Re: Cosmo Constant
From: Brian Tung (brian_at_isi.edu)
Date: 07/20/04
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Date: Tue, 20 Jul 2004 21:56:42 +0000 (UTC)
eric adam wrote:
> When einstien introduced the cosmological constant originally, it was
> a fudge factor that represented a force that counteracted the
> expansion of the universe. After its time in the trash bin of history
> it has been brought out again in the discussion of the acceleration of
> the expansion of the universe. I believe it now represents a repulsive
> force. Is that right? How can it be both? Is it only a mathematical
> element?
It's a mathematical element just as the value of g = 9.8 m/s^2 is a
mathematical element. However, they both represent physical phenomena.
Einstein introduced the cosmological constant because in his estimation,
the universe seemed to be in equilibrium. That doesn't mean that
everything was stationary, naturally, but by and large, the universe
was neither expanding nor contracting.
But gravity ought to cause everything to come collapsing together,
unless something else is holding it up. Imagine letting go of a tennis
ball in mid-air. The moment you let go, it ought to come falling down
to the ground, unless something holds it up. Einstein proposed that
there was some mysterious property of space-time that kept things from
falling together. This would be like an "anti-gravity" that held the
ball up.
However, one need not simply let go of the tennis ball. One might,
instead, throw it up in the air. By relaxing the condition that the
universe remain in equilibrium, we can do away with the cosmological
constant. The universe, in expanding, is like a tennis ball in its
upward flight. It might do one of two things. It might, after a time,
stop rising, and then come back down to earth under the force of gravity.
Or, if it's thrown upward at a speed equal to or greater than the escape
velocity of the Earth, it will continue rising forever. (Yes, I am
ignoring for the time being that the Sun's gravity would still affect
the ball's flight.)
In much the same way, an expanding universe might do one of two things:
stop expanding one day and come back together in a "Big Crunch"; or, if
it is expanding fast enough, continue expanding forever. This was
worked out in some detail by Friedman, and in each case, there is no
need for a cosmological constant to keep the universe from collapsing.
Now, to be sure, when general relativity was first formulated, there was
no firm evidence that the universe was in fact expanding. But first
Slipher's and then Hubble and Humason's studies into the red shifts of
different galaxies put the expanding universe hypothesis on a strong
foundation. Although it is in dispute by some astronomers, it is widely
accepted.
Only recently has there come evidence that the universe is not only
expanding, but that its expansion is, in some sense, accelerating. And
if the cosmological constant could "hold the tennis ball up," so to
speak, against the force of gravity, it stands to reason that if the
universe is expanding, the cosmological constant could also represent
some mysterious force making the universe expand even faster than it
would otherwise.
It is important that the cosmological constant is, as you say, just a
mathematical factor. It appears to model the behavior of the universe
in an accurate fashion, but it is silent on why that behavior exists.
We have begun documenting, quantitatively, the expansion of the universe
at various stages in its lifetime, but we are still early in our process
of understanding this new phenomenon.
Brian Tung <brian@isi.edu>
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt
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