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Since time is the one immaterial object which we cannot influence--neither speed up nor slow down, add to nor diminish--it is an imponderably valuable gift.

-- Maya Angelou

- Become familiar with the importance of the Hubble constant, matter density and the cosmological constant in understanding the Universe
- Compare predictions of the age of the Universe with observations of the ages of stars in the Galaxy

This lab will be using the Java applet from Chris Mihos's Javalab at Case Western Reserve University:

http://burro.astr.cwru.edu/JavaLab/Cosmo/CosmoMain.html

The Universe was born billions of years ago in the Big Bang, and has been expanding ever since. The exact age of the Universe, and its future fate, depend on a variety of factors, including the current expansion rate, the mass density of the Universe, and the possibility that the Universe is accelerating. In this JavaLab, you can explore how the age and fate of the Universe depend on these factors, and how we can constrain cosmological models through the ages of astronomical objects.

When we look at the galaxies in the Universe around us, we find a fascinating thing: nearly every galaxy appears to be moving away from us. Also, the further away a galaxy is, the faster it is moving away from us. This fact was first determined in 1929 by Edwin Hubble (for whom the Hubble Space Telescope is named), and it marks the starting point for modern cosmology.

That galaxies appear to be moving away from us at faster and faster speeds the further out we look is a sign that our universe is expanding. It's not that there was some explosion in space that sent galaxies flying away from us; instead, space itself is expanding, carrying all galaxies away from one another. An observer in any galaxy would see every other galaxy rushing away from them; it's not that we are at the center of the expansion (and in fact, there is no center of the expansion).

If space is expanding, let's think about what happened in the past. If we "run the clock backwards" space gets smaller and smaller until you have gone back so far in time that space occupies an infinitesimally small point -- this is the time of the Big Bang, the beginning of the universe. When did this happen? If we knew the expansion history of the Universe, we could solve for the universe's age. There are three dominant factors which control the expansion:

- the current expansion rate, known as the Hubble Constant, H
_{0} - the amount of mass in the universe, measured by a parameter called Ω
_{M} - the acceleration factor of the universe, measured by Ω
_{L}

If we can determine these three parameters, we can solve for the age of the Universe, as well as determine its ultimate outcome. Will it expand forever? Will it ultimately recollapse?

The first interesting parameter is the current expansion rate, or the Hubble constant H_{0}. When we look at galaxies around us, the speed at which they are moving away from us is proportional to their distance from us. This is known as "Hubble's Law" and can be written as

v = H_{0} x d

The recession speed, v , can be determined from the shift in wavelength of the galaxy's light. As a galaxy moves away from us, its light is shifted to longer wavelengths; the faster it moves away, the more the light is shifted. This shift is known as the redshift (called " z ") and can be determined by taking a spectrum of the galaxy. So the more "redshifted" the galaxy is, the further away it is.

To solve for the Hubble constant, though, we need to also know exactly how far away the galaxy is. This is the hard part, and has been a major stumbling block in determining the Hubble constant. There are several different ways to measure the distances to galaxies, for example using the brightness of variable stars, or correlations between a galaxy's luminosity and the speed at which it rotates, but all the methods have different levels of uncertainty.

So once we have measured the current expansion rate of the universe -- i.e., the Hubble constant -- the next step is to figure out how much mass is in the universe. Why is this important? Mass alters the expansion of the Universe through its gravitational effect on space. If there is enough mass in the universe, its gravity can actually act to halt the expansion, and perhaps even cause the universe to recollapse on itself. How do we characterize the amount of matter in the universe? We can then define a "critical density" -- the density of mass corresponding to the dividing line between a universe that recollapses and one that expands forever. We then parameterize the mass density of the universe by a term called Ω_{M}, which is the density of the universe (ρ_{0}) divided by the critical density (ρ_{c}):

Ω_{M} = ρ_{0 }/ ρ_{c}

If Ω_{M} = 1, the universe will keep expanding forever, but just barely. If Ω_{M} < 1, the density of the universe is too low and it will keep expanding. If Ω_{M} > 1, the universe a high enough density and will actually end up recollapsing on itself.

So what is Ω_{M}? This is a very hard parameter to measure, particularly since so much of the mass of the universe seems to be in the form of "dark matter" -- material that does not emit light. There are various ways of measuring the mass of the universe, by looking at the dynamics of galaxies and galaxy clusters, or even by measuring the way mass bends the light of background galaxies. With considerable uncertainties, the current "best estimate" of the mass density of the universe is somewhere around Ω_{M} = 0.3.

One other constraint is that most current theoretical models of the universe predict that the universe should have Ω = 1. Of course, this may not be the way the universe is...

So we have estimates for H_{0 }and Ω_{M}. Is that the whole story? Surprisingly not. Evidence is mounting that the universe may not only be expanding, but that its expansion may be accelerating with time.

