Einstein's Blunder


Victor J. