Date/Place
13:00-, 17(Wed), Apr. @ES606

Title
New year's impression

Abstract
New year's impression

Speaker
Shun Arai

Date/Place
16:00-, 15(Mon), Apr. @ES606

Title
The history of the structure formation via the angular cross power spectrum between radio galaxies and CMB lensing

Abstract
In the standard cosmology, it is believed that the first self-evolving objects are born within the first billion years after the CMB is emitted in the bulk Universe. The objects have gravitationally and thermally grown over the past 10 billion years as the CMB has passed in the structures formed, during which local physical phenomena in the structures are imprinted on the CMB. One of the imprints created by the structures is the gravitational lensing of the CMB (CMB lensing).
In this talk, we report properties of CMB lensing presumably sourced by radio galaxies. We compute the angular cross power spectrum between radio galaxies in NRAO VLA Sky Survey (NVSS) and CMB measured by Planck. We estimate the redshift distribution of the radio galaxies in the lensing kernels via the galaxies in Kilo-Square Degree Survey (KiDS) catalog. To be precise, we use radio galaxies in CENSORS as a reference to the redshift distribution of radio galaxies in high precision.
The theoretical predictions via the Planck 2015 standard cosmological model with assuming the redshift distributions the estimation from KiDS and CENSORS, the angular auto power spectrum of radio galaxies is C_l = \cal O(10^{-3}), and the theories predict that the correlation coefficient is significantly high over 0.4 at l <= 300. The auto power of the radio galaxies is in good agreement with the first measurement in C.Blake et al 2004 at l <=100. Meanwhile, in our measurement of C_l at l>=100, the data is completely covered by shot noise, ending up underestimating the coefficient well down the theoretical predictions. This suggests that a more careful subtraction of the noise is necessary to test the cosmology and the formation history of radio galaxies.

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