PHYS 3022
Introduction to Cosmology
Spring 2017
Week #1: Wednesday, January 18
Reading for Week # 1: Ryden: Chapters 1 & 2.1
Reading for Week # 2: Ryden: Chapters 2.2-2.5
Homework #1: Due Wednesday, January 25 at 11:05 AM.
Total of 25 points for this prob
PHY 475
Homework 3
(Due by beginning of class on Wednesday, April 25, 2012)
Submit neat work, with answers or solutions clearly marked by the question number.
Unstapled, untidy work will be charged a handling fee of 20% penalty. Writing only
an answer wit
U NIVERSITY OF C ALIFORNIA - S ANTA C RUZ
D EPARTMENT OF A STROPHYSICS
ASTR 113
Homework #4
Benjamin Stahl
May 29, 2015
Note that wherever I have note explicitly shown the numbers used to evaluate results or where I have changed
units, the capabilities of
U NIVERSITY OF C ALIFORNIA - S ANTA C RUZ
D EPARTMENT OF A STROPHYSICS
ASTR 113
Homework #2
Benjamin Stahl
April 17, 2015
Note that wherever I have note explicitly shown the numbers used to evaluate results, they are the constants encoded into Wolfram Alp
PHY 475
Homework 1
(Due by beginning of class on Monday, April 9, 2012)
Submit neat work, with answers or solutions clearly marked by the question number.
Unstapled, untidy work will be charged a handling fee of 20% penalty. Writing only
an answer without
U NIVERSITY OF C ALIFORNIA - S ANTA C RUZ
D EPARTMENT OF A STROPHYSICS
ASTR 113
Homework #3
Benjamin Stahl
April 24, 2015
1
RYDEN 3.2
In this problem the following scenario will be considered: a two-dimensional being lives on the surface of a sphere
with
U NIVERSITY OF C ALIFORNIA - S ANTA C RUZ
D EPARTMENT OF A STROPHYSICS
ASTR 113
Homework #4
Benjamin Stahl
May 20, 2015
Note that wherever I have note explicitly shown the numbers used to evaluate results or where I have changed
units, the capabilities of
U NIVERSITY OF C ALIFORNIA - S ANTA C RUZ
D EPARTMENT OF A STROPHYSICS
ASTR 113
Homework #1
Benjamin Stahl
April 8, 2015
1
QUESTION 1
The relativistic Doppler shift of light is given by the following equation:
v
u
1 + vc
fe u
=t
fo
1 vc
(1.1)
Where f e is
PHY 475
Homework 4
(Due by beginning of class on Wednesday, May 16, 2012)
It took me a while searching for good problems on dark matter, and in the end, I decided to make
up my own. So, this homework is being posted two days later than I would have liked
PHY 475
Homework 2
(Due by beginning of class on Wednesday, April 18, 2012)
Submit neat work, with answers or solutions clearly marked by the question number.
Unstapled, untidy work will be charged a handling fee of 20% penalty. Writing only
an answer wit
ASTRONOMY 113: INTRODUCTION TO COSMOLOGY
I. INTRODUCTION (Chapt. 1-2 Liddle, Chapt. 1-2 Ryden)
1.1 Prologue
1.1 The Cosmological Principle
1.2 Particles in the Universe
1.3 Elementary Properties of Radiation
1.4 Olbers Paradox
1.5 Doppler effect
II. STAND
PHYS 3022
Introduction to Cosmology
Spring 2017
Week #2: Monday, January 23 Friday, January 27
Reading for Week # 2: Ryden: Chapters 2.2-2.5
Reading for Week # 3: Ryden: Chapters 3.1-3.4 (M) & 3.5-3.6 (W) & 4.1-4.3 (F)
NOTE: We will have class on Friday,
PHYS 3022
Introduction to Cosmology
Spring 2017
Homework Solutions Week 1
Problem 1
There are several ways to approach this problem (equivalent within a factor of 2). You can use
Schwarzschilds equation for the radius of a black hole with the mass of the
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PHYS 3022
Introduction to Cosmology
Spring 2017
Homework Solutions Week 4
Problem 1 - Cosmological Constant
(a) Assuming ,0 = 0.69 and H0 = 0.68 km s1 Mpc1 as measured in the benchmark
universe and recalling the definition of critical energy density and t
PHYS 3022
Introduction to Cosmology
Spring 2017
Homework Solutions Week 2
Problem 1
Note: as mentioned in lecture, be careful not to make the mistake peak = c/peak . The
distribution of black body radiation (Plancks Law) as a function of frequency has a
d
PHYS 3022
Introduction to Cosmology
Spring 2017
Homework Solutions Week 3
Problem 1 - Critical Density
(a) For our universe, we find the critical energy density with = 0 and
these values in the Friedmann equation:
2
a
c2
8G
(t)
=
a
3c2
R02 a(t)2
= H(t)2
(a)
(b)
(c)
(d)
(e)
Imagine a universe with a flat space metric that is filled only with
radiation (and no matter or any other component), with the spectrum
of a blackbody. At the time when the radiation has a temperature T =
3 K, what would be the energy
PHYS 3022
Introduction to Cosmology
Spring 2017
Quiz 1 Solutions
Problem 1 [30 pts]
The Friedmann equation is given as:
2
kc2
8G
a
(t)
=
a
3c2
R02 a(t)2
(a) Identify each variable:
a :
scale factor
a : time rate of change of scale factor
(1)
(t) : energy