Chapter 2

An introduction to the physics of cosmology

John A Peacock

Institute for Astronomy, University of Edinburgh, United

Kingdom

In asking me to write on ‘The Physics of Cosmology’, the editors of this book
have placed no restrictions on the material, since the wonderful thing about
modern cosmology is that it draws on just about every branch of physics. In
practice, this chapter attempts to set the scene for some of the later more
specialized topics by discussing the following subjects:

(1) some cosmological aspects of general relativity,

(2) basics of the Friedmann models,

(3) quantum fields and physics of the vacuum and

(4) dynamics of cosmological perturbations.

2.1 Aspects of general relativity

The aim of general relativity is to write down laws of physics that are valid
descriptions of nature as seen from any viewpoint. Special relativity shares the
same philosophy, but is restricted to inertial frames. The mathematical tool for
the job is the 4-vector; this allows us to write equations that are valid for all
observers because the quantities on either side of the equation will transform in
the same way. We ensure that this is so by constructing physical 4-vectors out of
the fundamental interval

dxμ=(cdt,dx,dy,dz)μ= 0 , 1 , 2 , 3 ,

using relativistic invariants such as the the rest massmand proper time dτ.
For example, defining the 4-momentum Pμ = mdxμ/dτ allows an
immediate relativistic generalization of conservation of mass and momentum,

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