How can that be? Right now, astrophysicists and particle physicists are working hard to figure out that answer. One current theory is that empty space is filled with "virtual particles" and that these particles have energy -- in other words, there is a sort of "vacuum energy" associated with empty space, and that this energy may drive the expansion. These theories are in their infancy, though, and remain largely qualitative.

Nonetheless, if the Universe is being accelerated, it changes its expansion history and future evolution. For example, an Ω_{M} > 1 universe can keep expanding forever, if the acceleration can overcome the gravitational collapse. An accelerating universe also implies an older universe, since it was expanding more slowly in the past.

The acceleration factor is known as the cosmological constant and is given the designation Lambda (Λ). A density is associated with this cosmological constant so Ω_{L} is defined in such a way that it can be compared to the density parameter Ω_{M}. Remember that current cosmological models want Ω = 1, but that current estimates of Ω_{M} are < 1. We can reconcile these two numbers if Ω_{M} + Ω_{L} = 1, i.e., Ω_{TOTAL} = 1. So many astronomers are studying cosmological models for the universe where the combination of Ω_{M} and Ω_{L} equals one. Again, that not be the way the universe is, but its what the current models would like...

The best observational estimates of Ω_{L} come from the study of distant supernovae in galaxies in order to determine the relationship between redshift and distance. These estimates place Ω_{L} ~ 0.7, which nicely give us Ω_{M} + Ω_{L} ~ 1, but there are considerable uncertainties here...

So given our three parameters, H_{0}, Ω_{M}, and Ω_{L}, we can solve for the expansion age and future fate of the universe. We can also solve for something called the "lookback" time. Remember that when we look out in space we are also looking back in time, since the light from distant objects takes time to get to us. So we see distant galaxies as they were when the universe was young.

If we know the three cosmological parameters, we can determine the age of the universe at any given redshift we observe. Or, since we also can calculate the current age of the universe, we can solve for the "lookback time" -- ie how far back in time we are looking.

How is this useful for us? One basic constraint on all cosmological models is that the Universe should not be younger than the objects in it. For example, in our galaxy we estimate that the globular clusters have an age of 11-15 billion years (Gyr). This means that a cosmology which gives a universe age of 9 Gyr won't work. Other constraints come from distant galaxies at higher redshift. For example, an elliptical galaxy named LBDS 53W091 has been discovered at a redshift of z=1.55, and based on its spectrum it has been estimated to be 1.5-3 Gyr old. This means that at a redshift of 1.55, the universe had to be at least that old. We may be able to reject certain cosmologies based on this simple observation.

*This above text has been adapted from Chris Mihos’s JavaLab website at *http://burro.astr.cwru.edu/JavaLab

Begin the lab by opening the Cosmology JavaLab in an Explorer window:

http://burro.astr.cwru.edu/JavaLab/Cosmo/CosmoMain.html

Click on **APPLET **to open the Cosmo JavaLab.

A new window should open, that looks like this:

INSTRUCTIONS:

At the bottom of the applet you will see a table for entering data. For each cosmology case you may enter a Hubble Constant, a mass parameter, and an acceleration parameter. Any invalid values or values outside these ranges will automatically be set to the closest appropriate value. Note: Only cosmology cases with valid values for the Hubble Constant and one of the parameters will be calculated. For example, if you leave Omega Matter as zero, it will not be calculated.

To plot your results click on the graph, or select your plot type (Lookback, Age, or Size) from the pull-down menu.

**Analyzing Results**: Use the Trace function (see below) to get the values of specific points on the curve. You can overlay data onto the Age plot by clicking the 'Edit Data Points' button. After entering the data values click the graph again to see the data points overlay. You can return to editing the cosmology cases by clicking the 'Edit Cosmologies' button.

**Cosmology: **You may use this text-field to enter a description of this cosmology, such as "open". You can also leave the text as it is.

**Hubble Constant: **Enter a value for the Hubble Constant (H_{0}). Note that observational data suggest H_{0} is between 60 and 80 km/s/Mpc, but we allow a much broader range of values so that you can explore what happens with Edwin Hubble's original value of ~ 500 km/s/Mpc.

**Omega Matter: **Enter a value for the Mass Density Parameter (Ω_{M}). For the purposes of this applet the value is constrained between 0 and 2.5.

**Omega Lambda: **Enter a value for the Acceleration Parameter (Ω_{L}). For the purposes of this applet the value is constrained between 0 and 2.5.

**Trace: **Toggles the tracing function on and off. *You must use the keyboard for this!* Click the graph to make sure it has focus, then click the checkbox to turn Trace on. Use the left and right arrow keys to traverse a plot. The up and down arrows can be used to change which plot is currently being traced. The checkbox will be 'greyed out' and unable to perform the tracing function if the graph doesn’t not have keyboard focus.

*This above text has been adapted from Chris Mihos’s JavaLab website at *http://burro.astr.cwru.edu/JavaLab

Updated: 10/31/12 by SAM

Copyright Regents of the University of Michigan.