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?

deceleration

2. The Deceleration Rate

The rate of expansion:

H0	(Hubble's constant)

The rate of change of the expansion: the deceleration

q0

What does q₀ 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 (deceleration).

General Relativistic (Einstein's) view:

The higher the density, the more curved is space.

3. The Critical Density

=   density / critical density

=   2 q₀

=   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

NOT proven until very recently!

(once the passionate hopes of many theorists;
now the most likely interpretation of recent data)

If q₀ > 0 deceleration.

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?

Or is there a non-zero cosmological constant (constituting a cosmic pressure), which contributes to the energy density?

in which case:

      q₀ = /   2    -  .

The values currently favored on these somewhat prejudicial grounds:

    = 0.7
      = 0.3
        q₀   =   -0.55       (acceleration!)

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:

ASSUMING = , i.e., =   0

Consequences:

non-Euclidean geometry, where ...

not always 180 degrees in a triangle!

But if is non-zero, all bets are off, and the Universe is more complicated.
Specifically, the Universe's "fate" and "geometry" are no longer simply correlated. For example, a spatially flat universe can expand forever, and even accelerate -- which is exactly what we think is happening. This year. Check in again in a decade.

(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.