From: ted@physics20 (Emory F. Bunn)
Newsgroups: sci.physics
Subject: Re: Simple poser about the early universe
Followup-To: sci.physics
Date: 11 Nov 1992 22:22:22 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: physics20.berkeley.edu

In article <1992Nov11.195607.210@maths.tcd.ie> spock@maths.tcd.ie (Thomas G. Hayes) writes:

> I was just reading the other day that some satellite (Hubble I think)

COBE, actually.  Hubble sees in the visible and ultraviolet, while the
background radiation is at much longer wavelengths.

> has found variations in the background radiation of the universe.
> Now, some astro-physicists would like to take this as strong evidence
> for the inhomogenity of the early universe, whereas others take the
> variations to be a result of the gravitational waves created during
> the inflationary period of the universe.
>                              Now, the question I want to ask is this:
> Could not the gravitational waves have actually caused the 
> inhomogenities in the first place? If an area of space is compressed
> by a gravitational wave, surely this area is more dense than the 
> surrounding areas? If not, why not?

This is a good question, which touches on a couple of issues that have 
been presented obscurely at best in the recent early universe media blitz.
The early Universe seems to have been nearly uniform, but with small 
perturbations.  At any particular time, there can be a few different forms
of perturbations:

(1) The density could vary from place to place; relativity would then require
    the curvature of space to vary along with it.  
(2) The density could be uniform, while the composition of stuff could vary
    from place to place; for example, the ratio of protons to photons
    could be a function of position.  In this case, there are no perturbations
    to the spacetime geometry at that time, although such perturbations will
    develop later.
(3) There could be perturbations in the geometry but not in the matter.

Or of course you could have any combination of these.  In fact, there's no
reason to expect any of them to be absent.  As time passes, the various types
mix together:  Type-2 perturbations cause type-1 perturbations, and so on.
(What you point out above is that type 3 causes type 1, and that's quite 
correct.) However, at any instant it might be convenient to use these 
categories as a basis of sorts for describing the perturbations.  Of
course, it's tricky:  The field equations impose constraints on what 
perturbations are allowed; also, you have to be careful to distinguish 
real physical perturbations from "gauge modes" that simply arise from
an unfortunate choice of coordinates.

Now it turns out that some type-3 perturbations just propagate like
waves:  They introduce ephemeral distortions in the density field as they
pass by, but they don't cause any lasting (growing) effects.  These
are the ones people talk about when they refer to gravity wave perturbations.

One question that's important to cosmologists, of course, is whether the
microwave-background fluctuations are caused by perturbations of the
sort that will eventually grow into large structures, or whether they're
caused by the harmless gravity-wave perturbations (or some mixture of the
two).  Of course, without a credible theory to explain where the
perturbations come from, there's not much hope of answering that
question.  To make matters worse, it appears that the most popular
model for the origin of the perturbations, the inflationary model,
has a free parameter related to the ratio of gravity-wave to growing-mode
perturbations.  So things don't look good for distinguishing between
the two cases.

(It turns out that the simplest models of inflation predict that the
ratio of the amplitudes of microwave-background fluctuations on
different angular scales depends on whether the fluctuations come
from density perturbations or gravity waves, so if some of the small-
angular-scale experiments get solid results, it might be possible
to say something.)

-Ted

a theory of where the
Newsgroups: sci.physics