物理代写|宇宙学代写cosmology代考|PHYS 3080

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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”。

statistics-lab™ 为您的留学生涯保驾护航 在代写宇宙学cosmology方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写宇宙学cosmology代写方面经验极为丰富,各种代写宇宙学cosmology相关的作业也就用不着说。

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|PHYS 3080

物理代写|宇宙学代写cosmology代考|Standard Model of particle physics

The Standard Model of particle physics describes the known fundamental particles in nature and how they interact. The particles can be divided into two classes: spin-1/2 fermions and integer-spin bosons.

Fermions are the constituents of matter: the quarks, out of which baryons are built, and the leptons such as electrons and neutrinos. There are three generations with two quarks each for a total of six quarks, denoted $u, d ; s, c ; b, t$. Each generation of quarks is associated with a pair of leptons. For example, the $u, d$ pair is associated with the electron and its neutrino: $e^{-}, v_{e}$. The other lepton pairs are $\mu^{-}, v_{\mu}$ and $\tau^{-}, v_{\tau}$. The vast majority of matter in the universe is made up of the first generation, with the exception of neutrinos, which are mixed between the different generations. Unlike leptons, quarks do not exist on their own, but they form bound states under the strong interaction. Baryons, the most important ones being the proton and neutron, are made out of three quarks. Mesons are composed of a quark-antiquark pair.

Bosons contain the spin-1 (vector) force carriers, the most famous of which is the photon which mediates the electromagnetic force. There are eight gluons (massless, like the photon) that mediate the strong force. The weak force, responsible for example for neutron decay, is mediated by three massive bosons: the $Z, W^{+}$and $W^{-}$. These force mediators are complemented with the spin-0 (scalar) Higgs boson. The Higgs couples to all massive fermions as well as the $W$ and $Z$ bosons. This coupling gives mass to the particles through the Higgs’ homogeneous background field value.

The Standard Model has remained largely intact since its inception, gaining more and more experimental verification every year. However, neutrino masses are now a confirmed piece of physics beyond the Standard Model. Moreover, the evidence cosmologists have uncovered-that there is a need for dark matter, dark energy, and new physics leading to inflation-clearly shows that the Standard Model is not the final word in particle physics.

物理代写|宇宙学代写cosmology代考|the concordance model of cosmology

We are now ready to summarize the concordance model of cosmology: a Euclidean universe that is dominated today by non-baryonic cold dark matter (CDM) and a cosmological constant, with initial perturbations generated by inflation in the very early universe. Since all measurements are currently consistent with dark energy being a cosmological constant $\Lambda$, this concordance model of cosmology has become known as (flat) $\Lambda$ CDM. It is worth noting that none of these ingredients are part of the Standard Model of particle physics (Box 1.1)! Let us thus briefly discuss the status of these three ingredients.

CDM: The “Cold” part of this moniker comes from requiring the dark matter particles to be able to clump efficiently in the early universe. If they are hot instead, i.e., have large velocities, structure will not form at the appropriate levels; among others, this excludes the known neutrinos from being dark matter candidates. We have argued that BBN and the CMB imply the existence of non-baryonic matter. However, observations of structure in the universe independently lead to the conclusion that there must be dark matter. The inhomogeneities expected in a model without dark matter are far too small. In Ch. 8, we will come to understand the reason why a baryon-only universe would be so smooth. Moreover, dark matter is a familiar concept to astronomers; the first suggestion was put forth by Zwicky (1933), based on galaxy velocities within clusters. Ample evidence also comes from the rotation curves of galaxies. Indeed, a mismatch between the matter inferred from gravity and that which we can see in the form of baryons exists on all galactic and extragalactic scales, and it always points toward roughly 5 times more dark matter than baryons.

What is this new form of matter? And how did it form in the early universe? So far, we know only its overall abundance and the fact that it must be cold. The most popular idea currently is that the dark matter consists of elementary particles produced during early moments of the Big Bang. In Ch. 4, we will explore this possibility in detail, arguing that dark matter may have been produced when the temperature of the universe was of order hundreds of $\mathrm{GeV} / k_{\mathrm{B}}$. As we will see, the hypothesis that dark matter consists of fundamental relics from the early universe is being rigorously tested experimentally.

Cosmological constant: Evidence from a variety of sources, but most famously from distant supernovae (starting with Riess et al., 1998; Perlmutter et al., 1999) suggests that there must be energy, dark energy, besides ordinary matter and radiation. Unlike dark matter, this component does not cluster strongly. We already discussed the possibility that this new form of energy remains constant with time, i.e., acts as a cosmological constant, a possibility first introduced (and later abandoned) by Einstein. Cosmologists have explored other forms though, many of which behave quite differently from the cosmological constant. We will see more of this in Sect. 2.4.6.

