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 10-14 Gyr, with uncertainties ~ +/- 2 Gyr.
Ages of Lambda=0 Universes H_{0} Omega_{M} t_{0} (Gyr) A 72 1 9.0 B 40 1 16.3 C 72 0.3 11.0 D 72 0.1 12.2 E 85 0.1 10.3 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 Omega_{M}=1 universe.
- it's extremely hard to envision a high H_{0} universe (ie H_{0} > 80)
Ages of H_{0}=72 Universes Omega_{M} Omega_{Lambda} t_{0 }(Gyr)_{ } A 1 0 9.0 B 0.3 0 11.0 C 0.3 0.7 13.0 D 0.1 0.9 17.3
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
related:
Plugging in, we get
so the way we have defined things, lookback time can
be calculated this way:
so
or
analagous but messier equations exist for other
cosmologies
as well.
So we can plot lookback time and age as a function of the observable, redshift for any cosmology.
Here it is for H_{0}=72 universes with no cosmological constant:
And here it is for spatially flat H_{0}=72 universes with different mixes of matter and lambda:
And remember, I can always shorten (lengthen) the
ages by using a larger (smaller) Hubble constant. But then I run into
the problem of being in conflict with the measured value of the Hubble
constant (H_{0}=65-75 km/s/Mpc or so....).
So if we find an object of a given age at a given
redshift, that gives us a LOWER LIMIT on the age of the universe, and
this allows us to rule out certain cosmologies. For example globular
clusters today (z=0) give a lower limit on the age of the universe of
10-14 Gyr or so.
A while back, an elliptical galaxy was found at high redshift (z ~ 1.5) which looked to be at least 3.5 billion years old. How can this constrain cosmology? You tell me....