Rough Notes

Introduction

This page will be used to keep some (as full as possible) documentation of my hand-written note taking throughout this project. This will be on a range of media; my preferred canvas is usually a blackboard or on my iPad.

One will probably not be able to follow these notes as in the way you would a usual course, but I hope you may find some help in seeing how I went about the reading for my dissertation.

Feel free to contact me if you find any glaring mistakes.

03/08/26 (Blackboard, following Baumann's Cosmology, Chp. 6.1)

3rd August 2026

Time to start the project. I will mainly be following Baumann’s Cosmology textbook for now (see the Bibliography section, when uploaded) but my notes may include derivations the textbook doesn’t. These are to satisfy my own curiosity and oftentimes may be completely trivial to most.

In the picture above, I did not include the proof of the proposition. Although it is rather trivial, I will put that here:

We have $x^i \to \tilde x^i = x^i + \xi ^i (\eta, \vec{x}=x^k)$ Taking the total (exterior) derivative we have $$ d \tilde x^i = dx^i + d\xi^i = dx^i + \partial_\eta \xi^i d\eta + \partial_k \xi^i d\tilde x^k $$

Thus, $$ dx^i = d \tilde x^i - \partial_\eta \xi^i d\eta - \partial_k \xi^i d\tilde x^k$$ $\Box$

05/08/26 (iPad + Blackboard, continuing from 03/08/26)

5th August 2026

I chose to continue working through Baumann’s textbook, taking the time to derive the effect of coordinate changes on metric perturbations (as in an exercise in the book).

In the following blackboard working I am aware some of the indexing is lazily done, but I hope you can agree the working is still valid.

06/08/26 (iPad + Blackboard + Paper, continuing from 05/08/26)

6th August 2026

Today was not particularly productive, but I managed to move slightly forward with my prereading.

10/08/26 (iPad, continuing from 06/08/26)

10th August 2026