物理代写|宇宙学代写cosmology代考|Summary and outlook

As a way of summarizing the features of an expanding universe that we have outlined above and that we will explore in great detail in the coming chapters, let us construct a time line. We can equivalently characterize any epoch in the universe by the time since the Big Bang; by the value of the scale factor at that time; by the redshift freely traveling photons have experienced from then until today or by the temperature of the cosmic background radiation. For example, today, $t \simeq 13.7$ billion years; $a=1 ; z=0$; and $T=2.73 \mathrm{~K}=2.35 \times 10^{-4} \mathrm{eV} / k_{B}$. Fig. $1.11$ shows a time line of the universe using both time and temperature as markers. The milestones indicated on the time line range from those that involve known physics (nucleosynthesis and the CMB) to those that go beyond the Standard Model of particle physics (inflation and dark energy).

The time line in Fig. $1.11$ shows the dominant component of the universe at various times. We do not know what dominated the energy budget of the universe at very early times after the end of inflation. We do know, however, that the universe was dominated by radiation at the latest by the time BBN occurred. Eventually, since the energy of a relativistic particle falls as $1 / a$ while that of a nonrelativistic particle remains constant at $m$, matter overtook radiation. At relatively recent times, the universe has become dominated not by matter, but by dark energy, whose density remains approximately constant with time.
The classical results in cosmology can be understood in the context of a smooth universe. Light elements formed when the universe was several minutes old, and the CMB decoupled from matter at a temperature of order $k_{\mathrm{B}} T \sim 1 / 4 \mathrm{eV}$, when the universe was 380,000 years old. Heavy elementary particles may make up the dark matter in the universe; if they do, their abundance was fixed at very high temperatures of order $k_{\mathrm{B}} T \sim$ $100 \mathrm{GeV}$ or higher.

In this book, we will be mostly interested in the perturbations around the smooth universe. At the beginning of the time line, we allow for a brief period of inflation, during which primordial perturbations were produced. These small perturbations began to grow when the universe became dominated by matter. The dark matter grew more and more clumpy, simply because of the attractive nature of gravity. An overdensity of dark matter of 1 part in 1000 when the temperature was $1 \mathrm{eV}$ grew to 1 part in 100 by the time the temperature dropped to $0.1 \mathrm{eV}$. Eventually, at relatively recent times, perturbations in the matter ceased to be small; they became the nonlinear structure we see today. The observed anisotropies in the CMB tell us what the universe looked like when perturbations were very small, so they are a wonderful probe of the latter. Moreover, the CMB anisotropies provide a precise characterization of the initial conditions needed for detailed analytic and numerical studies of the growth of structure. To give you an idea of the road ahead, Fig. $1.12$ charts the way through the various ingredients going into this calculation that we will get to know in subsequent chapters of the book.

Some of the elements in the time line we have discussed may well be incorrect. However, since most of these ideas are testable, the data from the first half of the 21st century will tell us which parts of the time line are correct and which need to be discarded. This in itself seems more than sufficient reason to study the CMB and large-scale structure.

物理代写|宇宙学代写cosmology代考|PHYS 3080


物理代写|宇宙学代写cosmology代考|Standard Model of particle physics


费米子是物质的组成部分:构成重子的夸克,以及电子和中微子等轻子。有 3 代,每代有 2 个夸克,总共有 6 个夸克,记为在,d;s,C;b,吨. 每一代夸克都与一对轻子有关。例如,在,dpair 与电子及其中微子有关:和−,在和. 其他轻子对是μ−,在μ和τ−,在τ. 宇宙中的绝大多数物质都是由第一代组成的,除了中微子,它们在不同代之间混合。与轻子不同的是,夸克本身并不存在,而是在强相互作用下形成束缚态。重子,最重要的是质子和中子,由三个夸克组成。介子由夸克-反夸克对组成。

玻色子包含自旋 1(矢量)力载体,其中最著名的是介导电磁力的光子。有 8 个胶子(无质量,如光子)调节强力。导致中子衰变的弱力是由三个大质量玻色子介导的:从,在+和在−. 这些力介质与自旋 0(标量)希格斯玻色子相辅相成。希格斯对所有大质量费米子以及在和从玻色子。这种耦合通过希格斯的均匀背景场值为粒子提供质量。


物理代写|宇宙学代写cosmology代考|the concordance model of cosmology

我们现在准备总结宇宙学的一致性模型:今天由非重子冷暗物质 (CDM) 和宇宙学常数主导的欧几里得宇宙,初始扰动由早期宇宙中的膨胀产生。由于目前所有测量结果都与暗能量是宇宙学常数一致Λ,这个宇宙学的一致性模型被称为(平面)Λ清洁发展机制。值得注意的是,这些成分都不是粒子物理标准模型的一部分(框 1.1)!因此,让我们简要讨论这三种成分的状态。

