1. Cosmology I
Definition of Cosmology: The scientific study of the universe as a whole; how long ago it came into being, the nature of that beginning, the future destiny of the universe, and the physical laws that govern it.
Timeliness: One of the main fields of physics and astronomy nowadays. Status now is drastically different than years ago.

2. How we can talk about cosmology….
Large look-back times show the universe when it was different

3. The scientific basis of modern cosmology
Hubble’s Law
V = H0d
The universe is expanding

4. A Model Universe
Demo

5. With this “toy” model, you can show:
Hubble’s Law, v=H0d
There is no center to the expansion, if you see Hubble’s Law, there is still nothing special about your location
The physical significance of Hubble’s Constant: the time since the expansion began, thus the age of the universe

6. If the universe is expanding now, what will it do in the future?

7. If cosmology is to be a branch of physical science, there must be an underlying mathematical structure with quantitatively testable predictions
There are two things going on in the universe
Galaxies are flying apart due to the universal expansion
The force of gravity is acting to pull them back again
The story of the universe is competition between universal expansion and gravity

8. How to describe gravity: General Relativity
Dynamics takes place in a four dimensional spacetime
Mass induces warping or curvature of spacetime
Spacetime curvature may also exist in the absence of mass (cosmological constant)

9. A modern description of the evolution of the universe
The basic mathematical language that we use in describing the universe
What are the main observational results that have been obtained?
Will follow Chapter 26

10. Section 26.1, the Hubble Constant and the Age of the Universe…see lecture last Friday

11. Question 1: how can we describe the whole universe by a simple (to physicists) equation?
Say it with equations!

12. A physical theory of the universe
Start with Einstein field equations (too tough)
Assume universe approximated by smoothed-out paste, characterized by its mean density
Assume universe is homogeneous
Assume universe is isotropic
Cosmological Principle
Such a mathematical model is called a
Friedmann Universe

14. The theory of the universe says space is curved on large scales
The theory of the universe says space is curved on large scales. What does this mean?
I think it is simpler to interpret this statement mathematically…geometry is non-Euclidean.
Example of non-Euclidean geometry: theorem of Pythagoras is not true.
Curved surfaces in 3D space have non-Euclidean geometry

15. Example1: space with positive curvature: the surface of a sphere
You would have flunked
Sophomore geometry

16. Interesting historical aside
Karl Friedrich Gauss thought of this, and sent out surveyors to test if the geometry in Hanover really was Euclidean

17. The case of zero curvature: Euclidean space

18. Final case: that of negative curvature: the surface of a saddle

19. Within the context of General Relativity, all three cases of curvature (positive, negative, zero) are theoretical possibilities. All three possibilities give universes which expand with time The question is: what kind of universe do we live in?