The Known Extent of the Universe, Part II

The distances to other galaxies cannot be measured the way we measure most other distances. Parallax won’t work for any but the closest star systems. You cannot reflect signals off even the closest stars, as the travel time would be years. So to measure the distances to other galaxies, a different method is used.

There is a class of star called a Cepheid Variable Star, an enormously bright type of star with a periodic fluctuation in the intensity of its output. The period of these stars happens to be related to their power by a known function. See

Cepheid Variable Stars

. By measuring the apparent magnitude of these stars in other galaxies, and correlating them to the output that we expect, we can determine the vast distances between the galaxies.

An interesting phenomenon was discovered by an astronomer named Slipher: almost every galaxy in the sky is red shifted with respect to us – the light reaching us from these galaxies is redder than it should be – their spectra are shifted. (Astronomy: A beginner’s guide to the universe, pg 438, Chaisson McMillan). Not only is this the case, but the red shift is tightly correlated with the distance from our own galaxy. Red shifts and blue shifts are indicators of radial speed under relativity. Great enough speeds tend to increase or decrease the energy of the photons emitted by an object with respect to the observers. The red shift, interpreted as a measure of relative velocity, gives a surprising result: Almost every galaxy is moving away from us at a speed proportional to their distance from us: recessional velocity = H0 x distance. This doesn’t just go for our own galaxy (this phenomena does not require us to be at the center of the universe), but every galaxy is moving away from every other galaxy at a distance proportional rate. Hubble’s constant = 75 km/sec/Mpc (Mpc is a megaparsec, or 3.3*10^6 LY).

This startling discovery leads to the big bang theory of the origin of the universe – if every galaxy is moving away from every other galaxy at a speed proportional to distance, then it follows that at one time in the distant past, the universe was packed much closer together.

There are several modes to the expansion of the universe which are possible – we have only one space-time cross section which we are capable of observing (a light-cone extending backwards in space and time 1 year for every lightyear). These different modes of expansion are primarily dependent on a number called omega which is a ratio relating to the density of matter and energy in space.

Omega < 1 would yield a universe that should, according to our understanding of general relativity and gravity, expand indefinitely and with ever increasing speed, leading to an eventual heat death.

Omega > 1 would yield a “closed universe” which would be bounded in space as well as in time. The space would eventually curve back in on itself, and time would as well, leading the universe to accelerate back together in a “big crunch”. The concept of a bounded finite universe that will end someday has enjoyed tremendous popularity, though I have no idea why. The possibility depresses me. For philosophical reasons of my own, I would be extremely disappointed if the universe should turn out to be finite in either space or time.

Omega = 1 would yield a universe that would expand at an exponentially decaying rate. Eventually it would stabilize, and continue to exist indefinitely, neither exploding outwards into a cold heat death, or collapsing back in on itself.

Based on Hubble expansion alone, any of these scenarios is possible. Based on information from the cosmic microwave background radiation (radiation from the very early universe), astronomers believe that omega is, against all probability, extremely close, perhaps equal to 1. If this is the case, then the universe should have a spatial geometry that is globally “flat”, or which doesn’t curve back in on itself, and should therefore be literally infinite in extent space-wise (we can’t see all of it yet, because when we look, we look along a light cone, and eventually run into the big bang).

But all of the mass that we see in the universe today couldn’t possibly account for the mass and energy density required to make omega = 1. Going off of the visible mass, our universe should have a much lower omega, and should be in the process of exploding violently outwards.

This, along with certain other oddities in the rotation rates of galaxies (which are larger than they should be based on our estimates of the mass of stars), has led astronomers to the idea that there might be “dark matter” in the universe. Dark matter is a name for mass that we haven’t found yet, or cannot account for, in terms of the gravitational behavior of objects on a large scale. It could either take the form of matter which we have no means of detecting, or it could be some sort of correction term that is required in our understanding of gravity over large distances, but to make our models of the universe work, this missing mass has to be present. Some have wanted to replace the big bang theory with something else on account of this hole, but to date nothing else explains the Hubble red shift as well as the big bang theory has.

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In any case, it is quite possible that the universe is literally infinite in extent. Even if it is not literally infinite (in which case, I’d be somewhat disappointed), it is still for all intents and purposes practically infinite in extent, of which we can see 14.7 billion light-years, tens of billions of galaxies, each of which have hundreds of billions of stars.