Notes on the cosmological constant Lambda.




Here is the basic reasoning behind the cosmological constant "Lambda".

First, when Einstein wrote up his laws of gravitation,
he found that it resulted in a dynamic universe (not static),
which had to be expanding or contracting. He didn't like that.
He then noticed that he could add Lambda to his laws, without
affecting any of the then testable physics, and that lambda would
have the effect of accelerating the universe. He used lambda to
balance against gravity to make a static universe.
So at this stage, Lambda was just a mathematical construction
to make Einstein's laws of gravity allow for a static universe.

Once universal expansion was observed, Einstein dropped Lambda
in his famous recantation, and everyone considered Lambda to be
a silly curiosity.

Then people came up with the inflationary universe, which solves
other problems in the universe (why the background is so smooth,
and why Omega is so close to 1, even though it appears to be <1).
One aspect of inflation is that the universe has to undergo a period
of rapidly accelerating expansion. Alan Guth (its inventor) realized
that if you have a time when Lambda is large, you can pull this off.

Guth also noted that under quantum mechanics, the vacuum is not empty
because it is constantly creating particles, so the vacuum can contain
latent energy called the "vacuum energy". A funny property of vacuum
energy is that if you stretch out a region of space, the energy density
doesn't decrease, so you are gaining total energy in that region.
For normal matter, like a gas, if you expand the box that it's in,
you reduce the energy density, to keep the total energy in the box constant.
But vacuum energy increases, since the bigger box has more vacuum.
So if there is vacuum energy, you GAIN energy from expansion, and that
energy causes the space to expand faster, leading to acceleration.
Thus if there is a substantial amount of vacuum energy, it will give you
the bahaviour of adding a Lambda to the gravity laws.

One major consequence of inflation is that Omega = 1. However,
if vacuum energy is present, then Omega is the sum of the matter
Omega and the vacuum energy density. So with a large Lambda, you
can have the matter density much less than Omega=1 and STILL have
inflation. The tricky thing about Lambda is that somehow it has
to change from a large value down to the small or nonexistent value
that it has today. At present, there is no proper theory to explain
how this happens, but people vaguely theorize about a "scalar field"
which governs this process.

So, Lambda is important for 2 reasons:
(1) it allows inflationary cosmologies to be sensible, providing a
solution to the (Omega close to 1) and (smooth background) problems.
(2) A universe with Lambda will be older than one with the same
matter Omega but no Lambda. So if you include Lambda, there is
more time to make old clusters and galaxies, etc.
As a final note, we observe a matter Omega of 0.3 or so, and the
acceleration measured by Bob's supernova efforts suggests that
Omega(Lambda) is 0.7, which tidily fits into the picture.
Needs confirming, though.