### 物理代写|宇宙学代写cosmology代考|The zoo of theories

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• 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|The zoo of theories

To have a general idea of what concerns gravitational physicists nowadays, it makes sense to look through the program of some recent large gravitational conference. About a third of all talks presented will probably belong to classical GR, its astrophysical and cosmological applications. The mathematical tools are being refined, including the methods of solving the Einstein equations, new solutions are found and old ones are analyzed, questions of principle are discussed and new observational effects are suggested or predicted. In the experimental section, there are numerous works on gravitational wave detection and suggestion of measurements in space. There is inevitably a section or a few sections devoted to alternative theories of gravity, where the grand trend belongs to multidimensional theories and unification of interactions including gravity. (Let us note that the very word “alternative” – naturally, with respect to GR stresses the outstanding role of GR among gravitational theories.) A quantum section is also certainly there.

Those who work on alternative or generalized theories pursue quite diverse objectives. There are attempts to overcome the difficulties of GR (such as, for instance, the gravitational energy problem) while preserving or strengthening its advantages; there are attempts to take into consideration principles and phenomena absent in GR. But probably the main point in all new theories is an approach to gravity as a constituent of a future “theory of everything” (or much more if not everything). The unified theories that include gravity, as

a rule, use more complex geometric structures than 4D Riemannian geometry and new physical fields apart from the metric. Many of them employ ideas put forward as long ago as in the $1920 \mathrm{~s}$. Each of them reduces to GR under certain conditions or restrictions. And, as in GR, one seeks there solutions of physical interest (such as black holes, cosmologies, etc.) and observational predictions.

Let us mention some examples, by no means exhausting the whole diversity of approaches.

## 物理代写|宇宙学代写cosmology代考|Gravitation and the Universe

For gravitational theory, the application area of utmost importance is cosmology, the science on the Universe as a whole or on its part available to observation. Modern cosmology is a rapidly developing field of knowledge: the wealth of observational data is impetuously growing, and a lot of most diverse models are being developed. Some of the models will be discussed in detail in this book.

For a long time the Universe was considered as a kind of “vessel” containing different object: particles, stars, planets etc. It seemed that there is no relationship between the properties of this “vessel” and its content. The situation began to change with the advent of GR whose equations just established a relationship between matter and geometry. In cosmology, this relationship became even more evident after A.A. Friedmann’s discovery that a stationary state of the Universe was unstable, so that it must either expand or contract. It inevitably followed from an analysis of the Einstein equations in a cosmological context. The expansion or contraction rate depends on the density and other properties of matter. The properties of the “box” have turned out to depend on its content. Further studies have led to the conclusion that the presently observed part of the Universe some time ago (about 14 billion years) had a size of about $10^{-27} \mathrm{~cm}$ or even smaller. But it is smaller than the size of an atom by 19 orders of magnitude. Such a small region certainly could not contain the whole wealth of particles making the stars. It means that the Universe and the particles were born simultaneously or almost simultaneously and undoubtedly exerted influence on each other. By now it is quite clear that the Universe is not a “vessel” able to contain anything but a complex organism whose parts are all mutually intertwined and interrelated. Everything is of importance here: the particle properties, gravitational physics, statistical physics, electrodynamics…. and frequently all that at the same time.

## 物理代写|宇宙学代写cosmology代考|Fundamentals of general relativity

The basic content of general relativity (GR) is very widely presented in quite a number of well-known and well-written textbooks and monographs (e.g., $[366,409,525,549,554]$ and many more). Assuming that the reader is aware of these fundamentals, in this chapter, mostly for reference purposes, we will mention some of its basic facts and relations. Many geometric notions (such as those of a vector and a tensor, co- and contravariant components of vectors and tensors, contraction of tensors and so on) are supposed to be known and are used without explanation.

The space-time in GR is a four-dimensional manifold with a pseudo-Riemannian metric (the prefix “pseudo” is often omitted to say simply “Riemannian space-time”). The gravitational field is described in GR in terms of space-time curvature, which is expressed using the metric tensor and its derivatives with respect to the coordinates. Thus GR belongs to the class of metric theories of gravity [563]; it is historically the first, the simplest, and the most well-elaborated theory of this class.

We begin this presentation by recalling the basic facts of special relativity (SR), bearing in mind that in the close neighborhood of any point a Riemannian space-time coincides with its tangent flat (Minkowski) space-time, in which SR is formulated. So, GR is not only a generalization of SR including gravity: SR holds locally in all cases as long as gravitational effects can be neglected.

## 物理代写|宇宙学代写cosmology代考|Fundamentals of general relativity

GR 中的时空是一个具有伪黎曼度量的四维流形（通常省略前缀“伪”，简称为“黎曼时空”）。引力场在 GR 中用时空曲率来描述，它使用度量张量及其相对于坐标的导数来表示。因此，GR 属于引力度量理论类[563]；它在历史上是这一类的第一个、最简单和最详尽的理论。

## 有限元方法代写

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## 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。