物理代写|宇宙学代写cosmology代考|PHYSICS 1002

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宇宙学是天文学的一个分支,涉及宇宙的起源和演变,从大爆炸到今天,再到未来。宇宙学的定义是 “对整个宇宙的大尺度特性进行科学研究”。

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我们提供的宇宙学cosmology及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
物理代写|宇宙学代写cosmology代考|PHYSICS 1002

物理代写|宇宙学代写cosmology代考|Big Bang nucleosynthesis

Armed with an understanding of the evolution of the scale factor and the densities of the constituents in the universe, we can extrapolate backwards to explore phenomena at early times. When the universe was much hotter and denser, and the temperature was of order $1 \mathrm{MeV} / k_{\mathrm{B}}$, there were no neutral atoms or even bound nuclei. The vast amounts of highenergy radiation in such a hot environment ensured that any atom or nucleus produced would be immediately destroyed by a high-energy photon. As the universe cooled well below typical nuclear binding energies, light elements began to form in a process known as Big Bang Nucleosynthesis (BBN). Knowing the conditions of the early universe and the relevant nuclear cross-sections, we can calculate the expected primordial abundances of all the elements (Ch. 4).

Fig. $1.6$ shows the BBN predictions for the abundances of helium and deuterium as a function of the mean baryon density, essentially the density of ordinary matter (Sect. $2.4$ ) in the universe, in units of the critical density. The predicted abundances, in particular that of deuterium, which we will explore in detail in Ch. 4, depend on the density of protons and neutrons at the time of nucleosynthesis. The combined proton plus neutron density is equal to the baryon density since both protons and neutrons have baryon number one and these are the only baryons around at the time.

The horizontal lines in Fig. 1.6 show the current measurements of the light element abundances. The deuterium abundance is measured in the intergalactic medium at high redshifts by looking for a subtle absorption feature in the spectrum of distant quasars (see Burles and Tytler, 1998; Cooke et al., 2018 and Exercise 1.3). These measurements of the abundances, combined with BBN calculations, give us a way of measuring the baryon density in the universe, constraining ordinary matter to contribute at most $5 \%$ of the critical density (note that the $x$-axis in Fig. $1.6$ is the baryon density divided by the critical density, but multiplied by $h^{2} \simeq 0.5$ ). Since the total matter density today is significantly larger than this-as we will see throughout the book-nucleosynthesis provides a compelling argument for matter that is comprised of neither protons or neutrons. This new type of matter has been dubbed dark matter because it apparently does not emit light. One of the central questions in physics now is: “What is the Dark Matter?”

物理代写|宇宙学代写cosmology代考|The cosmic microwave background

Another phenomenon that falls out of energetics and a qualitative understanding of the evolution of the universe is the origin of the CMB. When the temperature of the radiation was of order $10^{4} \mathrm{~K}$ (corresponding to energies of order an $\mathrm{eV}$ ), free electrons and protons combined to form neutral hydrogen. Before then, any hydrogen produced was quickly ionized by energetic photons. After that epoch, at $z \simeq 1100$, the photons that comprise the CMB ceased interacting with any particles and traveled freely through space. When we observe them today, we are thus looking at messengers from an early moment in the universe’s history. They are therefore the most powerful probes of the early universe. We will spend an inordinate amount of time in this book working through the details of what happened to the photons before they last scattered off of free electrons, and also developing the mathematics of the free-streaming process since then. Among many other aspects, we will understand how the CMB constrains the baryon density independently, and in agreement with BBN as shown in Fig. 1.6, providing a ringing confirmation of the concordance model.

For now, we are only concerned with the crucial fact that the interactions of photons with electrons before last scattering ensured that the photons were in equilibrium. That is, they should have a black-body spectrum. The specific intensity of a gas of photons with a black-body spectrum is
$$
I_{v}=\frac{4 \pi \hbar v^{3} / c^{2}}{\exp \left[2 \pi \hbar v / k_{\mathrm{B}} T\right]-1} .
$$
Fig. 1.7 shows the remarkable agreement between this prediction (see Exercise 1.4) of Big Bang cosmology and the observations by the FIRAS instrument aboard the COBE satellite. In fact, the CMB provides the best black-body spectrum ever measured. We have been told ${ }^{2}$ that detection of the $3 \mathrm{~K}$ background by Penzias and Wilson in the mid-1960s was sufficient evidence to decide the controversy in favor of the Big Bang over the Steady State universe, an alternative scenario without any expansion. Penzias and Wilson, though, measured the radiation at just one wavelength. If even their one-wavelength result was enough to tip the scales, the current data depicted in Fig. $1.7$ should send skeptics from the pages of physics journals to the far reaches of radical internet chat groups.

