Dark energy could be designed to maintain the critical density.

The most amazing fine-tuning of our braneworld is its average density of matter, which is related to the curvature of space. If the density is close to a critical density, the space is flat; otherwise, it is curved. In a curved space, the Euclidean geometry that we are familiar with would not work. The shortest distance between two points would not be a straight line. Cosmological observations have confirmed that our space is indeed flat. Therefore, its density must be close to the critical density.

Based on Einstein's cosmological equation, if at any moment our braneworld's density is slightly greater than the critical density, it will become increasingly greater than the critical density. Eventually, the gravitational attraction will reverse our braneworld's expansion, leading to a big crunch. On the other hand, if the density is slightly less than the critical density, it will become increasingly less than the critical density. Eventually, our braneworld will fly apart and become essentially an empty space.  Thus, our braneworld appears to be an unstable system, like a pencil balanced on its point. Because the braneworld's density cannot afford for a slight deviation from the critical density, cosmologists believe that it must be "exactly" (to the accuracy of 1 part in 10⁶⁰) equal to the critical density when our braneworld was created (reference). Otherwise, we would not be here today.

My undergraduate major was in control and system engineering. At that time, my real interest was in philosophy. I did not spend much time learning the engineering stuff. However, after more than 30 years, I still remember the most basic principle: you cannot design an unstable system! Well, that is common sense. You do not need to go to an engineering school to learn this basic principle.

Since the Big Bang, our braneworld has been expanding for 13.7 billion years without a problem. It must be a stable system. God would not design an unstable system. There must be something missing in our understanding of the braneworld. The missing stuff could be the "dark energy" which was discovered in 1998.

To design a stable system, you need a counteracting force. If somehow the system is pushed away from its stable state, the counteracting force can pull the system back to its stable state. The major force that governs the braneworld's expansion is the gravitational force. For ordinary matter, the gravitational force is always attractive. Then, where could the counteracting force come from? Is there any matter that has the property of anti-gravity?

In 1998, two independent teams of astronomers discovered that our braneworld's expansion was accelerating. This was a total surprise. The gravitational attraction of ordinary matter can only slow down the expansion. There must exist something that can counteract the gravitational attraction. This mysterious stuff is called "dark energy". Its physical nature is not known. However, the discovery that our braneworld is expanding at an accelerating rate immediately explains why the matter density can be maintained at the critical density. From the cosmological equations, it can be shown that the braneworld's density will approach the critical density if the expansion is accelerating (reference). Therefore, with the help of dark energy, the braneworld's density can easily be maintained at the critical density. There is no need for unrealistic fine-tuning at the Big Bang.

Currently, there are two leading candidates for the dark energy: cosmological constant and quintessence. The cosmological constant is a parameter describing the vacuum energy density which has the anti-gravity effect, because it can exert a pressure to expand the universe, counteracting the gravitational force. In the quintessence model, the dark energy is assumed to be "exotic" particles that have the anti-gravity property. The mass of a quintessence particle is expected to be much less than an electron. They should permeate through our braneworld.

In the future, the two models may be distinguised by measuring the expansion rate of our braneworld in the earlier times. A project called the Joint Dark Energy Mission will collect data on 300 million galaxies spanning two-thirds of our braneworld's history. This may provide further insight into the physical nature of dark energy.

(Last updated: March, 2009)