*This is the third article in a series on modern cosmology. Read part one here and part two here.*

Suppose you have a powerful theory capable of modeling the universe. The math of the theory is difficult but learnable, and after about a year of study, you’ll be ready to create your model. However, they know very little about the universe. The year is 1917 and astronomy with large telescopes is still in its infancy. How are you? They take the equations seriously and play an informed guessing game. This is what theoretical physicists are good at. The equations have roughly the following structure:

GEOMETRY of SPACE-TIME = MATTER/ENERGY.

The left side shows you how curved or flat the geometry of spacetime is. What determines this curvature is what you put in the right hand side: the matter and energy that fill the space. Matter curves space, and curved space tells matter where to go. This is exactly what Einstein achieved with his general theory of relativity. (I’m writing this on his birthday, March 14, Happy Birthday Einstein! To celebrate, I’m including a signed photograph he took with my step-granduncle Isidor Kohn in Rio de Janeiro while he was visiting South America in 1925.)

## The first rough models of the universe

Last week we saw how Einstein used his equations to propose the first model of modern cosmology, his static spherical cosmos, and how he was forced to add an extra term to the above equations – the *cosmological constant* — to make his model stable against collapse. Einstein’s bold move caught attention, and soon other physicists were proposing their own cosmic models, all playing with the right-hand side of the equation.

The first was the Dutchman Willem de Sitter. The de Sitter cosmological solution, also working in 1917, was quite bizarre. He showed that besides Einstein’s static solution with matter and a cosmological constant, it was possible to find a solution without matter and a cosmological constant. A universe without matter was clearly an approximation of reality, as de Sitter well knew. But that was also Einstein’s universe, which had matter but no motion. Both models were rough representations of the universe. The reality, the authors hoped, lay somewhere in between.

De Sitter’s model had a very strange property. Any two points in it would move away from each other at a speed proportional to the distance between them. points at a distance *2d* moved away from each other twice as fast as points at a distance *D*. De Sitter’s universe was empty, but it had movement. Cosmic repulsion driven by the cosmological constant has pulled this universe apart.

## Our cosmic aquarium

Because De Sitter’s universe was empty, no observer could perceive its expansion. But by the early 1920s, de Sitter’s work, along with that of others such as astronomer Arthur Eddington, revealed some of the physical properties of this strange, empty universe. First, if a few specks of dust were scattered into the de Sitter universe, like the geometry itself, they would scatter apart at rates that increase linearly with distance. The geometry would pull them along.

If velocities increased with distance, some grains would end up being so far apart that they would retreat at velocities close to the speed of light. Thus every grain would have a horizon* *– a boundary behind which the rest of the universe is invisible. As Eddington put it, the region beyond is “entirely closed off from us by this time barrier.” The concept of a *cosmological horizon* is essential in modern cosmology. It turns out to be the correct description of the universe we live in. We cannot see beyond our cosmological horizon, which we now know to be 46.5 billion light-years in radius. This is our cosmic aquarium. And since no point in the universe is central – it grows in all directions simultaneously – other observers from other points in the universe would have their own cosmic aquariums.

Much like these receding grains, cosmic expansion predicts galaxies moving apart. Galaxies emit light, and motion would distort that light. Known as the Doppler effect, when a light source (a galaxy) moves away from an observer (us), its light is stretched to longer wavelengths – that’s how it is *redshifted*. (The same thing happens when the observer moves away from the light source.) As the source gets closer, the light is squeezed into shorter wavelengths, or *blueshifted*. So if astronomers could measure the light from distant galaxies, physicists would know whether the universe is expanding or not. This happened in 1929 when Edwin Hubble measured the redshift of distant galaxies.

## Universe learning could evolve

While these properties of de Sitter’s solution were being explored, Alexander Alexandrovich Friedmann, a meteorologist-turned-cosmologist in Saint Petersburg, Russia, decided to take a different path. Inspired by Einstein’s speculations, Friedmann looked for other possible cosmologies. He hoped for something less restrictive than Einstein’s, or something less empty than de Sitter’s. He knew that Einstein had included the cosmological constant to keep his model of the universe static. But why does it have to be like this?

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Perhaps inspired by the ever-changing weather that had occupied him for so long, Friedmann brought changes to the universe as a whole. Can’t a homogeneous and isotropic universe – one that is the same in all points and directions – have a time-varying geometry? Friedmann realized that the universe moves when matter moves. When the average distribution of matter changes uniformly, so does the universe.

In 1922 Friedmann presented his remarkable results in an essay entitled “On the Curvature of Space”. He showed that, with or without a cosmological constant, there are solutions to Einstein’s equations that show an evolving universe over time. In addition, Friedmann’s universes exhibit several possible behaviors. These depend on the amount of matter filling the space, whether or not the cosmological constant is present and, if so, how dominant it is.

## The hidden cosmic reality

Friedmann distinguished two main types of cosmological solutions: *expand *And* swing*. Expanding solutions lead to universes in which the distances between two points are ever increasing, as in de Sitter’s solution in which the universe is expanding forever. However, the presence of matter slows the expansion and the dynamics become more complex.

Depending on how much matter is present and how its contribution compares to the cosmological constant, it’s possible that the expansion will reverse and the universe will begin to contract, with galaxies moving closer and closer. In the distant future such a universe would collapse into what we call one *Big crunch*. Friedmann conjectured that the universe might actually alternate cycles of expansion and contraction. Unfortunately, Friedmann died four years before Hubble discovered cosmic expansion in 1929. He must have guessed that the universe we live in hid between his putative universes. But neither he nor de Sitter – nor Einstein – could have guessed how tricky this story was going to be.