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Chapter 21: Problem 14

The CMB is essentially uniform in all directions in the sky. This is an example of a. anisotropy. b. isotropy. c. thermal fluctuations. d. Wien's law.

Short Answer

Expert verified
b. isotropy

Step by step solution

01

Understand the Concepts

Understand the key terms: anisotropy means unequal or varied; isotropy means uniform in all directions; thermal fluctuations refer to variations in temperature; and Wien's law relates to black body radiation and temperature.
02

Identify Key Information

The problem states that the CMB is essentially uniform in all directions in the sky. This means we need to identify the term that describes uniformity in all directions.
03

Match the Definition

Isotropy is the term that means uniform in all directions. Therefore, the solution must align with this definition.
04

Choose the Correct Answer

Among the options provided, the correct answer that describes uniformity in all directions is 'b. isotropy.'

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Anisotropy
Anisotropy refers to variations or differences when observed from different directions. In the context of the Cosmic Microwave Background (CMB), anisotropy would mean that the temperature and properties of the CMB are not the same in every direction. Anisotropies in the CMB can tell us about the early universe, including density fluctuations that eventually led to the formation of galaxies. These small variations provide crucial information for cosmologists to understand the Big Bang and the evolution of the universe.
Isotropy
Isotropy means uniformity in all directions. This term is often used to describe the CMB because it is nearly the same temperature no matter where we look in the sky. Key properties of isotropy include:
  • Uniform temperature distribution.
  • Minimal variation when observed from different directions.
The isotropic nature of the CMB supports the Cosmological Principle, which states that the universe is homogeneous and isotropic on large scales. This principle is fundamental for models of the universe, including the Big Bang theory.
Thermal Fluctuations
Thermal fluctuations are variations in temperature over time or space. In the CMB, thermal fluctuations are the small differences in temperature detected in different parts of the sky, often measured in millionths of a degree. Even though the CMB is largely isotropic, these tiny fluctuations are significant because they represent early density perturbations in the universe. Studying these fluctuations helps scientists understand:
  • The distribution of matter in the early universe.
  • The formation of large-scale structures like galaxies and clusters of galaxies.
Thermal fluctuations in the CMB provide a snapshot of the state of the universe just 380,000 years after the Big Bang.
Wien's Law
Wien's Law is a principle in physics that describes the relationship between the temperature of a black body and the peak wavelength of its emitted radiation. Mathematically, it is represented as \(\frac{1}{λ_{max}} = \frac{T}{b}\), where \( λ_{max} \) is the peak wavelength, \( T \) is the temperature, and \( b \) is Wien's constant. This law helps in analyzing the thermal radiation emitted by objects, including the CMB. The peak wavelength of the CMB corresponds to a temperature of about 2.725 K. By applying Wien's Law, scientists can determine:
  • The temperature distribution across the CMB.
  • The black body nature of the CMB radiation.
Understanding Wien's Law is crucial for interpreting the thermal properties of the CMB and supporting the Big Bang model.

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Most popular questions from this chapter

A distant galaxy has a redshift \(z=5.82\) and a recession velocity \(v_{\mathrm{r}}=287,000 \mathrm{km} / \mathrm{s}\) (about 96 percent of the speed of light). a. If \(H_{0}=70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}\) and if Hubble's law remains valid out to such a large distance, then how far away is this galaxy? b. Assuming a Hubble time of 13.8 billion years, how old was the universe at the look-back time of this galaxy? c. What was the scale factor of the universe at that time?

Science's greatest strength is the self-correcting nature of scientific inquiry: minds can be changed in the face of new data, as described in the Process of Science Figure. Consider a modern paradigm of science such as the Big Bang, climate change, or the power source of stars. In a short paragraph, describe your current viewpoint, and give a piece of evidence that would make you change your mind if it were true. For example, Einstein believed the universe was static. Measurements of the movement of galaxies caused him to change his mind.

The general relationship between recession velocity \(\left(v_{r}\right)\) and redshift \((z)\) is \(v_{r}=c z .\) This simple relationship fails, however, for very distant galaxies with large redshifts. Explain why.

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