The Singularity Debate: The Friedmann Models

By Aaitijhya Goswami

The theory about the expanding universe and the studies on the red shifting of spectra emerging from various galaxies and celestial objects, and the inference that it signified that all of them were indeed moving away from us, by Edwin Hubble, was one of the best, if not the best intellectual discoveries of the 20th century, and one which contradicted the beliefs of many previous astronomers and physicists, including Einstein, who himself modified the theory of relativity by introducing a cosmological constant to make it satisfy the static universe narrative.

Only one man, it seems, was willing to take general relativity at face value. While Einstein and other physicists were looking for ways of avoiding general relativity’s prediction of a non-static universe, the Russian physicist Alexander Friedmann instead set about explaining it.

The equations of general relativity, which determine how the universe evolves in time, are too complicated to solve in detail. So what Friedmann did, instead, was to make two very simple assumptions about the universe: that the universe looks identical in whichever direction we look, and that this would also be true if we were observing the universe from anywhere else.

Based on general relativity and these two assumptions, Friedmann showed that we should not expect the universe to be static. In fact, in 1922, several years before Edwin Hubble's discovery, Friedmann predicted exactly what Hubble found. The assumption that the universe looks the same in every direction is not true in reality. For example, the other stars in our galaxy form a distinct band of light across the night sky called the Milky Way. But if we look at distant galaxies, there seems to be more or less the same number of them in each direction. So the universe does seem to be roughly the same in every direction, provided one views it on a large scale compared to the distance between galaxies.

For a long time, this was sufficient justification for Friedmann’s assumption— as a rough approximation to the real universe. But more recently a lucky accident uncovered the fact that Friedmann’s assumption is a remarkably accurate description of our universe. In 1965, two American physicists, Arno Penzias, and Robert Wilson, were working at the Bell Labs in New Jersey on the design of a very sensitive microwave detector for communicating with orbiting satellites. They were worried when they found that their detector was picking up more noise than it ought to and that the noise did not appear to be coming from any particular direction.

First, they looked for bird droppings on their detector and checked for other possible malfunctions, but soon ruled these out. They knew that any noise from within the atmosphere would be stronger when the detector is not pointing straight up than when it is because the atmosphere appears thicker when looking at an angle to the vertical. The extra noise was the same in whichever direction the detector pointed, so it must have come from outside the atmosphere. It was also the same day and night throughout the year, even though the Earth was rotating on its axis and orbiting around the sun. This showed that the radiation must come from beyond the solar system, and even from beyond the galaxy, as otherwise it would vary as the Earth pointed the detector in different directions.

We several know that the radiation must have traveled to us across most of the observable universe. Since it appears to be the same in different directions, the universe must also be the same in every direction, at least on a large scale. We now know that whichever direction we look in, this noise never varies by more than one part in ten thousand. So Penzias and Wilson had unwittingly stumbled across a remarkably accurate confirmation of Friedmann’s first assumption.

Now, at first sight, all this evidence that the universe looks the same whichever direction we look in might seem to suggest there is something special about our place in the universe. In particular, it might seem that if we observe all other galaxies to be moving away from us, then we must be at the center of the universe. There is, however, an alternative explanation: The universe might also look the same in every direction as seen from any other galaxy. This, as we have seen, was Friedmann’s second assumption. We have no scientific evidence for or against this assumption. We believe it only on grounds of modesty. It would be most remarkable if the universe looked the same in every direction around us, but not around other points in the universe.

In Friedmann’s model, all the galaxies are moving directly away from each other. The situation is rather like steadily blowing up a balloon that has a number of spots painted on it. As the balloon expands, the distance between any two spots increases, but no spot can be said to be the center of the expansion. Moreover, the farther apart the spots are, the faster they will be moving apart. Similarly, in Friedmann’s model, the speed at which any two galaxies are moving apart is proportional to the distance between them. So it predicted that the redshift of a galaxy should be directly proportional to its distance from us, exactly as Hubble found.

Despite the success of his model and his prediction of Hubble’s observations, Friedmann’s work remained largely unknown in the West. It became known only after similar models were discovered in 1935 by the American physicist Howard Robertson and the British mathematician Arthur Walker, in response to Hubble’s discovery of the uniform expansion of the universe.

Thus, this was how Friedmann contradicted the beliefs of the astronomers of his time and took the theory of relativity at face value to expand on Hubble’s findings and how an unexpected and unnecessary observation led to the confirmation of his assumptions about the universe. But the debate didn’t end here, as it traversed into the later part of the 20th century, where the origins of this expanding universe became the topic of interest and that was when the famous Big Bang theory was proposed.