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Cosmology and the Origin of Life
Okay so we live in curved spacetime and now you are telling me that the Universe is exanding:
Uniform Expansion of the Universe:
Hubble noticed a correlation between recessional velocity and distance. This is known as the Hubble law:
where V is velocity (in km/s), D is distance (in megaparsecs), H is the Hubble constant (present day expansion rate of the Universe)
This simple relation implies something remarkable about the Universe.
At some earlier time, all the galaxies had to have been together
in the same space at the same time --> the Universe was once
really small. It is important to realize that the galaxies are
stuck to the surface of the universe by gravity and its the surface
that expands. The galaxies themselves are not moving but travel
along with the surface as shown here .
So what do we know now:
Photons have an energy related mass. Photons are therefore effected
by gravity. Light is bent in a strong gravitational field as the
surface of the universe goes from being flat (light travels in
a straight line) to curved (light follow the curved trajectory).
This principle is shown in this
animation .
The distribution of mass on in the universe determines the detailed shape of the surface --> light is constrained to follow this surface and this allows the universe to be observed!
Returning now to the expansion of the Universe with the help of some handy demonstration ants:
Horizons and the Expansion Age of the Universe:
V = HD --> c = HD ==> D =c/H ==> This is our causal horizon -
beyond this distance something would have to travel faster than the
speed of light in order to communicate with us. All observers
are surrounded by such a horizon.
Horizons are okay. Our assumption about homogeneity means that the stuff beyond the horizon is the same stuff we already know about. This assumption must be correct due to horizon overlaps and causality.
Back to the Ants glued to the balloon:
Example: I attach the balloon to a slow pump which increases the
radius of the balloon by one foot each day. This is the expansion
rate that I measure. I measure the balloon to have a radius of
8 feet. This means the expansion age of the balloon is 8 days.
V = Hd ==> 1/H = D/V
Distance/Velocity = Time
1/H = the expansion age of the Universe.
This is how long the
Universe has been expanding. What it was doing prior to the expansion
is anybody's guess.
If you know the rate of inflation of the balloon (the expansion
rate of the surface) and the surface area of the balloon (which
is proportional to its radius) then you can determine how long it
has taken for the balloon to reach its present size.
___________________________________________________________________
The Electronic Universe Project
e-mail: nuts@moo.uoregon.edu