1. The Fate of the Universe

Will it expand forever?

unbound, or open

the ``deep freeze''

Will it expand, but slow to a stand-still after infinite time?

marginally bound, or critical

the ``long chill''

Will it stop expanding, turn around, and start collapsing?

bound

the ``big crunch''

Ultimately, what counts?

2. The Deacceleration Rate

The rate of expansion:

(Hubble's constant)

The rate of change of the expansion: the deacceleration

What does q depend on?

the density of the Universe

So, count up the amount of matter and energy per unit volume.

(remember, E = mc²)

As usual, easier said than done.

Why density?

* Classical (Newton's) view:

The higher the density, the stronger the gravitational attraction (deacceleration).

* General Relativistic (Einstein's) view:

The higher the density, the more curved is space.

3. The Critical Density

= density / critical density

= 2 x q

= 1 10^-26 kg/m³

or 6 H atoms (per cubic meter)

or 1 Milky Way Galaxy per Mpc³ (cubic mega-parsec)

Book claims: 1

(currently the passionate hopes of many theorists)

What we observe:

(luminous matter) = 0.01 to 0.02

But what about dark matter?

(luminous + 'observed' dark matter) = 0.2 to 0.3

- more dark matter on even larger scales?

- are dark ``voids'' not voids?

- biasing?

Wild and wooly speculation?

Maybe, but well worth investigating. After all, the stakes are high: The fate of the Universe itself hangs in the balance.

4. The Space Itself

Recall, General Relativity thinks of matter as ``curving'' space and time.

However the Universe always appears flat on small enough scales:

What we see around us in day-to-day life is ``flat'' space and time.

But on the large scales:

Consequences:

non-Euclidean geometry, where ...

not always 180 degrees in a triangle!

(a) The Universe is ``critical.''

(b) Space and time is shaped like a saddle.

(c) Large triangles drawn in space inscribe 180 degrees.

(d) = 1

(e) The Universe is ``closed.''

(a) the gas pedal.

(b) A sharp bend in the road.

(c) A big down-hill stretch in the road.

(d) the brakes.

(e) bald tires.