Cepheids are the key link One primary justification for the Hubble Space Telescope was to resolve Cepheids in galaxies far enough away to measure the Hubble flow properly, and thus obtain the age of the Universe. Along with other methods, this gives about 14 billion years.

Distances to Nearby Galaxies The distance to…Is measured by…Which gives you… VenusRadar echoesAstronomical Unit Nearby StarsParallaxMain sequence luminosities Star ClustersMain sequence fittingLuminosities of Cepheids Nearby GalaxiesApparent brightness of Cepheids Relation of distance to redshift There is a chain of links which get us out to the distances of galaxies. Errors in any one affect all the further ones.

Galactic Redshifts The relation is given by D=v/H ; D is distance, v is redshift velocity, and H is the “Hubble constant”. H is about 25 (km/s)/(million ly). The redshift is called “z”, where z =  ~ v/c. Remember, these are only apparent velocities, caused by the expansion of space.

Distances deep into the Universe You must use nearby galaxies to calibrate distance indicators that can be seen across the Universe. 1) brightest star (hypergiants), brightest HII regions (star formation) 2)“Tully-Fisher” relation: Luminosity in red or infrared correlated with 21-cm broadening (number of stars)(rotation rate) 3) largest spiral in cluster 4) brightest galaxy in cluster 5) Hubble expansion: distance is correlated with redshift

Assigning a distance by redshift The Hubble law lets us use a simple spectrum of a galaxy to figure out where it is along the line-of-sight. Higher redshifts indeed go with smaller and fainter looking galaxies.

Redshift takes us from 2-D to 3-D Huge surveys are ongoing to get redshifts for hundreds of thousands of galaxies. These give us the large-scale structure of the Universe.

Quasar Spectra and the “Lyman-alpha Forest” Galaxy “Filaments” QSO us Redshifts tell us where everything is…

Probing the Cosmic Foam Gravity acting on dark matter gives the basic layout of matter in space. Quasar absorption lines allow us to map out the gas not collected into galaxies. Clusters will continue to collect, but the space between them will continue to expand.

Hubble Expansion – what it is NOT In an explosion, the stuff that is moving faster will have gotten further, so you would see what Hubble saw. Despite the term “Big Bang” to describe the expanding Universe, that is NOT what is going on!

The motion is only “apparent” Galaxies stay fixed on the “co-moving” grid. Their separation only increases because the amount of space between them increases. The scale of the Universe increases, but not the scale of particles, galaxies, or even clusters (anything bound). The expansion is only apparent on scales of millions of light years.

Hubble Expansion – what it IS Space itself is expanding… into the future… The apparent increase of velocity with distance is due to the increase in the amount of space that has expanded in a given amount of time.

There is no spatial center of expansion… The center is the beginning… There is no edge (except the present)

Local structure interferes with Hubble flow Supercluster density field “Local” flow field We have to be careful in determining the expansion rate.

The Hubble Constant and the Age of the Universe If you plot the scale of the Universe vs time, the Hubble constant is the slope of the line now. If it’s really constant, then the age of the Universe is just 1/H [since H=v/D=(d/t)/d]. That’s because if you know how fast we are expanding, you can run the movie backwards and see when everything crunches together. If the Universe is slowing its expansion, you get a younger age. You can compare the age gotten this way with the oldest globular cluster, or other independent methods. Recently they have all come into agreement.

Density is Destiny The shape depends on the curvature of spacetime. The curvature of spacetime depends on density. “Flat” corresponds to the “critical density” ~ gm/cc, beyond which the Universe would recollapse.

Curvature of the Universe Since gravity is spacetime curvature, the density sets the geometry. Only in a “flat” Universe do parallel lines stay next to each other. In a “closed” Universe, in principle a beam of light eventually comes back upon itself. In principle, we can measure the geometry of spacetime through geometrical tests. For example, you can count the number of galaxies in a given patch of sky as you go further out. These tell us our ultimate fate.

Spacetime Diagrams In order to picture spacetime (which is 4-dimensional), it helps to get rid of some spatial dimensions, and keep time as a shown dimension. Here is a diagram with only 2 dimensions, one space and one time. Light is the fastest thing in it, and marks out “lightcones” which determine what can be seen, and when. An object’s existence is a “worldline”.

The Spacetime Diagram of an Expanding Universe If space expands with time, a 2-D spacetime diagram looks like this. All spatial points converge at the beginning. The Universe is opaque for a time, so you see the fireball in the distant past in all directions. You see more distant objects as they were in the more distant past. Beyond a horizon, the rest is unobservable (now).

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