Chapter 3: THE FRIEDMANN MODELS

3.8 The Big Bang
We have now calculated R(τ) for three generic models for a pressure-less expanding
Universe. Because gravity acts on matter to decelerate it, it should not be surprising
that these three all have R = 0 at some finite time in the past. As noted above, any
curvature present today will be less important at earlier epochs, as Ω → 1. We would
expect radiation to become dynamically dominant at some earlier point in time, but it
too has R = 0 at some point in the past. Of course, R = 0 implies a singularity and it is
likely that some new physics must be introduced at such early times (as we’ll see
below) but a compact, rapidly expanding state for the Universe is a strong prediction
of the Friedmann models.
As noted above, even a non-zero false vacuum density today would, if constant, be
unimportant before some earlier epoch.
The idea that the Universe was once in an extremely compressed state is the
fundamental feature of the Friedmann models. This compressed but rapidly expanding
state is known as the Big Bang. The term was introduced, in a derisory way, by Fred
Hoyle during a radio broadcast.
Chapter 3: Key points
1. The correct Friedmann equation in & R (from GR) can in fact
be generated from the Newtonian && R equation if we set the density to
be the so-called "active density".
2. The dynamics of the Universe depend on the equation of state
of the matter-radiation in the Universe as this determines how the
density changes as the Universe expands. Our matter-dominated
Universe was once radiation dominated.
3. The density parameter Ω determines in fundamnetal way
both the dynamics and the curvature of the Universe.
4. For a given equation of state, the term in the Robertson-
Walker metric mat be written in terms of (c/H 0 )Z q (z), where q is a
deceleration parameter.
5. A false vacuum energy density is equivalent to a non-zero Λ
term in the Friedmann equation.