AST5220/9420 –

Course presentation

Hans Kristian Eriksen

Fact: The universe has structure

Our main question: How did these form?

AST5220/9420 in three bullet points

• Goal:

– Understand the structure formation processes in the early

universe

• Main method:

– Compute numerically and (where possible) analytically the

evolution of structure

• Main deliverable in the form of a project:

– CMB power spectrum code; takes in cosmological parameters,

outputs spectrum

Main topics to be covered • Short introduction to General Relativity

• Boltzmann equations

– How do particles behave in non-equlibrium conditions?

• Baryons, photons, dark matter

– Recombination; how did the universe become transparent?

• Einstein equations

– How do space behave when matter is present, and moves around?

• Inflation

– How were the very first structures generated?

• Observables

– How can we predict what we will observe, given a theoretical

model?

Lectures, times etc.

• Two lectures per week – Tuesday 10.15 - 12.00

– Friday 12.15 – 14.00

• Style will vary:

– PowerPoint for review material

– Blackboard for derivations

– Sometimes I will sit at the computer, ”coding”

live

– Sometimes the ”lecture” will be a workshop

where you either code or do analytic

calculations

Evaluation

• The evaluation will consists of two parts

– Written exam – 70% of the grade

– Project – 30% of the grade

• The project will consist of four milestones, each counting 25% of the project score

• Date for exam is not settled yet

– Open for suggestions from you

The project • The project forms the skeleton of the

course

• What are you supposed to do?

– Compute the CMB temperature power

spectrum given cosmological parameters!

• How will you do it?

– Write a computer code that solves the

linearized Boltzmann and Einstein

equations for photons, baryons and dark

matter

– Follow step-by-step procedure; the code

will be built up piece by piece

• Why will you do it?

– Completing this project will form an

excellent foundation for both theoretical

and observational Master and Ph.d.

projects

More on the project

• Four milestones:

1. ”The background cosmology”

• Solve the Friedmann equations, to know how the average, large-scale

and uniform space itself behaves

2. ”Recombination”

• Compute the electron density of the universe as a function of time, to

know how often photons scatter at any time

• Done by solving the Saha and Peebles’ equations

3. ”Evolution of matter in the universe”

• Track the evolution of a single Fourier mode from just after inflation until

today, by solving the Boltzmann and Einstein equations in space and time

4. ”The CMB power spectrum”

• Compute the CMB temperature spectrum, by averaging the photon

fluctuations over all scales and random realizations, and projecting them

onto a sphere

Rules for the project

• Deliverables: – For each milestone, a short report (~1-2 pages of text, not

counting figures) is to be written

– Computer code is to be submitted in pdf

• Collaboration: – No collaboration on ”future” milestones

– No restrictions at all on passed milestones; copy codes if you want!

– Note that I should be considered a legal aid; do ask me if something doesn’t work or is unclear – I’ll do my best to help!

• Grading: – Each milestone can give 25 points

– Errors, bad coding practice will lead to lost points

• Note: Coding style gives points; write clear and well documented code!

Programming language?

• You are completely free to choose whatever language you want

• However, I only know F90 very well, and if you want help from me, you better choose F90 too.

• Recommendations: – If you trust yourself to be an experienced

programmer, choose whatever you are most comfortable with

– If you are less experienced, choose F90, so that I can help you out if and when you get stuck

Exam • Written exam will be held early June

– Suggestions?

• Problems will be a mix of

– analytic calculations

• e.g., linearize some equations

– interpretation of plots derived during project work

• e.g., what does this plot of the visibility function tell us?

– questions on physical intuition

• e.g., what is the reason that the third peak is higher than the

second peak in the CMB spectrum, if the baryon density is

high?

• Last years’ exams are available online

AST5220 vs. AST9420

• Main differences are:

– Ph. D. students will have to implement support for neutrinos and

polarization in their computer codes

– One problem will be different on the final exam

• Note that only the AST5220 web pages will be

continuously updated, but not the AST9420 pages

Textbook, curriculum etc.

• The curriculum is defined by

– Chapter 1 to 8 in ”Modern cosmology” by Scott Dodelson

– The material covered in the project work

• In addition, there are several other useful sources of information:

– ”How to calculate the CMB spectrum” by P. Callin

– ”Numerical recipes”; pdfs are available online at www.nr.com

– For those who chooses F90 as their programming language, Bo

Einarsson’s online reference is highly recommended • http://www.nsc.liu.se/~boein/f90/

Tips and hints! • Set up your coding environment (editor, directories,

Makefiles, etc.) as soon as possible!

– You don’t want to struggle with infrastructure problems just

before a deadline

• Take a quick look at the project summary pages, and

keep the various sections there in mind as we go along

• If possible, spend a weekend reading through chapter 1

to 8 in ”Modern cosmology” from start to finish, early in

the course

– You won’t understand everything, but you will get a rough idea of

what we are going to do, and even more importantly, why.

• As you start programming, you will probably find Callin

(2005) even more useful than Dodelson!

Practicalities

• Email addresses

• User accounts at ITA

• Exam date?