1. The Shape of the Universe: Part I
Basic premise:
Universe is isotropic
-This means that the Universe is the same in all directions…
Universe is homogeneous
-This means that the Universe is the same in all locations
So another way of putting the cosmological principal is that the “Universe is isotropic and homogeneous”

2. The “observable Universe”
This is the part of the Universe we can observe, as defined by the speed of light. The visible Universe is that which we are capable of observing with lightso out to the time of the “the era of atoms” when photons were free to travel. We see this as the Cosmic Microwave Background (CMB) In theory, we could use neutrinos or gravitational waves to look further back than the CMB if we had the technology.
Pablo Carlos Budassi via wikipedia

3. The “observable Universe”
So what is the size of the observable Universe?
Pablo Carlos Budassi via wikipedia

4. The “observable Universe”
Even though the Universe is 13.8 billion years old, the observable Universe is actually 93 billion light years across! How is this possible? How do we know this?
Pablo Carlos Budassi via wikipedia

5. The “observable Universe”
Remember! Space is expanding… So when the CMB photons were emitted some 13.8 billion years ago, space expanded. We use redshift to determine the extent to which space has expanded since that light was emitted. As we know what temperature the Universe was at that time, we know how much it was redshifted. See this video:
Pablo Carlos Budassi via wikipedia

7. Structure in the Universe
We can use the Cosmic Microwave Background to study the Universe on large scales…remember this is the light from the early time in the Universe (380,000 years old)

8. Structure in the Universe
This is a view of the Universe (everywhere) at that time. Thus, a study of the CMB can tell us about the Universe as it is now.

9. Structure in the Universe
The bumps in the CMB correspond to regions of slightly greater density when photons were free to start travelling. What we are really looking at regions of slightly different temperatures at that time.

10. 1 – 2 – 3 – 4 Dimensions
dimension… an independent direction of possible motion
A point moved in one direction creates a line (1D).
A line moved in a direction 90º to itself creates a plane (2D).
A plane moved in a direction 90º to itself creates a space (3D).
A space moved in a direction 90º to itself creates a 4D space.
Unfortunately we can not perceive this 4-D hyperspace…any space > 3D

11. The Rules of Geometry
The geometry you know is valid when drawn on a flat surface.
The rules change if the surface is not flat.
spherical (curved-in) geometry
flat (Euclidean) geometry
saddle-shaped (curved-out) geometry

12. Density parameter = Critical
The density parameter (Ω) is the average density of the universe divided by the mass-energy needed for a flat universe
Density parameter > Critical
Density parameter < Critical

13. Density parameter = Critical
Correction from last time!!!
The CMB suggests the Universe is flat!
Here’s how we know this:
Density parameter > Critical
Density parameter < Critical

14. Fate of the Universe
Because of dark energy, rather than a slowing expansion, our ‘flat’ Universe has expansion that continues at a faster rate! So it behaves like an ‘open’ universe

15. Fate of the Universe
Because of dark energy, rather than a slowing expansion, our ‘flat’ Universe has expansion that continues at a faster rate! So it behaves like an ‘open’ universe

16. Fate of the Universe

17. Fate of the Universe So what might happen?
Heath death: Universe continues to expand and cool. There is no more free energy and the universe reaches maximum entropy. Photons decay (over long periods of time). Even black holes will have evaporated (due to Hawking radiation) >10100 years