|
Sonoma State University |
J.S. Tenn |
The Friedmann Models
- If we assume the validity of the general theory of relativity in its simplest form (cosmological constant = 0),
- and if we asssume that the universe is the same everywhere (homogeneous) and the same in all directions (isotropic),
- then there are only three possible universes (The Friedmann models):
- and if we asssume that the universe is the same everywhere (homogeneous) and the same in all directions (isotropic),
Property | Closed | Just Open | Open |
| Geometry of Universe | "like surface of sphere" | Euclidean or "flat" | "like surface of saddle" |
| Fate of Universe | Expand, then contract | Expand forever with v —> 0 | Expand forever |
| Size of Universe | finite | infinite | infinite |
| Age of Universe | < (2/3)TH | = (2/3)TH | > (2/3)TH but < TH |
| Average Density | > critical density | = critical density | < critical density |
| The Hubble Time TH = 1/H0 |
If H0 = 50 (km/s)/Mpc then TH = 20 billion years. If H0 = 70 (km/s)/Mpc then TH = 14 billion years. (favored in 2003) If H0 = 100 (km/s)/Mpc then TH = 10 billion years. | ||
| The Critical Density |  | ||
From the 1930s into the ’80s it was widely believed that one of the Friedmann models described the Universe. Cosmology was thought to be “A Search for Two Numbers” [Allan Sandage, Physics Today 23, 34 (1970)].
- However, by the end of the 1990s it was becoming increasingly clear that the above models are too simple. The fluctuations in the cosmic microwave background radiation reported by WMAP in 2003 and other observations are best fit by a universe in which the matter density is about 27% of the critical density while the cosmological constant ("dark energy") provides the other 73% of what it takes for the universe to be "just open" or "flat." In this model the age of the universe is a bit less than the Hubble time, about 13.7 billion years.
| Please send comments, additions, corrections, and questions to joe.tenn@sonoma.edu |
JST 2006-03-16 |