Predicting the Fate of the Expanding Universe

What Determines the Fate of the Universe?

The fate of the Universe will ultimately be determined by the balance between the violence of the initial explosion (the driving force behind the expansion) and the gravity if all the matter within the universe (which would tend to slow down the expansion). There is also the possibility that some additional source of energy tends to accelerate the expansion.

Before we go on to examine possible futures, we need to recall the concept of the escape speed because it is necessary in our discussion. The escape speed is the minimum speed at which an object must be launched from the surface of a planet or a star in order to escape its gravitational pull and travel to infinity. If the launch speed is smaller than the escape speed the projectile will travel to a maximum height, gradually slowing down, and then turn around and fall back to the surface. The condition for the escape of a projectile can also be expressed in terms of the density, since a more dense object is more compact (it can pack more mass in the same volume).

This is very relevant to the expanding Universe. If the Universe contains enough mass, gravity will be able to slow down the expansion and perhaps bring it to a halt. Otherwise, the Universe may expand forever. The determining factor is the present day density of the Universe. An interesting example is provided by stars in a galaxy. Even though the space that the stars are embedded in is expanding, their mutual gravity keeps them together and the galaxy itself is not getting bigger.

The Critical Density

We know that the Universe is expanding and galaxies seem to be moving away from each other. We also know that galaxies are attracted to each other because of gravity, which means that gravity works against the expansion and slows it down. The question then becomes, do galaxies have enough of a speed to escape their mutual attraction? The answer to this question depends on the density of the Universe.

To be more specific we can define the critical density of the Universe. If the density is larger than the critical density, then there is enough mass and hence enough gravitational attraction to halt the expansion and turn it around. If, on the other hand, the density of the Universe is lower than the critical density, then the available mass of the Universe does not exert enough of a gravitational attraction to stop the expansion.

For convenience we express the present-day density of the universe in terms of the present-day critical density as follows:

Note that both of the quantities that enter the definition of Ω0 change with time, so we use their values at the present time in this definition. If the density of the Universe today is equal to the critical density, then Ω0 = 1, if the density is greater than the critical density, then Ω0 > 1, and if the density is less than the critical density, then Ω0 < 1. The fate of the Universe depends on which one of these possibilities actually holds, as explained below.

So What Will Become of the Universe?

The possible futures of the Universe are depicted in the figure below. The figure below is a plot of the size of the Universe versus time, according to our theory of the expansion process. Here we are considering only the competion between the violence of the initial explosion and the slow-down effect of gravity. The effect of energy source that accelerates teh expansion will be discussed later.

If the density is smaller than the critical density (i.e., Ω0 < 1), the Universe will expand forever, since gravity is not string enough to stop the expansion. This is called an open Universe and it will eventually die in a cold death. That is all the gas will turn to stars and all the stars will live their lives and die leaving behind white dwarfs, neutron stars, and black holes. These will, in turn cool off and fade away just like the embers of a fire.

If the density is higher than the critical density (i.e., Ω0 > 1), the Universe will expand up to a maximum size, gradually slowing down because of gravitational attraction between galaxies. Then it will turn around and start to collapse again until all the galaxies run into each other in a big crunch. This is called a closed Universe.

Finally, there is the special case of the Universe having a density equal to the critical density (i.e., Ω0 = 1). Such a Universe is called a flat Universe. It will continue to expand at an ever decreasing expansion rate, but it will never turn around.

Measuring the Density of the Universe.

To get the critical density we need to know how much mass there is in the Universe, which we could find by adding up the mass in all of the constituents of the Universe. To add up all the mass correctly we need to know how much matter there is. Hence the importance of understanding the nature of dark matter .

By the way, if you want to read a summary of how the masses of galaxies are measured, how dark matter was discovered, and what attempts were made to find out what it is, see this link.

Current estimates of the mass of the Universe show that there is not enough mass in it to halt the expansion. If we only count the luminous matter (things that we can see, like galaxies) we find that the density of the Universe is only about as few percent of the critical density, i.e., Ω0 = 0.04. If we include the dark matter whose presence we infer indirectly, we find that the density is about 20–30% of the critical density,i.e. Ω0 = 0.2–0.3. So, judging just from our census of luminous and dark matter, the Universe appears to be open.

Evidence for an Accelerating Universe

Observations carried out since the mid-1990s and aimed at measuring an accurate value of the Hubble constant, have yielded a major surprise. They have uncovered evidence that the expansion rate of the Universe is accelerating. This observational campaign was carried out by two different groups independently (it started in the 1990s and it is still underway). The strategy is to measure distances to galaxies using Type Ia supernovae as distance indicators, as well as the redshifts of those galaxies. The methos of using Type I a as distance indicators is discribed in the context of teh "cosmic distance ladder" in this Wikipedia article. More details about the Type Ia supernova method are give iin Astrobites at this link.

Plotting the redshift against the distance was expected to give a straight line, whose slope is the Hubble constant. However, the observations showed that at large distances (approximately 3 Gpc), the measured redshifts did not conform with the expectations based on the Hubble law. Instead, the observations suggested that the Universe is now expanding faster than one would expect, in other words, the expansion rate is increasing, i.e., the Universe accelerating. This result was obtained by two different groups independently so we are very confident about it. In fact, the result is so profound that the teams that got it won the Nobel Prize in Physics in 2011.

The figure below is an updated version of the figure shown above, depicting how the size of the Universe evolves with time.

What is the significance of an accelerating expansion rate? As we noted above, the expansion rate should be slowing down since gravity tries to keep galaxies. If the rate is accelerating, there must be some other physical effect that comes into play when galaxies are far enough apart that overcomes gravity and adds energy to the expansion process and invigorates it. The origin of this effect is currently unknown but we do have a name for it: Dark Energy.

It is interesting to note that this effect can be represented mathematically in Einstein's equations of general relativity as a quantity called the "cosmological constant." (these are the equations used to predict the fate of the Universe and the curves depicted in the figure above are their solutions). Historically, Einstein was the first person to introduce a cosmological constant in his equations in the early 1920s. In those days it was thought that the universe was infinite in size and age, and unchanging, so the introduction of a cosmological constant allowed Einstein to describe such a Universe using his equations. Soon thereafter, however, Hubble announced his discovery of the expansion of the Universe and the entire idea of a cosmological constant was completely abandoned: Einstein's equations could easily describe an expanding universe without a cosmological constant. Now the cosmological constant is back in order to explain the acceleration of the Universe.

A more detailed discussion of the accelerating expansion of the universe can be found at this Wikipedia page.

Contributions to the Energy Density of the Universe

The latest measurements of the constituents of the universe are summarized in the table below. The constituents are luminous matter (things we can see), dark matter (invisible but detected indirectly) and dark energy (detected via the acceleration of the expansion rate of the universe but otherwise mysterious). These constituents are quantified by their fractional energy density. Luminous and dark matter are expressed in term of energy for direct comparison.

The latest measurements were made by studying the cosmic microwave background:

 luminous matter  4 %
 dark matter  23 %
 dark energy  73 %

In essence, we only really understamd 4% of the contents of the Universe and we have a vague idea about another 23% (the dark matter, whose existence has been known for a few decades). But more than 2/3 of the contents of the Universe are in a mysterious form (dark energy or "vaccuum pressure"). Several experiments are now being designed to measure the properties of Dark Energy in the hope that they will give us some hints about its nature.