1 Introduction

The discovery of the expansion of the universe by Edwin Hubble in 1929 kick-started observational cosmology. If we mentally rewind the expansion, we find that the universe was hotter and denser in its past. At very early times the temperature was high enough to ionize the material that filled the universe, and at earlier times still the energies were so high that the laws of physics were barely recognizable compared to those operating today. Yet during this course we’ll sketch out how physics at the grand-unified energy scale seems to have given rise to structure in the universe today.

The observed universe has the following properties, which we’ll largely take for granted in our course:

1. 1.

   it is homogeneous (the same everywhere) and isotropic (the same in all directions) when averaged over sufficiently large scales;

2. 2.

   it appears to be topologically trivial (i.e. it is not periodic within $\mathrm{3\hspace{0.17em}000}$ Mpc);

3. 3.

   it is expanding (distant objects are moving away from us);

4. 4.

   this expansion has recently (a few billion years ago) started accelerating;

5. 5.

   it was vastly hotter in the past (evidence for this is provided by the cosmic microwave background which we will discuss later in the course);

6. 6.

   it contains vastly more matter than antimatter;

7. 7.

   its chemical composition is roughly 75% H, 25% He by mass plus a trace of heavy-elements;

8. 8.

   today it is highly inhomogeneous on small scales ($\ll 100$ Mpc);

9. 9.

   but it was highly homogeneous on these scales when it was young;

10. 10.

    the space appears to have negligible curvature.

To explain these and other observations, cosmologists have put together a remarkable history of the universe that has been confirmed through many successful predictions (though of course many open questions and puzzles remain). It is summarized in Fig.  1, emphasizing the “known unknowns” in our understanding of its composition and evolution. Bear in mind that there might be “unknown unknowns” as well!

The following table, reproduced from Liddle and Lyth, summarizes key events in the history of the universe and the corresponding time– and energy–scales:

During most of its history, the universe is very well described by the hot Big Bang theory – i.e. the idea that the universe was hot and dense in the past and has since cooled by expansion. The observational pillars underlying the Big Bang Theory are:

• •

  the relationship between redshift and distance, known as the Hubble diagram;

• •

  the observed abundance of elements in the universe, explained by Big Bang Nucleosynthesis (BBN);

• •

  the existence of the Cosmic Microwave Background (CMB).

This course touches on all these topics but we will go through them quite fast, on the assumption that you have come across them before (e.g. in the pre-requisite course PHAS3137).

Cosmological observations have indicated several properties of the universe that cannot be fully explained within the “standard model” (i.e. the hot Big Bang theory coupled to the Standard Model of particle physics):

• •

  dark matter – an additional matter component in the universe with apparently no (or nearly no) interaction with the standard model sector, except through gravity;

• •

  dark energy – a recent acceleration in the expansion rate of the universe;

• •

  the small amplitude and organised nature of the anisotropies in the CMB;

• •

  the large scale structure of the distribution of matter (LSS).

Again we’ll treat the first two topics pretty quickly in this course. The real focus will be on the third and fourth points, which we’ll tackle using relativistic perturbation theory.

We will need to draw heavily on concepts from general relativity (GR). While the course aims to be self-contained, GR is a hard subject in itself – all we can realistically do in the time available is to recap the required ideas, rather than develop them from scratch. Consequently, as advertised in the course description, it will be very helpful if you’ve either taken a GR course (such as MATH3305) or have self-studied this area before. If not, you should expect to do extra work to get up-to-speed. My personal recommendation is for Sean Carroll’s textbook (see item 2 on the list of complementary books on page 1), or if it’s hard to get a copy, he has made some closely-related lecture notes available free-of-charge: http://preposterousuniverse.com/grnotes/.

The main concepts we’ll recap are those of the metric and the geodesic; we’ll apply Einstein’s equations to the Friedmann-Robertson-Walker metric, relating the metric parameters to the (energy) density of the universe. In the first section of the course, we will apply Einstein’s equations to the homogeneous universe. In the second section of the course, we will apply them to the inhomogeneous universe by using perturbation theory.

Throughout the course, we will use natural units, $\mathrm{\hslash }=c=k_B=1$, unless explicitly knowing the dependence on these quantities is necessary to develop understanding.