sub specie aeternitatis

The Expansion and Future of the Universe

August 14, 2011

I took a cosmology class last semester, which I found very fascinating.  This post is my attempt at explaining how it is we know that our universe is expanding and what it will do in the future.  There could easily be some mistakes in here, and if so, feel free to contact me to let me know.

We live in an accelerating expanding universe.  What does this mean? On the biggest of scales, scientists observe that all observable galaxies are moving away from each other, the expanding part.  But the rate at which they are expanding away from each other is accelerating at the same time, and the rate of acceleration itself is increasing.  If there is any intelligent life in our Milky Way galaxy some billions of years from now, these sentient beings will never know that they live in a Universe populated with hundreds of billions of galaxies, each populated with a hundred billion stars.  They will only see their own galaxy because, at the moment they look up into the sky,  all other galaxies in our vast universe will have moved away from ours so fast that even the light from their stars will never reach them.  This idea of the accelerating, expanding Universe is a quite new idea, in fact only being revealed in the last 20 years.  But how do we know this?  How can you, if you sat in front of the world’s most powerful telescopes, determine even how far away a given star or galaxy is, let alone say with any bit of confidence how far away it is?  The answer is in something called standard candles.  Imagine, if you will, a typical light bulb.    Florescent or incandescent doesn’t matter in this case.  What does matter is how bright of a light bulb it is, and in your case pretend you have a 100-watt light bulb.  This brightness is what is known as it’s intrinsic luminosity.  Now place your light bulb on one end of a long room, move to the other end of the room, and take a measurement of the brightness of the light that is hitting your detector at that end of the room.  Since you know the energy level of the emitting body (the intrinsic luminosity), by plugging your numbers into some basic physics equations, you can determine exactly how far away your light bulb is.  This same basic technique is used to determine distances to far away stars by building up what is called the cosmic distance ladder.  First, using the principle of parallax, the distance to the closest star, our sun, was determined.  Just as distance can be measured if luminosity is known, so can the opposite be determined.  By measuring the distance to the sun and using the apparent brightness, the sun’s intrinsic luminosity is revealed.  The next step is to look further out into the cosmos and find other stars that are very similar to our own sun (and hence have the same intrinsic luminosity).  Once a sun-like star is found, cosmologists look for other, different types of stars that are about the same distance away as the sun-like star.  Since this distance is now known, the intrinsic luminosity for these new types of stars is measured.  The first rung in the cosmic distance ladder is in place.  Armed with the intrinsic luminosity of this new type of star, cosmologists look even further out in the universe for this same type of star and repeat the process.  A star whose intrinsic luminosity is known is found, the distance is measured.  Nearby stars at the same distance are found, and their intrinsic luminosity is measured.  The next rung in the cosmic distance ladder is found. Repeating this process allows for the measuring of more and more distant objects.

Now you can determine the distance to a variety of distant objects in the Universe, but how can you determine if these objects are moving relative to you?  The answer lies within measuring a star’s red shift, which is accomplished using something known as emission lines.  As electrons flow around the nucleus of an atom, they are always found in discrete energy levels (discrete here meaning that an electron can be in either one energy state or another, there is no “in between” energy states).  When an electron of, say, Hydrogen, moves from a higher energy state to a lower energy state, it emits a photon of a specific energy.

(Hydrogen Emission Line)

As different types of stars are different sizes and different temperatures, they also emit more strongly in some elements than others.  Depending on the type of star, different emission lines can be examined.  But examined how?  Look at the Hydrogen emission line above.  There are 5 distinct emissions at 5 different wavelengths.  Take a star whose distance is known and observe these emission lines.  If the star was stationary compared to your location, the emission lines would be the exact same wavelength.  But if the star was moving relative to you, the wavelength of the emission lines will have changed.  If the star is moving towards you, it is said to be blue shifted, and the wavelength becomes shorter.  In the example above, if the star was moving closer, then the last emission line at 656.3 would be smaller.  Conversely, objects that are moving away are said to be red shifted, and result in longer wavelengths, taking the 656.3 to a higher number.  Anyone who has heard an ambulance zoom by and noticed the change in tone of the siren has witnessed this effect.  It is known as the Doppler Effect, and this same principle applies directly to measure the movement of distant stars and galaxies.  And it is this that answers the first part of the expanding universe puzzle.  It was in the early years of the 20th century that Edwin Hubble, by measuring the red shift of many different stars of known distance, discovered that the heavens were not static.  Objects in our universe were moving away from us, and, even more intriguing, the further away the object, the faster it was moving away.  This applies to every object that we can measure out in distant space.  Star, galaxy, black hole, it does not matter.  They are all speeding away from us.  Perhaps most intriguing of all, some very distant galaxies are zooming away from the Milky Way faster than the speed of light.  But how is this possible, you might ponder, isn’t the speed of light the universal speed limit?  For all matter, yes, nothing can break this speed.  As it turns out, however, it is not the galaxies themselves which are moving away from us, it is space itself that is expanding, and space can expand as fast as it likes.

