# 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 10-14 Gyr, with uncertainties ~ +/- 2 Gyr.

 H0 OmegaM t0 (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":

• it's extremely hard to envision an OmegaM=1 universe.
• it's extremely hard to envision a high H0 universe (ie H0 > 80)
The Cosmological Constant may be real

 OmegaM OmegaLambda t0 (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

## 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):

• Lookback time tL(z): How far back in time we are looking.
• Cosmic age t(z): the age of the universe at that redshift
Let's calculate this for one model: OmegaM=1, Lambda=0
For this model, we had (from last time) an expression for how scale factor grows with time: 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 H0=72 universes with no cosmological constant: And here it is for spatially flat H0=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 (H0=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....