Cosmic Expansion
We can observe cosmic microwave background at least we would like to
know the mathematics behind this expanding universe. The expanded universe
itself is governed by the force of gravity, Einstein's theory
of general relativity.
So according to Einstein,
it's actually simple thing. It's like we keep a ball in our hand. We stand on
the surface of the earth and throw it upwards, and initial thrust is the big
bang. The way a ball keeps going up is the expansion of the universe. Now imagine
if we throw a ball with a high speed it would eventually go up, slows down and
stop, and come back down. Maybe the universe would do the same thing. It may
start expanding, but at some point stops, and would come back down, and collapse.
So that's one possibility for the fate of the universe.
But as far as we can tell,
anything that goes up should slow down, at least. So that's the equation for
the cosmic expansion. Imagine the entire universe has mass m and size r place a
probe, a tiny mass, as a way of describing a motion of this whole universe put
this initial thrust and that's the big bang. Try to separate everything away
from each other and that's how universe got started to expand.
Look at these equations.
F = m a (Newton's equation)
F=-G Mm (Universal
gravitation) given for this size of
R2 object.
a=d2 R (Acceleration)
dt2
Combine above three equations
d2 R = -G M
dt2 R2
It doesn't depend on the mass
of the object you're using to study it, because of the gravity, is actually the
nature of space itself, it doesn't depend on the particular mass of your
particular object. Negative sign here is telling that universe must be slowing
down.
Given this, we have three
possible fates. So if we use this equation, which is the same thing as the
throwing the ball upwards, from the surface of the Earth.
We can immediately see there
are three possibilities.
1. One
of them is the ball keeps going up to some extent but slows down and stops and
then comes back down.That’s this black curve. As time goes on, the universe
gets bigger and bigger but slows down, stops here, and starts to come down, and
then eventually ends up with the big collapse. This is called the big crunch. The
universe starts with the big bang, and may end up with the big crunch.
2. If we
managed to throw ball with incredible thrust, let's say launch a rocket with it
have big speed to begin with beyond escape velocity .Rocket may escape the
gravity of the Earth, and just may keep going farther and farther away from Earth.
That possibility would be in this red curve. Initial thrust is so big, it keeps
going away from the Earth with, pretty much, constant speed at the end of the
day.So that would be a universe that keeps expanding forever.
3. In
between the black curve and red curve, there is a possibility that the initial thrust
is just right to escape the force of gravity. Then it just keeps going upwards,
but slows down and down and down and it almost stops. That would be this blue
curve. Either way universe keeps expanding forever, but with this choice,
universe would have an end to it.
So that leads to this
interesting question, is there an end, to the universe?
With energy equation
E=1 (dR)2-G
M
2
dt R
This quantity is conserved
quantity as it is time independent.
1. If this energy is positive, the corresponding situation escapes the gravity it keep expanding red curve.
2. If
energy is negative, it looks trapped by gravity i.e. if we go up eventually
come down that is black curve.
3. And
the blue curve corresponds to situation when this energy is exactly zero.
So that's the way you can
mathematically describe three possible fates of the universe. But either way, the
universe seems to be slowing down.
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