Milestone I - General Relativity and Background cosmology:
Update 6 February: After I broke my hip and had to delegate the teaching to HÃ¥vard and David I will not update this page while out since I don't know what is being covered in the lectures. Take a look at the course website for this info. Also take a look at the schedule for last year to see suggested problems (and videos of lectures in case you did not make a given lecture).

# Schedule Spring 2022

This page will show what we are meant to go through (and what we actually did go through) every week. It will be updated as we go along. See the official course website for when lectures are given (Wednesday and Thursday 1215-1400). You can also find the schedule for last year here (contains slides and videos for all lectures).

## Week 1 (19-20 Jan)

### Problems:

Basic problems on working with tensors and the Einstein summation convention (UiO login required) here.

### Summary:

We give an overview of what you are supposed to learn in this course and give some practical information about the course and the project. We then start on a crash course in General Relativity. We will first go through Newtonian gravity (the differential formulation) and then go on to introduce the concepts of tensors, a metric, connections, parallel transport, curvature, the geodesic equation and finally the Einstein Equations. Finally we show how Newtonian gravity arises as a limit of General Relativity. The main aim here (since we don't have much time for this) is simply to give you the operational knowledge of doing calculations with GR.

### Learning goals:

• Know what a tensor is and be able to evaluate simple tensorial expressions. Know the Einstein summations convention.
• (Next week) You are supposed to know the algorithm for evaluating the Einstein equations and (after next week when we have gone through this in detail) be able to perform this kind of calculation, i.e. start from a given metric and compute the inverse metric, the connections coefficients, the Ricci tensor, the Ricci scalar and use this to evaluate the left hand side of the Einstein equation.
• (Next week) You should also know about the geodesic equation: the key equation in GR that tells us how particles move in a given spacetime (but we will get back to this in more detail later in the course).

Download: Lecture 1; Lecture 2. NB: Videos have a size of $\sim$ 300 MB.

## Week 2 (26-27 Jan)

### Problems:

Problems on working with the metric tensor (UiO login required) here.

### Summary:

We finished our introduction to GR. We gave an introduction to theoretical cosmology at the background level. The cosmological principle and its implication for the geometry of the Universe. We went through how to model matter/radiation at the background (perfect fluids) and how different components evolve in time.

### Learning goals:

The aim is to know the basics of background cosmology: the cosmological principle $\to$ Friedmann metric and (next week) going from the Friedmann metric to the Einstein equations and obtaining the Friedmann equations. You should know how each energy component evolves in an expanding Universe.

### Video:

Download: Lecture 1, Lecture 2. NB: Videos have a size of $\sim$ 200 MB.