Cosmological Times

One thing that comes out of all the different models is the age of the Universe, t0. t0 depends on H0, OmegaM, and Lambda, so we can't uniquely determine cosmology just from measuring the age of the Universe. But we can place constraints. How?
 

The Ages of Globular Clusters

Obviously, globular clusters can't be older than the Universe. We measure the age of a globular cluster by measuring the main sequence turnoff in the color-magnitude diagram of GCs:


By measuring the luminosity and color of the turnoff, and comparing to models of stellar evolution, we can determine the ages of the globular clusters. For M92 above, we get an age of ~ 11 Gyr (di Cecco et al 2010)

Typical numbers are 10-16 billion years (see, eg, the analysis by Chaboyer and Krauss 2003):
 
 
 
 
Ages of Lambda=0 Universes
 
H0
OmegaM
t0 (Gyr)
A
65
1
10
B
40
1
15
C
65
0.3
12
D
65
0.1
15
E
75
0.1
13
F
50
0.1
19.5

We can see from this table that some models are "ruled out":

The Cosmological Constant may be real
 
Ages of H0=65 Universes
 
OmegaM
OmegaLambda
t0
A
1
0
10
B
0.3
0
12
C
0.3
0.7
13.5
D
0.1
0.9
19.5

The Ages of High Redshift Objects

When we look at distant objects, we are seeing the young universe. How old are objects in a young universe? If we measure an object that is 3 Gyr old at a time when the Universe was only 2 Gyr old, that's bad...

Now we need to introduce a few concepts. When we look at an object at a given redshift, we can define (in a model-dependent way):

Let's calculate this for one model: OmegaM=1, Lambda=0


Recently, an elliptical galaxy was found at high redshift (z ~ 1.5) which looks to be at least 3.5 billion years old. How can this constrain cosmology? You tell me....