1. Lecture 40 Cosmology IV In spite of all this, there are arguments that Omega must be 1 There is observational evidence that space is Euclidean, not curved “Inflation” (see p634) requires Omega to be 1 If Omega is approximately 1, it is probably exactly 1 (??!!!***)

2. Simply stated: if Omega =1, it stays 1 through the history of the universe. If Omega 1, the value depends on the Cosmic Scale Factor a. Since a has changed enormously (infinitely) throughout the history of the universe, it shouldn’t be anywhere near 1 now if it wasn’t very, very close to 1 early on. So if it is close to 1 now, it is probably exactly 1

3. Important new piece of information in and about 1997 If you have a “standard candle”, an object with constant, known M, you can measure how a(t) has changed throughout the history of the universe Basic idea: expanding universe says light from a source has to “fan out” into a larger volume than in a static universe. Fall-off of intensity is steeper than the inverse square law The degree of extra “fan out” depends on how a(t) has changed with time

4. For Omega =1, the fan out is the smallest For Omega =0.33, it is larger For Omega = 0, it is larger still, and the maximum for a Friedmann universe

6. Use cosmological model to calculate m of z

7. Now need objects to fill up the plot. Real standard candles Type Ia supernovae….white dwarfs “shoved over the edge” http://antwrp.gsfc.nasa.gov/apod/ap000312. htmlhttp://antwrp.gsfc.nasa.gov/apod/ap000312. html

8. What do the data on Type Ia supernovae show? http://www- supernova.lbl.gov/public/misc/forrosen/scie ncesnpop.pdfhttp://www- supernova.lbl.gov/public/misc/forrosen/scie ncesnpop.pdf Distant Type Ia supernovae are even fainter than in an empty universe The scale factor has increased even more than for Omega = 0

9. Points to the following form for a(t) An accelerating universe How is it possible?