The Cosmological Constant

For those who don't know, the cosmological constant was originally proposed by Albert Einstein to account for the expansion of the universe (which he believed to be static). He later called would call it the "biggest blunder" of his career. Ironically, in the 1990's the cosmological constant went through somewhat of a renaissance as cosmologists struggled to describe the accelerating rate of an expanding universe and turned to the cosmological constant. What Einstein once considered to be his biggest blunder has now been experimentally verified and exists in accordance with modern cosmological theory. What are the implications of a universe expanding at an accelerating rate? They are many and far reaching. Before I delve into the interesting possibilities this entails, I shall offer a brief explanation of the relevant cosmological science necessary to understand these ideas. Consider a projectile is trying to escape the earth’s gravitational pull. It starts with an initial velocity after being launched from a super strong catapult and has a rocket strapped to it that gives it a constant acceleration. The acceleration given to this projectile by the rocket isn’t as strong as that of the earth’s gravity so the projectile is going to need to rely on its initial velocity to escape the earth’s gravitational pull. There is a specific distance from the earth that the acceleration of the projectile (which is constant) will eventually overtake that of gravity (which lessens as we get further from the center of the earth), lets call this distance Distance X. On the earth’s surface lets say the rocket gives the projectile an acceleration of 5m/s^2 and the acceleration due to earths gravity is -9.8m/s^2, this gives the object a net acceleration of -4.8m/s^2 at the surface of the earth. But as we move further and further from earth the effect of gravity becomes less and less until eventually, the acceleration that the projectile experiences due to the rocket equals the acceleration of gravity at that distance. At this distance, Distance X, the net acceleration is zero, because the acceleration of the projectile is +5m/s^2 and the acceleration due to gravity is -5m/s^2.

For every second that the projectile approaches Distance X the projectile gets slower and slower, although the rate which the object slows at is decreasing as the acceleration due to gravity becomes less and less. Therefore in order for the projectile to reach Distance X it needs to have an initial velocity greater then or equal to the escape velocity required to leave a mass with an acceleration due to gravity of -4.8m/s^2. The velocity of the object at Distance X can be infinitesimally small; it just needs to be greater than 0 in order for the object to move outward forever. If the initial velocity is less then this escape velocity (which is a real, calculable number) then the object will plummet back to earth. But if indeed the initial velocity of the object is great enough for it to reach Distance X, the net acceleration of the object (which has its own constant acceleration) will begin to increase until the effect of gravity is negligible and the only acceleration acting on the object will be the objects own, constant acceleration.

In this example we can consider the projectile to be all of the matter in the universe and the rocket strapped to the projectile to be the cosmological constant. If the cosmological constant is not great enough to overcome the gravitational pull opposing the expansion of the universe, all of the matter will collapse back in on itself in what is known as the Big Crunch. But the universe is not collapsing in on itself, nor is it expanding at a decelerating or constant rate, rather, space itself is expanding at an accelerating rate, and with it, all of the matter in the universe. (A great way to illustrate this is to mark three points on a deflated balloon and measure their distance apart, then blow the balloon up and measure their distance again. The expansion of space is similar to that of the balloon, three objects can lie along a straight line and all three will experience an increase in distance between them! Think about if this would be possible if the universe wasn't expanding...try the same exercise on a piece of paper.)

What does this mean? Well, for starters it means that the Universe is expanding and will continue to do so indefinitely. This means not only that galaxies will continue to move further away from each other, but that space itself is expanding. While matter may not move faster than the speed of light, as governed by the laws of relativity, space is not governed by such laws and as this expansion is occurring at an increasing rate, eventually space will expand faster than the speed of light!

This is not the only implication of a universe expanding at an increasing rate however, there are other interesting consequences! The cosmological constant (omega) has already overcome gravity over large distances, as evidenced by the redshift of galaxies. If this were not the case these galaxies would not be accelerating away from us but would be experiencing an acceleration due to gravity (think again of the projectile example, if omega (the rocket) was not large enough the galaxies (planets) would fall back towards each other (earth)). BUT the cosmological constant IS large enough and the galaxies ARE moving away at an accelerating rate. Since this rate of expansion is increasing asymptotically, so will the effects of this expansive force. Eventually the force of gravity will be overcome by this force, first gravitational force between galaxies will be overwhelmed (already done), then the galaxies themselves will start to break apart, and then planets will break off of solar systems, etc. This will happen on continuously smaller scales until eventually, the gravitational forces that hold planets such as the earth together will be overwhelmed!

Once omega has dispatched gravity, the weakest of the four fundamental forces, it will move on to the other forces. Eventually, electromagnetic forces will be overwhelmed and even further down the road, the strong and weak nuclear forces will be overwhelmed, breaking down the matter of the universe even further. Omega will keep increasing in strength until eventually, matter reaches its fundamental units and cannot be broken down any further. What will happen past this point? One can only guess...perhaps when omega breaks whatever bonds there are that make an electron an electron an infinite number of big bangs will occur, starting an infinite number of new universes on completely different spatial scales!

What particularly interests me about this problem is the consequences this has for black holes. Black holes are collapsed stars whose masses were so great that once their internal reactors stopped producing energy (and providing an outward force, in opposition to gravity) they collapsed to a density so great that the gravitational pull reached a magnitude where nothing, not even light, could escape. But if omega is going to increase in strength until it eventually overwhelms the force of gravity, what will this mean for black holes? Black holes have remained an interesting problem for physicists, some of whom have dedicated their entire careers to the study of the subject. Certainly a mathematical model with an increasing spatial scale would prove an interesting problem for a theoretical black holes physicist. At any rate, it is interesting to ponder what one would see if you were sitting on the edge of the event horizon of a black hole at the very moment that its gravitational pull was overwhelmed by the expansion of space!