The expansion of space may seem impossible, but it is this expansion which seems to be causing the acceleration of the expansion of the universe.  To understand this mystery force, we must first discuss a more intuitive and familiar force: gravity.  Recall that early on in the 20th century, Edwin Hubble showed that the universe was expanding.  Shortly after this discovery scientists were not sure if the universe would continue to expand or if it would level off or perhaps even begin to accelerate back in upon itself.  The universe was expanding due to the big bang, the initial burst of energy in the universe.  That energy was still acting upon these heavenly bodies, but keep in mind that while this initial push was still in play gravity was pulling on these objects as well.  Since there was only so much energy supplied by the big bang, these earlier cosmologist thought that once the initial bang energy was depleted, gravity could take over, pulling everything back together in the opposite scenario than what we know see today.  Distant stars and galaxies would produce a blue shift due to an accelerating, compacting motion from the pull of gravity. As we have already established, this is not the case, but to understand why this is and how it was discovered, we must go back to standard candles.   Objects which are standard candles are stars whose intrinsic luminosity is known, thereby giving us the distance to these stars.  Brighter standard candles are needed in order to determine distances further and further out into the universe.  The further out a star, the further back in time cosmologists are seeing.  Saying a star is 50 million light years distant means that the light is 50 million years old[add footnote here].  The person studying that star is looking 50 million years in the past.  With this data cosmologist can not only determine that rate at which distant objects flee our little corner of the galaxy, but can also plot the rate of expansion over time.  But, as was just mentioned, these standard candles can only be seen out to a certain distance because individual stars are too dim to observe too far away.  Or they were until the 1990’s, when a new type of standard candle was discovered.  This new type of standard candle, called a super nova 1A, is a white dwarf binary pair.  Without going into too much detail, just understand that what happens is that the smaller star, the white dwarf, pulls in extraordinary amounts of matter into itself from a larger, nearby star.  It can only take in so much of this star before physics dictate that it can take no more, causing the white dwarf to explode.  This explosion is of such fantastic force that the resulting light can outshine an entire galaxy of stars.  Cosmologists were able to determine it’s intrinsic brightness, and, since these objects allowed them to see further and further out (and further and further back in time), they were able to plot a more complete graph of the expansion of the universe.  What they discovered was that the further back in time they went, the slower the expansion of the universe.

(Expansion of the Universe over time)

If you look towards the beginning of the graph you notice that the acceleration slowed down for a while before picking up again.  This slowing down is what cosmologists had originally thought they would see.  The energy from the big bang is running out and gravity may or may not take over at this point.  But, obviously, it didn’t. What is driving this expansion?   The energy in empty space.

Within empty space there is energy.  Stop for a moment and try to take that in.  Imagine traveling in a (faster than light) spaceship to someplace far away from any galaxy or planet or star or alien.  For thousands of light years all around you there is absolutely nothing but space, empty space.   Yet within this seemingly empty nothingness, there is a mysterious form of energy, dubbed by scientists dark energy.  What is dark energy?  Scientists have no idea. No one has ever seen it, detected it, or even devised a way that it might be detected.  It is, at this point, purely hypothetical.  Why, then, do scientists claim that this hypothetical energy is driving the acceleration of the expansion of the universe?  Look again at the chart above.  The expansion of the universe was actually slowing down a few billion years after the big bang.  Gravity was exerting it’s pull on everything within, slowing the expansion.  But before gravity could pull everything back together, some other force took over and the expansion began again, this time accelerating with time.  Even though the expansion was slowing down, everything was still moving apart.  Gravity was tugging at everything, but the further apart everything moved, the weaker the force of gravity pulling on everything.  Dark energy, our mystery force, was also present during this slower expansion, but it was not strong enough of a force to push everything away due to the force of gravity pulling everything together.  It was not until everything within the universe became just far enough apart that suddenly the pushing force of dark energy was too strong for the pulling force of gravity.  Once this point was reached, there was no going back.  Gravity was too weak due to the distance between objects, and the further dark energy pushed things apart, the weaker the force of gravity.  Hence the acceleration of the expansion of the universe.

What does this tell us about the future of our universe?   If this dark energy continues to behave as it is, then we are heading for the heat death of the universe.  If this happens, galaxies will continue to expand and expand, and everything within those galaxies will also eventually continue to expand.  Eventually, after trillions upon trillions of years, every last thing, down to the last atom, the last proton, will decay, leaving the universe in a state with no thermodynamic free energy.  In other words, the universe has now reached maximum entropy, a state that can support no life or motion.  Will the Universe stay in this state forever?  The truth is that science cannot predict that, even if the Universe does end up in this state, that it will stay in this state forever.  Some familiar with the laws of quantum physics suggest that another big bang could be triggered from this pool of nothingness, this eternal stretching of empty space.  Perhaps our universe came from such a state, which came from another such state, ad infinitum?  This is all out of the realm of evidence and no answer has more merit than any other, but theorists have developed many varied, fascinating answers to the fate of our universe.