5 Inflation I: homogeneous limit
Matter is distributed very homogeneously and isotropically on scales larger than a
few hundred megaparsecs. The CMB gives us a “photograph” of the early universe,
which shows that at recombination the universe was extremely homogeneous and
isotropic (with accuracy∼ 10 −^4 ) on all scales up to the present horizon. Given that
the universe evolves according to the Hubble law, it is natural to ask which initial
conditions could lead to such homogeneity and isotropy.
To obtain an exhaustive answer to this question we have to know the exact
physical laws which govern the evolution of the very early universe. However,
as long as we are interested only in the general features of the initial conditions
it suffices to know a few simple properties of these laws. We will assume that
inhomogeneity cannot be dissolved by expansion. This natural surmise is supported
by General Relativity (see Part II of this book for details). We will also assume that
nonperturbative quantum gravity does not play an essential role at sub-Planckian
curvatures. On the other hand, we are nearly certain that nonperturbative quantum
gravity effects become very important when the curvature reaches Planckian values
and the notion of classical spacetime breaks down. Therefore we address the initial
conditions at the Planckian timeti=tPl∼ 10 −^43 s.
In this chapter we discuss the initial conditions problem we face in a decelerating
universe and show how this problem can be solved if the universe undergoes a stage
of the accelerated expansion known as inflation.
5.1 Problem of initial conditions
There are twoindependentsets of initial conditions characterizing matter: (a) its
spatial distribution, described by the energy densityε(x)and (b) the initial field of
velocities. Let us determine them given the current state of the universe.
Homogeneity, isotropy (horizon) problemThe present homogeneous, isotropic do-
main of the universe is at least as large as the present horizon scale,ct 0 ∼ 1028 cm.
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