Astrophysics γ

Takahiko MATSUBARA Associate Professor

Department: School of Science / Graduate School of Science

Class Time: 2006 Fall Friday
Recommended for: Students majoring in
1) Elementary particle astrophysics
2) Material science

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Course Aims

Cosmology is the study of space, its beginning, and evolution. With rapid improvements in observation methods, cosmology is growing as well. In this course, we will go through some of the latest topics and developments in the field of cosmology.

Key Features

Modern cosmology has an aspect of being a field for the synthetic application of physics. In addition to the basic subjects that physics students will learn in university, such as dynamics, electromagnetism, quantum physics, statistical dynamics, more advanced knowledge-methods of modern physics like the general relativity theory and non-equilibrium statistical physics-must also be used to study the evolution of space, and then, combined with the latest observation reports, reveal the essence of space itself. That is what modern cosmology is all about.

This course is intended to introduce students to such wonders of space. I try to give them a good view of the underlying physics inside modern cosmology while at the same time explaining the used methods and formulas in the best way possible. Although the formulas and equations introduced in this course are in most cases complex, in order to spare the labor of writing each and every one of them on the blackboard, all the necessary information will be handed out to each student on paper. For students who wish to go deep in to cosmology, working out the formulas on the paper will give them a better understanding of the lecture. And those who wish to learn the basics can concentrate on the lessons, without having to jot down minor notes themselves.

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Course Requirements and Recommended Courses

This course requires a basic understanding of the general relativity theory. It is also highly recommended that you take the course, "Observational Cosmology (2006 sem.I)" beforehand.


  1. The Basics of Cosmology

    In this section, we will review major points of `homogeneous universe' theory, which forms the basics of cosmology. From the Robertson-Walker measurement define the parameters of space via Freidmann equation.Discuss the behaviors of space, particularly from the viewpoint of `Dark Energy', a subject recently under great debate. After going over relations between the redshift phenomenon and cosmological distance, talk about classic definition methods of the space parameter.

  2. The Linear Perturbation Theory

    We will work on some theories that deal with the fluctuations of space, an important concept in modern cosmology. We'll begin with the linear perturbation theory, which deals with the concept based on Einstein's general relativity theory. After discussing the gauge degree of freedom within the general relativity theory, we will draw a conclusion from the linear Einstein equation, then move on to the explanation of linear theory of relativistic Boltzmann equation in curved space-time, a necessity in dealing with systems of many particles.

  3. Origination and Development of Fluctuations within a Homogeneous Universe

    We will apply the linear perturbation theory to determine the development of fluctuations in actual space. First, there will be a briefing on the origination of fluctuations under the inflationary theory. Then, we'll look into its growth process within an evolving universe. Here, to grasp a general idea of the growth, we will use an approximation method to explain it. Finally, we will apply the transfer function, a concept closely related with structuring of the universe, to understand its behavior. Lectures on major effects of photons and baryons will be given at this time.

  4. Observations of Perturbing Space

    We will study a few methods used to measure cosmic fluctuations. There are two main methods to determine the Universe's wide-range structure, observation of either the fluctuations in cosmic background radiation or the large-scale structure of the universe. We'll see how these measurements relate to the theoretical growth of cosmic fluctuations.


None required


Credit for this course will be counted under Group B ONLY when combined with one of the following courses (credit total is 3): Astrophysics α, Astrophysics β, Astrophysics δ Credit will be accounted for in combination with any one of the three courses regardless of year or term. However, please note that two courses of the same name cannot be combined in any case.

Related Resources

"Gravitation and Cosmology", S. Weinberg (John Wiley and Sons, Inc.) 1972

"Cosmological Inflation and Large-Scale Structure", A. R. Liddle, D. H. Lyth (Cambridge Unviersity Press) 2000

"Theoretical Astrophysics, Volume III: Galaxies and Cosmology", T. Padmanabhan (Cambridge University Press) 2002

"Modern Cosmology", S. Dodelson (Academic Press) 2003

"Physical Foundations of Cosmology", V. Mukhanov (Cambridge Unviersity Press) 2005

Backdrop in photo used under permission from Russel Croman

Russell Croman Astrophotography


Report 1 (PDF, 13KB)

Report 2 (PDF, 21KB)

Course Schedule

class calender
1 - Einstein's equation of the Robertson-Walker measurement
- Method of the Friedmann equation
- In the case of multi-component base
- Cosmological Parameter
2 - The General Behavior of Space
- Summary of the redshift phenomenon and cosmological distance
- Classic' Definition Methods of the Cosmological Parameter
3 - Linear Perturbation in the Robertson-Walker measurement
- The Gauge Degree of Freedom and Gauge Fixing
- The Linear Einstein Equation
4 - The Linear Boltzmann Equation
- Origination of Fluctuations in Inflation Theory
5 - Growth of Fluctuation in single component system
- The Power Spectrum and transfer function
- Photons, Baryons, and their Interactive Effects
- Growth of Fluctuations after recombination
6 - Fluctuations in Cosmic Background Radiation
7 - Distribution of galaxies in space
- A Weak-Gravitational Lens (Field)


Students' evaluations are based on two reports assigned to them during the course.

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Page last updated November 4, 2008

The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.

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