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Graduate School
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 
Course Overview
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 knowledgemethods of modern physics like the general relativity theory and nonequilibrium statistical physicsmust 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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Syllabus
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.
Contents
 The Basics of Cosmology
In this section, we will review major points of `homogeneous universe' theory, which forms the basics of cosmology. From the RobertsonWalker 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.
 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 spacetime, a necessity in dealing with systems of many particles.
 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.
 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 widerange structure, observation of either the fluctuations in cosmic background radiation or the largescale structure of the universe. We'll see how these measurements relate to the theoretical growth of cosmic fluctuations.
Textbooks
None required
Note
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 LargeScale 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
http://www.rcastro.com
Assignments
Report 1 (PDF, 13KB)
Report 2 (PDF, 21KB)
Course Schedule
class  calender 

1   Einstein's equation of the RobertsonWalker measurement  Method of the Friedmann equation  In the case of multicomponent 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 RobertsonWalker 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 WeakGravitational Lens (Field) 
Grading
Students' evaluations are based on two reports assigned to them during the course.
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Class Materials
Lecture Handouts
The files below are copies of notes handed out to students during the lesson. The notes, housing some of the equations and formulas used throughout the course of the lesson, are supplementary to the lectures.
 class 1
  Einstein's equation of the RobertsonWalker measurement /Method of the Friedmann equation /In the case of multicomponent base /Cosmological Parameter (PDF, 42KB)
 class 2
  The General Behavior of Space /Summary of the redshift phenomenon and cosmological distance /Classic' Definition Methods of the Cosmological Parameter (PDF, 40KB)
 class 3
  Linear Perturbation in the RobertsonWalker measurement /The Gauge Degree of Freedom and Gauge Fixing /The Linear Einstein Equation (PDF, 43KB)
 class 4
  The Linear Boltzmann Equation /Origination of Fluctuations in Inflation Theory (PDF, 54KB)
 class 5
  Growth of Fluctuation in single component system /Photons, Baryons, and their Interactive Effects /Growth of Fluctuations after recombination (PDF, 53KB)
 class 6
  Fluctuations in Cosmic Background Radiation (PDF, 45KB)
 class 7
  Distribution of galaxies in space /A WeakGravitational Lens (Field) (PDF, 50KB)
 Appendix
  Elemental geometric quantities in General theory of relativity and Cosmology (PDF, 46KB)
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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.