In this chapter and the next, we consider the perturbation in the energy density of the Universe, as it exists when the run-up to nucleosynthesis begins at temperature T ~ 1MeV. Although it is not essential, we will take T to actually be a bit below 1MeV so that the positrons have annihilated leaving just the cold dark matter (CDM), baryons, photons and neutrinos, with the last decoupled.

Perturbations existing at this epoch may be called primordial perturbations because they provide a simple initial condition for the subsequent evolution of the perturbed Universe. That evolution and its contact with observation will occupy us for the rest of Part II.

We will also study what is called the curvature perturbation. It is a powerful quantity, because on superhorizon scales it is conserved provided that the pressure of the cosmic fluid depends only on its energy density. The curvature perturbation determines the perturbation in the total energy density, defined on a given slicing of spacetime. We consider also the isocurvature perturbations which determine the distribution of energy density between different components of the cosmic fluid.

The strategy will be to study the perturbations themselves in this chapter, and their stochastic properties in the next. The study is important both in its own right, and because it introduces basic concepts that will be used throughout the book.