物理代写|宇宙学代写cosmology代考|Structure in the universe

The existence of structure in the universe was known long before the detection of CMB anisotropies: various efforts to map out the distribution of galaxies in the local universe clearly showed that they are not distributed homogeneously. The number of galaxies and volume covered by such surveys has grown exponentially. Two surveys in particular broke new ground: the Sloan Digital Sky Survey (SDSS; Fig. 1.8) and the Two Degree Field Galaxy Redshift Survey (2dF), which between them compiled the redshifts of, and hence the distances to, over a million galaxies. Projects over the ensuing decades have and will provide deeper and more detailed maps than these ground-breaking surveys, by orders of magnitude.

The galaxies in Fig. $1.8$ are clearly not distributed randomly: the universe has structure on large scales. To understand this structure, we must develop the tools to study perturbations around the smooth background. We will see that this is straightforward in theory, as long as the perturbations remain small. To compare theory with observations, we must thus try to avoid regimes that cannot be described by small perturbations. As an extreme example, we can never hope to understand cosmology by carefully examining rock formations on Earth. The intermediate steps-collapse of matter into a galaxy; star formation; planet formation; geology; etc.-are much too complicated to allow comparison between linear theory and observations. In fact, perturbations to the matter on small scales (less than about $10 \mathrm{Mpc}$ ) have become large in the late universe; that is, the fractional density fluctuations on these scales are not small, but comparable to or larger than unity. We say that these scales have grown nonlinear. On the other hand, large-scale perturbations are still small (quasi-linear). So they have been processed much less than the small-scale structure. Similarly, anisotropies in the CMB are small because they originated at early times and the photons that we observe from the CMB do not clump on their way to us. Because of this, the best ways to learn about the evolution of structure and to compare theory with observations are to look at anisotropies in the CMB and at large-scale structure (LSS), i.e. how galaxies and matter are distributed on large scales. However, we will learn in Chs. 12-13 that valuable cosmological information can also be extracted from smaller, nonlinear scales provided we choose our observables wisely.

It is paramount therefore to develop statistics that can empower us to compare maps like that shown in Fig. $1.8$ to theories while isolating large scales from small scales. For this purpose, it is often useful to take the Fourier transform of the distribution in question; as we will see, working in Fourier space makes it easier to separate large from small scales. The most important statistic in the cases of both the CMB and the large-scale structure is the two-point function, short-hand for two-point correlation function. When measured using Fourier-space fields, it is called the power spectrum.

物理代写|宇宙学代写cosmology代考|PHYSICS 1002

宇宙学代考

物理代写|宇宙学代写cosmology代考|Big Bang nucleosynthesis

了解了尺度因子的演变和宇宙中成分的密度后,我们可以向后推断以探索早期的现象。当宇宙变得更热更稠密,并且温度有序时1米和在/ķ乙,没有中性原子,甚至没有结合的原子核。在如此炎热的环境中,大量的高能辐射确保产生的任何原子或原子核都会立即被高能光子摧毁。当宇宙冷却到远低于典型的核结合能时,轻元素开始在被称为大爆炸核合成(BBN)的过程中形成。了解早期宇宙的条件和相关的核截面,我们可以计算所有元素的预期原始丰度(第 4 章)。

如图。1.6显示了 BBN 对氦和氘丰度的预测,它是平均重子密度的函数,本质上是普通物质的密度(Sect.2.4) 在宇宙中,以临界密度为单位。预测的丰度,特别是氘的丰度,我们将在第 1 章详细探讨。4、取决于核合成时质子和中子的密度。质子加中子的组合密度等于重子密度,因为质子和中子都有第一号重子,而这些是当时唯一的重子。

图 1.6 中的水平线显示了轻元素丰度的当前测量值。通过寻找遥远类星体光谱中的细微吸收特征,在高红移的星系际介质中测量氘丰度(参见 Burles 和 Tytler,1998;Cooke 等,2018 和练习 1.3)。这些丰度测量,结合 BBN 计算,为我们提供了一种测量宇宙中重子密度的方法,限制普通物质最多贡献5%的临界密度(注意X- 图中的轴1.6是重子密度除以临界密度,但乘以H2≃0.5)。由于今天的总物质密度远大于此——正如我们将在整本书中看到的那样——核合成为既不由质子也不由中子组成的物质提供了令人信服的论据。这种新型物质被称为暗物质,因为它显然不发光。现在物理学的核心问题之一是:“什么是暗物质?”

