The Cosmological Constant
Remember, Einstein didn't like a expanding/contracting
Universe,
so
he put it a term (called the cosmological
constant)
to counteract this and produce a static universe. When Hubble
discovered
the expansion of the Universe, Einstein called the cosmological
constant
his "biggest mistake."
Well,
it's
back.
If you go back to the Einstein field equations and work
out the most general form of the dynamical equation, you get
With this term, the Friedmann equation looks like
this:
What is this Lambda term? It corresponds to an additional form of energy in the Universe,
which provides an
outwardly directed force on the Universe, like a pressure
(which
could in principle balance the force of gravity).
But what is it????
The cosmological constant
 ... seems to be a manifestation of the energy
density of empty space...
 ... may(?) come from the energy associated with
virtual
particles...
 ... affects the
dynamics
and curvature
of the Universe...
 ... seems like it
could
be real
(based on observations of the universe)!
Sounds like a great problem for the physicists! Models
to
explain the cosmo constant abound, including some very creative ones.
However,
predictions for the magnitude of the cosmological constant are
currently
50100
orders of magnitude off from the current (tentative!) observed
value... Doh!
Note that just as we wrote Omega to
mean the density
of matter relative to the critical density, we can write another Omega
to mean
the energy density of "lambda" relative to the critical density.
So we
now
have OmegaM and OmegaL, and if the universe is critical (flat), then
OmegaM + OmegaL = 1.
So what values for lambda do we get from the
supernovae?
Things to notice.
 An accelerating
Universe is older.
(ie the expansion rate was slower in the past, so the universe took
longer
to grow to its present size.
 Even universes
which
expand forever
can be spatially flat or closed, and universes which collapse may yet
be
spatially open.
 As time goes by,
Lambda wins.
F_{lambda} ~ R, F_{gravity} ~ R^{2}. If the
cosmological
constant exists, it was end up dominating the expansion.
Wild times indeed...


Latest "union" plot multiple datasets,
multiple methods
CMB = microwave background, sensitive to shape of space
SNe = supernovae, sensitive to curvature in R(t)
BAO = galaxy clustering, sensitive to matter density parameter