At the very beginning, our Universe went through a period of exponential, faster-than-the-speed-of-light
stretching of space known as inflation.
The stretching was caused by a repulsive form of gravity and the Universe doubled in size
at least 100 times, going from the from the size of a billionth of a proton to the size
of a grapefruit.
Inflation ended when the repulsive energy decayed into ordinary matter and energy,
at which point ordinary Big Bang expansion took over.
The theory of inflation explains two properties of our observable universe;
(i) the uniformity of space and (ii) the apparent flatness of the universe.
The observable universe, as the name indicates is the universe that we can observe from earth;
that is light from the contents of the observable universe has had time to reach our instruments
on earth.
Assuming that the universe is the same in all directions, the distance to the edge of
the observable universe is the same in every direction, so the shape of our observable
universe is a spherical ball with the observer at its centre.
At the largest of scales the observable universe displays an extraordinary level of uniformity.
There are of course distinct structures in space, such as galaxies and stars, however
from a distance far enough away, all of space seems to look the same from all directions,
similar to how sand in a desert will appear uniformly distributed if observed from a plane
flying high up enough in the sky.
The theory of inflation allowed the contents of the baby Universe sufficient time to interact
and come to a uniform density of energy and temperature before the rapid expansion occurred.
It is that uniformity which is the present uniformity of space we observe today.
Without inflation the Big Bang model would not have given the baby Universe enough time
to reach uniformity in this way.
Spacetime incorporates the three dimensions of space (up and down, left and right
and back and forth) and the fourth dimension of time.
General relativity describes how mass and energy can curve spacetime, and accordingly
the mass and energy of the Universe can also curve space time.
There are three possible curvatures the Universe could have:
1). positive curvature 2). negative curvature or
3). no curvature at all, i.e. be flat
The critical density of the Universe is the mass and energy contained per unit
volume of space needed for a universe to be flat.
That means the gravity produced by the mass and energy in the universe is such that it
perfectly balances out the stretching of the Universe.
When the Universe has critical density it continues to stretch at a decreasing rate
forever until infinite time has passed whereupon the stretching will finally halt.
But as we all know, infinity has no end.
The density parameter, symbolised by the letter Omega in the greek alphabet is used
to determine what curvature the universe has. It is the average mass-energy density of the
Universe divided by the critical density.
If the density parameter > 1, there is positive curvature. If the density parameter < 1 there is negative curvature.
If the density parameter is exactly 1, i.e the average mass-energy density
of the Universe is the same as the critical density, then the Universe is flat
For the Universe to have positive curvature there is enough mass-energy density in the
Universe to produce gravity that will warp spacetime enough to eventually overcome the
stretching of space so that the Universe will collapse back in on itself to form a closed Universe.
For the Universe to have a negative curvature there is not enough mass-energy density to
produce enough gravity that can halt the stretching of space, so the Universe will be an open,
saddle-shaped, Universe which continues to stretch forever at a decreasing rate.
And we have already covered, that in a flat Universe there is just enough mass-energy
density to produce gravity that perfectly balances out the stretching of the Universe.
When describing the Universe as flat, it is not meant that it's flat in the same sense
as a 2D shape is flat, but rather that the geometry of the universe is such that parallel
lines will never cross, the angles in a triangle will always add up to 180 degrees, and the
corners of cubes will always make right angles.
In a closed Universe the angles of a triangle would be more than 180 degrees, in the open
saddle-shaped Universe, the angles of a triangle would add up to less than 180 degrees and
in the flat Universe, as mentioned, the angles of a triangle would add up to 180 degrees.
We can calculate the density parameter of our Universe using two methods and both methods
indicate that it is very close to 1, therefore suggesting that our Universe is very close
to being flat.
The first method involves counting up all the mass-energy in the universe, taking its
average density then dividing that average by the critical energy density.
The second method involves drawing a massive imaginary triangle on the cosmic microwave
background radiation and seeing if the angles of the triangle add up to 180 degrees.
The cosmic microwave background radiation also known as the CMB is the oldest light
in our Universe that has travelled to our instruments. As the photons of light travelled
across the universe their wavelengths stretched transforming the photons into microwave radiation.
When the imaginary triangle was drawn on the CMB it turned out that the sum of its angles
did indeed add up to 180 degrees indicating that our universe is indeed flat.
Before we get too excited and state definitively that our Universe is flat we have to remember
that the exponential stretching of space brought on by inflation drives the Universe toward
flatness, smoothing out the fabric of the Universe.
We can only measure the observable universe which may be part of a much larger Universe
which might not be flat.
The analogy that is often used is how an ant sitting on the surface of a large inflating
balloon would assume that the surface it is sitting on is flat because that's how it
would always appear to him from his tiny perspective.
We may be that ant and the Universe is so massive that whatever we can measure
will appear flat to us.
And that in a nutshell is cosmic inflation.
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