Big Bang for beginners-10: The cosmological constant


(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

For previous posts in this series, see here.

To understand what is going on with dark energy, we need to look at something called the cosmological constant.

Einstein’s General Theory of Relativity, when expressed as equations in their most general form, contains a constant term (called the cosmological constant) whose value is unspecified by the theory itself but influences how the universe evolves with time. A positive value for this constant would have the effect of acting like an outward pressure trying to ‘push’ the universe apart, counteracting the gravitational attraction that is trying to pull it together. A zero value would do nothing, leaving gravity as the only (attractive) force. A negative value would be like a ‘pull’, adding to the attractive force of gravity.

There is nothing mysterious about such constants. Their appearance is common in scientific theories (they are sometimes called parameters) and their values are determined by experiment. Once the value of such a constant has been calculated using some data, it is fixed and the same value must be used in all applications of the theory which is why it is called a ‘constant’. For example, our normal everyday theory of gravity also has such a constant G called the universal gravitational constant whose value is found by measuring the size of the gravitational attractive force between two objects that have mass. But once that has been done for any two masses, the same value of G is used everywhere and ever after, which is why such constants are so important and thus measured with great care and precision.

When Einstein first used his General Theory of Relativity that he developed in 1915 to build a model of the universe, he too needed data to obtain the value of the cosmological constant. He, like most people of that time, assumed that the universe was static and so he gave a positive value for that term, choosing it to have such a value that its repulsive force would exactly balance the attractive gravitational force. This choice gave him the static universe solution he thought he needed to get, although it was soon pointed out that the static solution he obtained was unstable and thus problematic. (The Runaway Universe, Donald Goldsmith (2000), p. 12)

The catch with the cosmological constant term lay in trying to interpret its physical meaning. Its behavior in the equation is like that of an energy density and giving it a positive value implied that the universe was filled throughout with something that had the same units as energy. But it could not be the same kind of massless energy that we are familiar with (which is electromagnetic) since we know how to detect that and this new form of energy (like dark matter) seemed to be invisible to us, except for its large scale gravitational effects.

Einstein’s Special Theory of Relativity had just a decade earlier convinced scientists to abandon belief in the ‘ether’, which had for a long time been assumed to exist and to also permeate all of space while remaining undetectable. So one can see why people would be wary of introducing a new substance with ether-like elusiveness that might also turn out to be spurious. So having a non-zero cosmological constant term, while not violating any laws, was not something people at that time were particularly happy with and it was tolerated simply because there seemed to be no other way of obtaining a static universe.

Fortunately, the problem seemed to go away by itself. When around 1930 it was realized that the universe was not static but expanding, the need for a cosmological constant disappeared and it was assigned the value zero, in essence removing it from the equations. The theory of gravity that emerged resulted in an expanding universe solution, but one whose expansion was slowing down due to the unopposed gravitational attraction of the rest of the universe. It is like the way that a ball thrown upwards slows down because of the gravitational attraction of the Earth below it.

This remained the standard model until recently. But measurements made in 1998 of the speeds of distant galaxies and supernovae (which consist of massive stars exploding at the end of their lives and becoming so extremely bright that they can be seen at immense distances) suggest that rather than slowing down due to this gravitational attraction, those distant objects are actually speeding up. We seem to be living in a universe whose rate of expansion is increasing, not decreasing.

The emergence of observations supporting both a flat and accelerating universe has brought the cosmological constant back into the spotlight. It turns out that one can explain both these features by adding the cosmological constant back into the equations governing the laws of gravitation and giving it a positive value. But this once again raises the question of the physical meaning of this term. Since it behaves like an energy density, some scientists have postulated that in addition to dark matter (invoked to explain the otherwise anomalous behavior of the stars in spiral galaxies), the universe must also contain vast and uniform amounts of something they call ‘dark energy‘ that we have not as yet been able to detect directly.

This dark energy is even more mysterious than dark matter. Like the electromagnetic energy associated with the photon that I discussed earlier, it may have no mass but it cannot be the same kind of energy as that because we are familiar with that form of energy and know its properties well and so would be able to identify its presence easily. So if dark energy exists, it must be a new kind of energy.

If we take the dark matter and dark energy hypotheses at face value as the explanations for the spiral galaxy and the flat and accelerating universe problems, then the results provided by the WMAP satellite has made highly precise measurements of them possible. The best current estimates are that the Universe today is made up of about 72.1% dark energy, 23.3% dark matter, with the remaining 4.6% being all the other matter that we are familiar with and know exists.

Next: Some background on dark energy, how it acts, and where it originates.

POST SCRIPT: Why don’t we have more advertisements like this?

John Cleese shows us how it might be done.

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