1.  The Hubble constant - characterizes the present rate of expansion
 
 

the rate that galaxies are moving away from us / distance from us

converts red-shift to distance

can be used to estimate the time since the singularity

for a very simple explanation, see "On the Cosmic Horizon", J. Bennett, Mystery #3.

~65 kilometers per second  /  megaparsec    (1 megaparsec = 3.26 million light years)

 
 

 

2.  W_m - The mass density of the universe
 
 
 

 determines the fate of the universe (assuming no dark energy):   the greater the mass density the greater the gravitational attraction
 

W_m > 1 :    the expansion will eventually stop and the universe will collapse

W_m < 1 :    the universe will continue to expand forever

W_m = 1 :    the "critical" density, the dividing line between the two fates

"less than an ounce of matter spread through the volume the size of Jupiter."

K. Croswell, Magnificent Universe, pg 175.

 
 
 
 

also determines the shape of the universe (assuming no dark energy):
 

W_m > 1 :    a "closed" universe, space-time curves back on itself - shape is analogous to the surface of a sphere

W_m < 1 :    an "open" universe, space-time forms a saddle shape

W_m = 1 :    a "flat" universe, space-time forms a shape analogous to a flat plane
 
 

 possible geometries of the universe

significance for inflation theory:
 

"In fact, inflation makes only one known, directly testable prediction, which is the prediction that tied up our third loose end.  The universe should be flat and have precisely the critical density."

J. Bennett, "On the Cosmic Horizon", p 131.
 
 

combining visible matter  +  "dark matter",  W_m= ~ 0.3

 
 
 
 
 
 

3.   W_L - the vacuum energy density   (the "cosmological constant"  or  ? )
 

based on recent observations of type I supernovae in distant galaxies that suggest that the more distant galaxies seem to be moving more slowly with expansion than nearby galaxies - implies that the expansion has accelerated with time for some portion of the recent past.
 

W_L represents a force of repulsion and accelerates the expansion, the opposite of W_m
 

still highly controversial
 

significance for inflation theory:

"If the cosmological constant proves real, at least one group of scientists will be popping champagne corks:  the theorists of inflation.  ...  because Einstein showed that mass and energy are equivalent, the energy embodied in the cosmological constant can also add to the total density in the universe."

J. Bennett, "On the Cosmic Horizon", pg 149.
 
 
 
 

Current status:
 

"Here at the dawn of the millennium, the data are not yet sufficient to say definitively whether the expansion is really accelerating and there really is a cosmological constant.  The case should become clear within a few years, however, as additional observations allow us to improve our measurements of the Hubble constant both for the present and for the past."

J. Bennett, "On the Cosmic Horizon", pg 148.
 
 

 summary of current status

From Supernovae, Dark Energy, and the Accelerating Universe, S. Perlmutter, Physics Today, April 2003 p 59.
 
 
 

Inflationary expectation (flatness):   W_m + W_L = 1
 
 

Three independent sets of observations - high-redshift supernovae, galaxy cluster inventories, and the CMB converge near W_m  = 0.3  and  W_L = 0.7
 
 

If true, then 97 % of "everything" in the universe is dark matter or dark energy!