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
- it's extremely hard to envision an OmegaM=1 universe.
- it's extremely hard to envision a high H0 universe (ie H0 > 80)
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
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):
from this we solve for t:
We also know how scale factor and redshift are
Plugging in, we get
so the way we have defined things, lookback time can be calculated this way:
analagous but messier equations exist for other cosmologies as well. For Labmda=0 universes:
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....