Re: The Fractal Universe

From: Damien Broderick (
Date: Mon Jul 24 2000 - 20:58:38 MDT

At 10:15 AM 24/07/00 -0600, Brent wrote:

> The "abrupt end"? Is brief a million years, a femtosecond...?
> And what and why is there this 'boundary' where things change
>so dramtically?

Why, I'm glad you asked that question.

The potential function V changes with the temperature of the Universe, and
it is this that induces the phase transition, as it becomes energetically
favourable for the state of the field to change when the Universe cools
sufficiently. In the language of thermodynamics, the potential V() plays
the role of the free energy of the system. A graph of V() will typically
have a minimum somewhere, and that minimum value determines the value of
which is stable at a given temperature. Imagine an inverted parabola with
its minimum value at = 0; the configuration of the field can be
represented as the position of a ball rolling on this curve. In the stable
configuration it nestles in the bottom of the potential well at = 0. This
might represent the potential V() at very high temperatures, way above the
phase transition. The vacuum is then in its most symmetrical state. What
happens as the phase transition proceeds is that the shape of V() changes
so that it develops additional minima. Initially these `false' minima may
be at higher values of V() than the original, but as the temperature
continues to fall and the shape of the curve changes further, the new
minima can be at lower values of V than the original one. This happens at a
critical temperature Tc at which the vacuum state of the Universe begins to
prefer one of the alternative minima to the original one.

The transition does not occur instantaneously. How it proceeds depends on
the shape of the potential, and this in turn determines whether the
transition is first or second order. If the phase transition is second
order it moves rather smoothly, and fairly large `domains' of the new phase
are generated (much like the Weiss domains in a ferromagnet). One such
region (bubble or domain) eventually ends up including our local patch of
the Universe. If the potential is such that the transition is first order,
the new phase appears as bubbles nucleating within the false vacuum
background; these then grow and coalesce so as to fill space with the new
phase when the transition is complete.

Inflation arises when the potential term V greatly exceeds the kinetic term
U in the action of the scalar field. In a phase transition this usually
means that the vacuum must move relatively slowly from its original state
into the final state.

No, sorry, I'm cheating horribly, and plagiarising to boot. That (with the
symbols fubar'd in the phase transition to email) is from which I
found in about three seconds of googling. Go thou and do likewise.

Damien Broderick

This archive was generated by hypermail 2b29 : Mon Oct 02 2000 - 17:35:13 MDT