## An Introduction

The physical laws that govern the Universe prescribe how an initial state evolves with time. In classical physics, if the initial state of a system is specified exactly then the subsequent motion will be completely predictable. In quantum physics, specifying the initial state of a system allows one to calculate the probability that it will be found in any other state at a later time. Cosmology attempts to describe the behaviour of the entire Universe using these physical laws. In applying these laws to the Universe one immediately encounters a problem. What is the initial state that the laws should be applied to? In practice, cosmologists tend to work backwards by using the observed properties of the Universe now to understand what it was like at earlier times. This approach has proved very successful. However it has led cosmologists back to the question of the initial conditions.

### The initial conditions

Inflation (a period of accelerating expansion in the very early Universe) is now accepted as the standard explanation of several cosmological problems. In order for inflation to have occurred, the Universe must have been formed containing some matter in a highly excited state. Inflationary theory does not address the question of why this matter was in such an excited state. Answering this demands a theory of the pre-inflationary initial conditions. There are two serious candidates for such a theory. The first, proposed by Andrei Linde of Stanford University, is called chaotic inflation. According to chaotic inflation, the Universe starts off in a completely random state. In some regions matter will be more energetic than in others and inflation could ensue, producing the observable Universe.

The second contender for a theory of initial conditions is quantum cosmology, the application of quantum theory to the entire Universe. At first this sounds absurd because typically large systems (such as the Universe) obey classical, not quantum, laws. Einstein's theory of general relativity is a classical theory that accurately describes the evolution of the Universe from the first fraction of a second of its existence to now. However it is known that general relativity is inconsistent with the principles of quantum theory and is therefore not an appropriate description of physical processes that occur at very small length scales or over very short times. To describe such processes one requires a theory of quantum gravity.