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

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 50-100 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. Flambda ~ R, Fgravity ~ 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