CDM:这个绰号的“冷”部分来自于要求暗物质粒子能够在早期宇宙中有效地聚集。如果它们是热的,即速度很大,则不会在适当的水平上形成结构;除其他外,这将已知的中微子排除在暗物质候选者之外。我们认为 BBN 和 CMB 暗示了非重子物质的存在。然而,对宇宙结构的观察独立地得出结论,即一定存在暗物质。在没有暗物质的模型中预期的不均匀性太小了。英寸。8,我们将理解为什么只有重子的宇宙会如此平滑。此外,暗物质是天文学家熟悉的概念。第一个建议是 Zwicky (1933) 基于星系团内的星系速度提出的。充足的证据还来自星系的自转曲线。事实上,从引力推断出的物质与我们以重子形式看到的物质之间存在不匹配,存在于所有银河系和银河系外的尺度上,它总是指向比重子多约 5 倍的暗物质。

这种新形式的物质是什么?它是如何在早期宇宙中形成的?到目前为止,我们只知道它的总体丰度以及它一定很冷的事实。目前最流行的想法是暗物质由大爆炸早期产生的基本粒子组成。英寸。4,我们将详细探讨这种可能性,认为暗物质可能是在宇宙温度达到数百摄氏度时产生的G和在/ķ乙. 正如我们将看到的,暗物质由早期宇宙的基本遗迹组成的假设正在经过严格的实验检验。

宇宙常数:来自各种来源的证据,但最著名的是来自遥远的超新星(从 Riess 等人,1998 年;Perlmutter 等人,1999 年开始)表明除了普通物质和辐射之外,还必须有能量、暗能量。与暗物质不同,该成分不会强烈聚集。我们已经讨论过这种新形式的能量随时间保持不变的可能性,即作为宇宙常数,这是爱因斯坦首先引入(后来放弃)的可能性。不过,宇宙学家已经探索了其他形式,其中许多的行为与宇宙学常数完全不同。我们将在 Sect 中看到更多这样的内容。2.4.6。

物理代写|宇宙学代写cosmology代考|Summary and outlook

作为总结我们上面概述的膨胀宇宙特征的一种方式,我们将在接下来的章节中详细探讨,让我们构建一个时间线。我们可以等价地描述宇宙大爆炸以来的任何时代;由当时的比例因子的值;从那时到今天,自由行进的光子经历了红移,或者宇宙背景辐射的温度。例如,今天,吨≃13.7亿年;一个=1;和=0; 和吨=2.73 ķ=2.35×10−4和在/ķ乙. 如图。1.11使用时间和温度作为标记显示了宇宙的时间线。时间线上显示的里程碑范围从涉及已知物理学(核合成和 CMB)到超出粒子物理学标准模型(膨胀和暗能量)的里程碑。

时间线如图。1.11显示了不同时期宇宙的主要组成部分。我们不知道在暴胀结束后的早期,是什么主导了宇宙的能量收支。然而,我们确实知道,最迟在 BBN 发生时,宇宙已被辐射支配。最终,由于相对论粒子的能量下降为1/一个而非相对论粒子的粒子保持不变米,物质超过了辐射。在最近的一段时间里,宇宙不再由物质主导,而是由暗能量主导,其密度随时间保持大致恒定。
宇宙学的经典结果可以在平滑宇宙的背景下理解。轻元素在宇宙诞生几分钟时形成,而 CMB 在一定温度下与物质分离ķ乙吨∼1/4和在,当宇宙有 38 万年的历史时。重基本粒子可能构成宇宙中的暗物质;如果他们这样做了,他们的丰度就被固定在非常高的秩序温度下ķ乙吨∼ 100G和在或更高。

在本书中,我们最感兴趣的是围绕平滑宇宙的扰动。在时间线的开始,我们允许短暂的暴胀时期,在此期间会产生原始扰动。当宇宙被物质支配时,这些微小的扰动开始增长。暗物质变得越来越块状,仅仅是因为引力的吸引力。温度为 1000 分之一的暗物质超密度1和在到温度下降到 100 分之一0.1和在. 最终,在最近的一段时间里,对此事的扰动不再很小。它们变成了我们今天看到的非线性结构。在 CMB 中观察到的各向异性告诉我们,当扰动非常小时,宇宙是什么样子的,因此它们是对后者的一个很好的探索。此外,CMB 各向异性提供了对结构生长的详细分析和数值研究所需的初始条件的精确表征。为了让您了解未来的道路,图。1.12图表显示了计算中的各种成分,我们将在本书的后续章节中了解这些成分。

我们讨论过的时间线中的一些元素很可能是不正确的。然而,由于这些想法大部分都是可以检验的,21世纪上半叶的数据会告诉我们时间线的哪些部分是正确的,哪些需要丢弃。这本身似乎是研究 CMB 和大型结构的充分理由。

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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。





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。


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 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。