Course Information:

Prof. Matthew Buckley (office: Serin W329, mbuckley@physics.rutgers.edu)

Lectures: Monday/Wednesday 2:00-3:20 Serin 401 (Busch Campus)

Office Hours: Tuesday 10-11, Thursday 3-4

Course Description

This course is an advanced undergraduate-level study of the origins and evolution of the Universe. We will cover the 13.8 billion year history of our Cosmos, as we understand it today. The course covers the expansion of the Universe, our understanding of that expansion in the context of General Relativity, the energy content of the Universe, and epochs of particularly interesting and important physics, including the formation of the Cosmic Microwave Background, Big Bang Nucleosynthesis, the formation of large-scale structure, and cosmic inflation. 

The textbook for the course is Introduction to Cosmology by Barbara Ryden (2nd Edition, 2003, Addison Wesley ISBN 0-8053-8912-1). Please note that the 2nd Edition is the version used in this class; the 1st Edition was published prior to major cosmological discoveries in the 2000’s and thus lacks important content on the Cosmic Microwave Background.

Grading

  • Grades will be based on weekly problem sets (60% of final grade), an in-class midterm (20%), and a final exam (20%).

  • Weekly homework will be assigned on Wednesday in class and due on the following Wednesday in class.

  • Collaboration with other students is strongly encouraged, but your write-up of the solutions must be your own. You must write down the names of your collaborators on your write-up. You must also cite any external sources you use (other than the textbook). You may not refer to notes, assignments, or solutions from previous years of Physics 444. You may not use the output of Large Language Models (LLMs) in your homework solutions (see discussion of coding, below).

  • Always show your work. You will not receive full credit if you do not show your work. I am always looking for the reasoning behind the answer.

  • Some homework problems will ask you to use a numeric equation solver, and plot your results. See the bottom of this page for a discussion of possible programs to use and some example documents to get you started. If the homework asks for numeric solutions, you must submit the code you used on Canvas. The code must include the names of all people you worked with. It is acceptable to use LLMs to construct basic code snippets (i.e., how to make a plot, how to integrate a function), but you may not use an LLM to create the physics content of a solution. For example, you can use an LLM to see how to create a python code block to numerically integrate a function and how to plot the output of a function vs input, but you can't ask the LLM to integrate the Hubble parameter over cosmic history and plot it for you.

  • You may hand in homework in person or submit online. In either case, the homework must be written legibly. If submitting online, please organize your written submission into a single file (code may be submitted separately).

  • In general, late homework will automatically receive a maximum of half points. If possible, seek arrangement with me at least 24 hours in advance if you think you have a legitimate excuse for late work. After I have graded and handed back an assignment, I will not accept that late submissions.

Student Accommodations

If you require special accommodation in the course, please speak with me as early in the semester as possible. Visit this linkLinks to an external site. for information on Rutgers policies.

Course Schedule

  • Week 1 (Sept. 3, 8, 10). Chapters 1 & 2. Introduction, Hubble's Law

  • Week 2 (Sept. 15, 17) Chapter 3. Relativity, Space-time Metric

  • Week 3 (Sept. 22, 24) Chapter 4. Friedmann, Fluid, Acceleration Equations

  • Week 4 (Sept. 29, Oct. 1) Chapter 5. Single-Component Universes

  • Week 5 (Oct. 6, 8) Chapter 5 & 6. Single-Component Universes. Multiple Component Universes

  • Week 6 (Oct. 13, 15) Chapter 6 & 7. The Benchmark Model. Cosmological Distances

  • Week 7 (Oct. 20, 22) Chapter 8. Dark Matter

  • Week 8 (Oct. 27, 29) In Class Midterm (Oct. 29)

  • Week 9 (Nov. 3, 5) Chapter 9. The Cosmic Microwave Background

  • Week 10 (Nov. 10, 12) Chapter 9. The Cosmic Microwave Background.

  • Week 11 (Nov. 17, 19) Chapter 10. Big Bang Nucleosynthesis.

  • Week 12 (Nov. 17, 19) Chapter 11. Inflation.

  • Week 13 (Nov 24) Chapter 11. Inflation Thanksgiving (No Class)

  • Week 14 (Dec. 1, 3) Chapter 12. Structure Formation

  • Week 15 (Dec. 8, 10) Chapter 12. Structure Formation

Numeric Computation

This course will ask students to numerically computer properties of the Universe in the homework.

There are many tools available to allow one to solve differential equations and other numeric manipulations. I will recommend two of them (these are the two I'm most familiar with, so these are the two I will provide support for in office hours). These are Mathematica (current version is 14.2) and Python3 (Python2.7 is very similar, but has some annoying non-compatibilities).

Mathematica is an extremely powerful mathematical tool. It is very flexible, very useful, and individual licenses are very expensive. 

DO NOT PURCHASE A MATHEMATICA LICENSE FOR THIS COURSE.

As Rutgers students, you should be able to download a free Mathematica license from the Rutgers network.. Keep in mind it will require yearly renewal, so when you leave Rutgers, you will not have necessarily have Mathematica available. If you continue in academia, or work in a job that requires it, you will have to get a license elsewhere.

Python. is a programming language with many open-source free packages that allow sophisticated mathematical manipulations. In particular the packages NumPy. and SciPy. are incredibly useful for scientists working with statistics and mathematical problems. You will have to download and install these, along with Python itself. It should be available on all operating systems. In recent years, a useful manager for Python and associated packages is the Anaconda. (or Miniconda) management system. It should be available for all operating systems. Using Conda will allow you to use Jupyter notebooks, which allow for interactive python coding (i.e., you can execute code line by line, see if it works, and edit and update as you go). You can also integrate Jupyter notebooks into code management programs (VSCode seems to be the most popular among my grad students and postdocs working in machine learning right now).

Additionally, to make plots, I recommend the MatPlotLib package.

The learning curve for Python is probably a bit steeper than for Mathematica, especially if you are not familiar with programming languages. However, it will be available to you where ever you go, and can do many tasks with greater speed and flexibility than Mathematica.

This is not a course on programming, and I will not be asking you to do extremely complicated programming tasks. However, modern science is increasingly computational, and these tools will be very useful. If you are thinking of a career in science or computing, I would recommend taking the plunge and learning Python (I would especially recommend Jupyter notebooks for ease-of-use).

An example documents for Mathematica is here Download here, and covers most of the type of tasks you will be asked to do in the course. The equivalent for Python is here Download here A Jupyter notebook (identical in most respects to the Python code, but needs to be opened in Jupyter or a program like VSCode) is here Download here.