CMB光谱失真的统计各向异性研究

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"CMB频谱失真中的统计各向异性" 宇宙微波背景（CMB）是宇宙大爆炸后遗留下来的辐射，它包含了宇宙早期结构形成的重要信息。CMB光谱的精确研究对于理解宇宙学模型至关重要。"CMB频谱失真中的统计各向异性"这一主题涉及到对CMB光谱的非均匀性，即CMB频谱的各向异性进行分析，以探测可能存在的宇宙结构或物理过程的迹象。文章中提到的"y畸变"是指CMB光谱中由于高能粒子与CMB光子相互作用产生的频率偏差，通常由大尺度结构的热化效应引起。这些畸变可以提供关于宇宙早期密度扰动的线索，特别是在0.01≲kMpc≲1的尺度上，这个尺度对应于宇宙中小到中等规模的结构。作者Atsuhisa Ota等人通过计算y畸变的1点整体平均值来检查统计各向同性，这是假设宇宙均匀且各向同性的关键检验。如果在统计各向同性的扰动中发现各向异性，那可能意味着存在尚未被揭示的物理过程或者对现有宇宙模型的挑战。四极统计各向异性是研究的重点，其中4π〈y2m〉 = −6.8A2×10−9Y2m（d）的表达式表示四极矩的各向异性。这里的A2是各向异性功率谱的四倍勒让德系数，Y2m(d)是球谐函数，指示了观测到的各向异性方向d。这个发现表明，即使在统计各向同性的框架下，CMB的y畸变仍然显示出微弱的各向异性特征。此外，论文还探讨了在统计各向异性宇宙中y畸变各向异性的宇宙方差。宇宙方差是测量数据中的自然波动，反映了测量不确定性以及可能存在的宇宙结构的内在随机性。理解这种方差对于正确解读观测结果和提取物理信息至关重要。这篇研究工作加深了我们对CMB的理解，特别是其各向异性特征如何反映宇宙的初始条件和物理过程。通过精密的观测和理论分析，科学家们可以更深入地探索宇宙的起源、演化和基本物理定律。开放获取的标签意味着这篇研究对公众和同行科学家都是可访问的，有助于促进科学知识的传播和进一步研究。

Physics Letters B 790 (2019) 243–247

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Statistical anisotropy in CMB spectral distortions

Atsuhisa Ota

a,b,∗

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK

Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands

a r t i c l e i n f o a b s t r a c t

Article history:

Received

13 October 2018

Received

in revised form 16 January 2019

Accepted

16 January 2019

Available

online 21 January 2019

Editor:

H. Peiris

Measurements of the cosmic microwave background (CMB) spectral y-distortion anisotropy offer a test

for the statistical isotropy of the primordial density perturbations on 0.01  k Mpc  1. We compute

the 1-point ensemble averages of the y-distortion anisotropies which vanish for the statistically isotropic

perturbations. For the quadrupole statistical anisotropy, we ﬁnd 4π y

 =−6.8A

× 10

−9

(d) with

the quadruple Legendre coeﬃcient of the anisotropic powerspectrum A

and the  = 2spherical

harmonics Y

(d) for the preferred direction d. Also, we discuss the cosmic variance of the y-distortion

anisotropy in the statistically anisotropic Universe.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

There exist 10

−5

of anisotropies in the cosmic microwave back-

ground (CMB),

the fossil of the radiation emitted about 380,000

years after the Big Bang [1–3]. These ﬂuctuations are random

ﬁelds on top of the statistically isotropic background spacetime,

and cosmic inﬂation can explain their origin as the quantum ﬂuc-

tuations

in the very early stage of the expanding Universe [4–6].

However, such a rotational invariance is not a mandatory require-

ment.

Indeed several inﬂationary models can break the rotational

symmetry in the early Universe [7–10]. For example, avector

ﬁeld during inﬂation leads to a preferred direction and produces

the quadrupole asymmetry in the primordial powerspectrum of

the density perturbations [8–10]. More generally, spinning parti-

cles

imprint the multipole asymmetry of the primordial corre-

lators [11–13],

and hence the statistical asymmetries are sensi-

tive

to the matter contents during inﬂation. Thus, the statistical

isotropy is an assumption to be tested through observations, and

its probes have been discussed with the powerspectra of the CMB

anisotropies, the 21-cm lines and galaxies [14–24].

this Letter, we point out another way to link the pri-

mordial

statistical anisotropy with a cosmological observable, i.e.,

adeviation of the CMB energy spectrum from the blackbody

one. In particular, we discuss the sensitivity for the short wave-

length (

O(0.01) < k Mpc < O(1.)) statistical anisotropy. We focus

on the spectral y-distortion, a kinetic deviation from the Planck

distribution due to the Compton scattering in the late epoch of

the early Universe [25,26]. Atypical source of the y-distortion is

Correspondence to: Department of Applied Mathematics and Theoretical

Physics, University of Cambridge, Cambridge, CB3 0WA, UK.

E-mail

address: a.ota@damtp.cam.ac.uk.

energy release from dissipation of acoustic waves on small scales.

It produces the y-distortions at second-order in the cosmological

perturbations, and hence the ensemble average of them is related

to the short wavelength primordial powerspectrum [27–29]. In

particular, the isotropic spectral distortion has been studied for the

small-scale primordial powerspectrum. Here, we investigate im-

prints

of the primordial statistical anisotropy on the y-distortion

anisotropy. In contrast to Refs. [30–32], we do not discuss the 2- or

higher correlation functions of the spectral distortion anisotropy.

Instead, we compute a simple 1-point ensemble average of the

y-distortion anisotropy in an explicit way based on the second-

order

Boltzmann equation. Such a quantity is zero in the statis-

tically

isotropic Universe, but we show that it is sensitive to the

statistical anisotropy. Also, we comment on the cosmic variance in

the statistically anisotropic Universe.

Primordial

powerspectrum—. Let d be the preferred direction in the

Universe. The powerspectrum of the curvature perturbation on the

uniform density slice ζ depends on d, and we write it in Fourier

space as

ζ

=(2π)

(3)

). (1)

The SO(3) rotational symmetry is broken to SO(2) in the presence

of d. The Universe is still statistically symmetric under the rotation

around the d axis; therefore, the anisotropy can be parameterized

by the angle between d and k. Then, we generally expand the

powerspectrum by the Legendre polynomial P

(d ·

k) as

(k) = P

(k)

∞



L=0

(−i)

(2L +1) A

(k)P

(d ·

k), (2)

https://doi.org/10.1016/j.physletb.2019.01.030

0370-2693/

SCOAP

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