物理代写|宇宙学代写cosmology代考|The cosmic microwave background

另一个脱离能量学和对宇宙演化定性理解的现象是 CMB 的起源。当辐射温度正常时104 ķ(对应于秩序的能量和在),自由电子和质子结合形成中性氢。在此之前,产生的任何氢都会被高能光子迅速电离。在那个时代之后,在和≃1100,构成 CMB 的光子停止与任何粒子相互作用并在空间中自由行进。当我们今天观察它们时,我们正在观察宇宙历史早期的信使。因此,它们是早期宇宙中最强大的探测器。我们将在本书中花费大量时间来研究光子在最后一次散射出自由电子之前发生的事情的细节,并从那时起开发自由流过程的数学。在许多其他方面,我们将了解 CMB 如何独立约束重子密度,并与 BBN 一致,如图 1.6 所示,提供一致性模型的振铃确认。

目前,我们只关心最后一次散射之前光子与电子的相互作用确保光子处于平衡状态这一关键事实。也就是说,它们应该具有黑体光谱。具有黑体光谱的光子气体的比强度为

我在=4圆周率ℏ在3/C2经验⁡[2圆周率ℏ在/ķ乙吨]−1.
图 1.7 显示了大爆炸宇宙学的这一预测(见练习 1.4)与 COBE 卫星上的 FIRAS 仪器的观测结果之间的显着一致性。事实上,CMB 提供了有史以来最好的黑体光谱。我们被告知2该检测3 ķ彭齐亚斯和威尔逊在 1960 年代中期的背景足以证明大爆炸对稳态宇宙的争议,这是一种没有任何膨胀的替代方案。然而,彭齐亚斯和威尔逊只测量了一种波长的辐射。如果即使他们的单波长结果也足以使天平倾斜,那么图 1 中描绘的当前数据。1.7应该将怀疑论者从物理期刊的页面发送到激进的互联网聊天组的远端。

物理代写|宇宙学代写cosmology代考|Structure in the universe

早在探测到 CMB 各向异性之前,宇宙中结构的存在就已为人所知:绘制局部宇宙中星系分布的各种努力清楚地表明它们分布不均匀。此类调查所涵盖的星系数量和体积呈指数增长。特别是两项调查开辟了新天地:斯隆数字巡天(SDSS;图 1.8)和两度视场星系红移调查(2dF),它们之间汇总了超过一百万个星系的红移以及与它们之间的距离. 随后几十年的项目已经并将提供比这些开创性调查更深入和更详细的地图,数量级。

图中的星系。1.8显然不是随机分布的:宇宙具有大尺度的结构。为了理解这种结构,我们必须开发工具来研究围绕平滑背景的扰动。我们将看到这在理论上是直截了当的,只要扰动仍然很小。因此,为了将理论与观察结果进行比较,我们必须尽量避免使用小扰动无法描述的状态。作为一个极端的例子,我们永远无法通过仔细检查地球上的岩层来理解宇宙学。中间步骤——物质坍缩成星系;恒星形成;行星形成;地质学; 等等-太复杂了,无法在线性理论和观察之间进行比较。事实上,对小尺度物质的扰动(小于约10米pC) 在宇宙晚期变大了;也就是说,这些尺度上的分数密度波动并不小,而是与统一相当或更大。我们说这些尺度已经变得非线性。另一方面,大尺度扰动仍然很小(准线性)。因此,它们的加工量远低于小型结构。同样,CMB 中的各向异性很小,因为它们起源于早期,而且我们从 CMB 观察到的光子在到达我们的途中不会聚集。正因为如此,了解结构演化以及将理论与观测结果进行比较的最佳方法是观察 CMB 和大尺度结构 (LSS) 中的各向异性,即星系和物质在大尺度上的分布情况。但是,我们将在 Chs 中学习。

因此,开发能够使我们能够比较如图所示的地图的统计数据至关重要。1.8理论,同时将大尺度与小尺度隔离开来。为此,对所讨论的分布进行傅里叶变换通常很有用;正如我们将看到的,在傅立叶空间中工作更容易区分大尺度和小尺度。在 CMB 和大尺度结构的情况下,最重要的统计量是两点函数,即两点相关函数的简写。当使用傅里叶空间场测量时,它被称为功率谱。

物理代写|宇宙学代写cosmology代考 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

tatistics-lab作为专业的留学生服务机构,多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务,包括但不限于Essay代写,Assignment代写,Dissertation代写,Report代写,小组作业代写,Proposal代写,Paper代写,Presentation代写,计算机作业代写,论文修改和润色,网课代做,exam代考等等。写作范围涵盖高中,本科,研究生等海外留学全阶段,辐射金融,经济学,会计学,审计学,管理学等全球99%专业科目。写作团队既有专业英语母语作者,也有海外名校硕博留学生,每位写作老师都拥有过硬的语言能力,专业的学科背景和学术写作经验。我们承诺100%原创,100%专业,100%准时,100%满意。

随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

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