V.

A Cosmological Constant and Dark Energy

A possible explanation of dark energy that fits very simply within the framework of Einstein’s theory of general relativity is the existence of a cosmological constant. Einstein originally introduced the cosmological constant into his equations in an attempt to render the universe static (neither expanding nor contracting). Einstein’s equations for general relativity predicted that the universe could not be static, but at the time Einstein formulated them, he and other scientists believed that the universe was unchanging. So Einstein introduced the cosmological constant to balance gravity. When Hubble later discovered that the universe is expanding, Einstein called the introduction of the cosmological constant “the biggest blunder” of his life, according to American physicist George Gamov, writing in 1971.

The possibility that the equations of general relativity should include a cosmological constant is now being seriously reconsidered because of the discovery of dark energy. Instead of having the value needed to keep the universe static, however, the cosmological constant would now have the value required to make the expansion of the universe accelerate at the observed rate.

The model of the universe that includes the cosmological constant, combined with other strong evidence that the dark matter in the universe is slow-moving as compared to the speed of light (a property called “cold”), is now the dominant model of the universe. Because all observations to date are consistent with this model, astronomers call it the “concordance” model or the “Lambda-CDM” model. (Lambda is the symbol used for the cosmological constant, and CDM stands for Cold Dark Matter.)

A.

Quantum Problems for a Cosmological Constant

Dark energy is not associated with matter or with electromagnetic radiation. Rather it is a property of space itself. Calculations based on quantum mechanics indicate that even in empty space, there is a probability that a particle and its antiparticle can appear for a short amount of time, before recombining with each other and disappearing. The combined energies of these virtual particles could account for the dark energy. One interpretation is that the tiny elementary particles that are flickering in and out of existence give space a kind of springiness that pushes it apart. Unfortunately, theoretical attempts to calculate the energy associated with this process derive a value for the cosmological constant that is about 10¹²⁰ times too large to account for the measured acceleration of the expansion of the universe. (To imagine this large number, think of ten, followed by 120 zeros.) This huge mismatch has been referred to as the most unsuccessful computation in the history of theoretical physics. It is a sign that there is some new fundamental physics about our universe that remains to be understood.

Prior to the discovery that the universe is accelerating, physicists believed that in fact the cosmological constant would turn out to be zero, and that some still-to-be discovered physical processes or particles would be found to cancel the energy associated with empty space that was predicted by conventional quantum mechanics. Perhaps such a mechanism does exist, but if so, it must provide what seems to be an unlikely answer, one that is very large and that almost but not quite compensates for the calculated very large energy of the vacuum.

B.

The Coincidence Problem

Another observation that current theory cannot explain is the fact that we seem to live at a special time in the universe’s history when the dark energy density is of the same order of magnitude as the matter density. The matter density in the universe (26 percent) is only about a factor of 3 smaller than the energy density (74 percent). This similarity is a temporary phenomenon, astronomically speaking. In fact, there is only about a 1 percent chance that an observer living at a randomly chosen time since the beginning of the expansion would observe the matter and energy densities to be so nearly the same. The fact that we happen to be alive at this special time is called the “coincidence problem.”

It is easy to understand why the relative densities of matter and energy change with time. As the universe expands, its volume increases. But according to the law of conservation of energy, the total energy remains the same. That means that the densities of matter, radiation, and vacuum energy must all decrease with time. These densities do not, however, all decrease at the same rate. The density of radiation decreases fastest, followed by that of matter, and then vacuum energy. Initially, the universe was very, very hot, and the radiation-energy density was the highest of the three; it is now the lowest. For a time, the matter density was highest, and then was diluted by expansion. Now the vacuum energy is beginning to take over. About 10 billion years ago, the density of energy in the vacuum was about ten times less than the density of matter, and billions of years from now, the vacuum-energy density will be ten times higher than the density of matter. If there is a physical explanation for why we are at a stage in the universe’s history when the matter and energy densities are roughly the same, we do not yet know what it is.