PHYS 480/581: Cosmology

Prof. Francis-Yan Cyr-Racine
Office: PAIS 3214

Teaching assistant
Loc Ngo
Office: PAIS 3414

Description of the class

This course will cover the entire evolution of the Universe, from the early epoch of inflation to the formation of all the complex structure we observe around us today. We will start by exploring the fundamental assumptions underpinning our current cosmological model, and derive the key equations governing its evolution. We will also discuss the global geometry of the Universe and how to measure distances in an expanding Universe. We will then turn our attention to the thermal evolution, describing how the Universe went from a primordial hot plasma to a world dominated by dark matter and cold baryonic gas in the first million years of the Universe. Finally, we will study how structure forms in our Universe, from the quantum origins of primordial fluctuations in the inflationary epoch to the gravitational growth of perturbations in a matter-dominated Universe.


The detailed syllabus can be found here.

Research Projects

Detailed instructions (including suggested topics) for the final research project can be found here.


Mondays and Wednesdays, 10:00-11:15am in PAIS 1160.


Textbook for the class
An Introduction to Modern Cosmology (3rd Edition) by Andrew Liddle.

Additional resource
Modern Cosmology (2nd Edition) by Scott Dodelson and Fabian Schmidt. The older edition is fine too.

Office hours

Mondays and Wednesdays 11:30am-12:30pm at my office PAIS 3214 These are my preferred "office" hours. If you can't make my regular office hours, or if your questions cannot wait, please send me an email to set up an appointment.

Teaching assistant
The teaching assistant is Loc Ngo ( He will be available Mondays 11:30am to 12:30pm for you to come by in PAIS 3414 and discuss any homework grading issues you may have. If you need to schedule an appointment outside of the TA's office hours please send him an email.


The grading in the course will be based on your performance in homework assignments, two midterm exams, and a final exam. The contribution to the final grade is as follows:

  1. Class participation and in-class worksheets will count for 25% of the final grade.
  2. Homework: there will be 6 assignments, which will represent the 40% of the final grade.
  3. A research paper and final presentation will represent the 35% of the final grade.

If you missed a class in which a worksheet was worked on, please do the worksheet on your own and hand in to me at a later date to make sure you don't lose participation points. You can find all worksheets in the table below.

Homework assignments

There will be 6 assignments during the semester. The assignments will be posted in the tentative schedule about 15 days before they are due. The login information necessary to access the homework PDFs will be provided in the first class. The homework must be submitted in class on the day they are due. Late Homework assignments will be accepted but with a 25% penalty for each day past the deadline. So a homework handed-in within 24 hrs of the deadline will carry a 25% penalty, one handed-in within 48 hrs will carry a 50% penalty, as so on. Let me know if you are planning on submitting your homework late such that I can delay the posting of the solutions. The corresponding solutions will be posted here, and homework assignments submitted after solutions post will not be graded.

While I strongly encourage you to discuss the homework assignments with your classmates, the work you hand in must be entirely yours.

Tentative schedule

Date Lecture Notes Liddle Reading Homework HW Due Solutions
Week 1
Worksheet 1
Distances and the metric
Worksheet 2
Ch. 1, 2.1-2.4

Week 2
Symmetry and the metric
Worksheet 3
The Friedmann Equation
Worksheet 4
Advanced Topic 1, Ch 3.1-3.3
Homework 1
Homework 1 Solutions
Week 3
Labor Day 09/05: No Lecture
The fluid equation
Worksheet 5
Ch 3.4, Ch. 5.3

Week 4
Worksheet 6
Density parameters and age
Worksheet 7
Ch 4.1-4.6, 5.1-5.2

Week 5
Distances I
Worksheet 8
Angular diameter distance
Worksheet 9
Ch 5.1-5.2, Advanced Topic 2
Homework 2
Supernova data
Homework 2 Solutions
Week 6
Luminosity distance
Worksheet 10
Detailed energy content of the Universe
Advanced Topic 2, Ch. 7, Advanced Topic 6.4

Week 7
Summary and Acceleration
Worksheet 11
Thermodynamics for cosmologists
Pressure aside
Ch. 3.5, 6.3, 7.3

Week 8
Relativistic thermodynamics
Worksheet 12
Non-relativistic thermodynamics
Worksheet 13

Homework 3
Homework 3 Solutions
Week 9
Effective degrees of freedom in the early Universe
Neutrino Temperature after e+e- annihilation
Advanced Topic 3

Week 10
Neutron freeze out and intro to nuclear physics
Worksheet 14
Worksheet 15
Ch 12
Homework 4
Homework 4 Solutions
Week 11
Helium abundance
Worksheet 16
Matter-radiation equality and recombination
Ch 12, 10, 11

Week 12
Out-of-equilibrium hydrogen recombination
Worksheet 17
Photon Decoupling: Cosmic Microwave Background
Ch 10

Week 13
Inflation 1
Inflation 2
Worksheet 18
Ch 13
Homework 5
Homework 5 Solutions
Week 14

Reheating after inflation
Dark matter 1
Dark matter 2
Ch 9

Week 15

Growth of Structure during radiation domination
Worksheet 19
Growth of structure during matter domination
Worksheet 20
Advanced Topic 5
Homework 6
Homework 6 Solutions
Week 16
Final Presentations