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assignmentutor-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。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Dark Energy

We have recently learned that matter and radiation aren’t enough to describe the evolution of the universe. Instead, the universe today is dominated by a mysterious form of dark energy with negative pressure, $P=-\rho c^{2}$, and hence constant energy density,
$$\rho \propto a^{0} .$$
Since the energy density doesn’t dilute, energy has to be created as the universe expands. As described above, this doesn’t violate the conservation of energy, as long as equation (2.106) is satisfied.

• Vacuum energy A natural candidate for a constant energy density is the energy associated to empty space itself. As the universe expands, more space is being created and this energy therefore increases in proportion to the volume. In quantum field theory, this so-called “vacuum energy” is actually predicted, leading to an energy-momentum tensor of the form
$$T_{\mu \nu}^{\mathrm{vac}}=-\rho_{\mathrm{vac}} c^{2} g_{\mu \nu} .$$
As expected from Lorentz symmetry, the energy-momentum tensor associated to the vacuum is proportional to the spacetime metric. Comparison with (2.100) shows that this indeed gives $P_{\mathrm{vac}}=-\rho_{\mathrm{vac}} c^{2}$. Unfortunately, as I will describe below, quantum field theory also predicts the size of the vacuum energy $\rho_{\mathrm{vac}}$ to be much larger than the value inferred from cosmological observations.

## 物理代写|宇宙学代写cosmology代考|The cosmological constant problem

When the cosmological constant was discovered, it came as a relief to observers, but was a shock to theorists. While the cosmological constant reconciled the age of the universe with the ages of the oldest stars within it, its observed value is much smaller than all particle physics scales, making it hard to understand from a more fundamental perspective. This cosmological constant problem is the biggest crisis in modern theoretical physics. Let me digress briefly to describe the problem.
In Section 2.4, we will see that the observed value of the vacuum energy is
$$\rho_{\Lambda} c^{2} \approx 6 \times 10^{-10} \mathrm{Jm}^{-3} .$$
To compare this to our expectation from particle physics, we need to write this in units that are more natural from the perspective of high-energy physics. These units are electron volts $(\mathrm{eV})$. Using $1 \mathrm{~J} \approx 6.2 \times 10^{18} \mathrm{eV}$ and $\hbar c \approx 2.0 \times 10^{-7} \mathrm{eVm}$, we get $(\hbar c)^{3} \rho_{\Lambda} c^{2} \approx\left(10^{-3} \mathrm{eV}\right)^{4}$. Written in natural units, with $\hbar=c \equiv 1$, we then have
$$\rho_{\Lambda} \approx\left(10^{-3} \mathrm{eV}\right)^{4} .$$
We see that the scale appearing in the vacuum energy, $M_{\Lambda} \sim 10^{-3} \mathrm{eV}$, is much smaller than the typical scales relevant to particle physics. In the following, we will dig a bit deeper into the issue.

# 宇宙学代考

## 物理代写|宇宙学代写cosmology代考|Dark Energy

$$\rho \propto a^{0} .$$

• 真空能量恒定能量密度的自然候选者是与真空空间本身相关的能量。随着宇宙的膨胀，更多的空间被创造出来，因此这种能量与体积成正比增加。在量子 场论中，这种所谓的“真空能量“实际上是被预测的，导致形式为能量-动量张量
$$T_{\mu \nu}^{\mathrm{vac}}=-\rho_{\mathrm{vac}} c^{2} g_{\mu \nu} .$$
正如洛伦兹对称性所预期的那样，与真空相关的能量-动量张量与时空度量成正比。与 $(2.100)$ 的比较表明，这确实给出了 $P_{\mathrm{vac}}=-\rho_{\mathrm{vac}} c^{2}$. 不幸的是，正如 我将在下面描述的，量子场论也预测了真空能量的大小 $\rho_{\text {vac }}$ 远大于从宇宙学观测推断的值。

## 物理代写|宇宙学代写cosmology代考|The cosmological constant problem

$$\rho_{\Lambda} c^{2} \approx 6 \times 10^{-10} \mathrm{Jm}^{-3}$$

$$\rho_{\Lambda} \approx\left(10^{-3} \mathrm{eV}\right)^{4} .$$
㧴们看到真空能量中出现的刻度， $M_{\Lambda} \sim 10^{-3} \mathrm{eV}$ ，远小于与粒子物理学相关的典型尺度。接下来，我们将深入探讨这个问题。

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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。

assignmentutor™您的专属作业导师
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