Edward J. Barlow
Member of National Academy of Engineering
Recipient of NASA Public Service Award
Previous member Report Review Committee of the National Research Council
Retired Vice President, Research & Development, Varian Associates

Model I- Fixed space

We will develop and present a series of models from a very simple one to the ones now most used by cosmologists and we will bring the story up to recent discoveries of just the last few months. Let us start with Model I. This is the picture which people not familiar with general relativity and the more refined models might be thinking with. Assume galaxies are rushing away from us in all directions through fixed space and they are not accelerating or decelerating, each galaxy is receding from us at a constant velocity, obeying the Hubble equation.

There will be a redshift in the spectral lines of each galaxy related to its recession velocity. For this model, this redshift is called the Doppler shift. The redshift, z, is defined as z=(l-lo)/lo so that z+1=l/lo which is simply the observed wavelength at our telescope of a particular spectral line divided by the emitted wavelength (the wavelength measured in the laboratory). For low velocities and hence low values of z, this leads to the relation v=cz. For velocities of recession approaching that of light we need to use the equations of special relativity in this model to get the relativistic Doppler effect equation tying the recession velocity, v, to the redshift, z. The equations are:

When v=c, this redshift is infinite, so no velocities greater than that of light can be observed in this model.

There is a problem with this model. Consider a galaxy rushing away from us at a constant velocity of very nearly the speed of light. Light that it emitted when the universe was half as old as it is now would just be getting to us now and we could not have a lookback time, tlb, (tlb=to-te), greater than half the age of the universe. We find we are able to see much further back in time than this. The cosmic microwave background radiation, CMBR, coming to us from all directions was emitted when the universe was very young (something like 300,000 years after the big bang or about 1/50,000 of its present age), and we can detect this radiation now. It is this background radiation that greatly strengthened the arguments for the big bang theory. We are also able to look back now to galaxies as they were when the universe was less than 10% of its present age. Also, consider a light packet just reaching us now. In this first simple model that packet coming toward us, if it started at nearly the birth of the universe, would have been some 14 billion light years away from us at the big bang - but the big bang model assumes that all of the presently observable region of space was in a very tiny volume at that time.

We can see these problems by examining Figure I which plots distance in billion light years against time in billion years and shows the behavior of galaxies departing from us at the big bang and of light packets reaching us now. In this figure, the intersection of the line for a galaxy with the line for a light path gives the time after the big bang that the light was emitted that we see now, te, and the distance away the galaxy was then, De.

The distance away the galaxy is now, Dr, is where the galaxy line intersects the right vertical axis at an illustrative tr or t0 of 15 billion years in this example. For the reasons given above, and others, we will have to discard Model I, even though it is the easiest for most of us to visualize.

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