Where Is the Cosmic Density Fine-Tuning?

Where Is the Cosmic Density Fine-Tuning?

In addressing audiences about the fine-tuning of the cosmic expansion rate, I have used the illustration that adding or subtracting a single dime to the mass of the observable universe would be enough of a change to make physical life impossible.

This word picture helps to demonstrate a number used to quantify that fine-tuning, namely 1 part in 1060. Compared to the total mass of the observable universe, 1 part in 1060 works out to about a tenth part of a dime.

Let’s consider a universe that contains only matter. If the matter density is sufficiently large, gravity will overcome the expansion and cause the universe to collapse on itself. If the density is sufficiently small, the cosmos will continue to expand forever with negligible slowing. If the density is just right, the universe will expand forever, but continually slow down its expansion rate until it becomes static at an infinite time into the future. In a universe that contains only matter, this corresponds to a “flat” geometry for the universe. Life and flatness are related because only a flat universe meets two life-essential requirements. First, a flat universe survives long enough for an adequate number of generations of stars to form that will make the heavy elements and long-lived radiometric isotopes that advanced life requires. Second, a flat universe expands slowly enough for the matter to clump together to form galaxies, stars, and planets, but not so slowly as to form only black holes and neutron stars.

Until the mid-1990s, astrophysicists found it remarkable that the universe was so close to a flat geometry because such flatness is unstable with respect to time. Even though they could detect only about 4 percent of the mass required to make the universe flat, this required the early universe to be exquisitely close to “flat” to within one part in 1060. The previous statement holds true even given the uncertainties that existed twenty years ago (and to a lesser extent still do) in measurements of the cosmic mass density. Thus, in the absence of dark energy, the expansion rate would have changed so dramatically that the galaxies, stars, and planets necessary for physical life would never have formed.

Over the past fifteen years the picture has changed significantly. First, measurements of the radiation left over from the cosmic creation event, also known as the cosmic microwave background radiation, confirmed (with an error bar of about 3 percent1) that the universe is geometrically flat. Second, the concept of an extremely early epoch of cosmic inflation (a brief period of hyperexpansion of the universe when it was less than a quadrillionth of a quadrillionth of a second old) was developed into a scientifically testable hypothesis that later measurements partially confirmed.2 Third, astronomers discovered another density parameter for the universe, namely space energy density or what is now known as dark energy. For most astronomers and physicists an early epoch of cosmic inflation solves the one part in 1060 fine-tuning problem because such inflation in the early universe drives it exquisitely close to a flat geometry regardless of the universe’s initial mass density.

A cosmic fine-tuning problem remains, however. The total cosmic mass density measured through several independent methods falls short by a little more than a factor of three from that required to make a flat-geometry universe,3 which measurements of the cosmic microwave background radiation have established. Dark energy comes to the rescue to make up the deficit, but not without a price. By any accounting, the source or sources of dark energy are at least 120 orders of magnitude larger than the amount detected. This implies that somehow the source(s) must cancel so as to leave just one part in 10120 in order to match the small amount of dark energy detected by astronomers. Therefore, while inflation and dark energy can “eliminate” the one part in 1060 fine-tuning in the mass density of the universe, they can only do so by introducing the far more exquisite one part in 10120 fine-tuning in the dark energy density.

RTB scholars Jeff Zweerink and Dave Rogstad contributed to this article.

  1. D. N. Spergel et al., “Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology,” Astrophysical Journal Supplement Series 170 (June, 2007): 377-408.
  2. D. N. Spergel et al., 392-94.
  3. D. N. Spergel et al., 379-90.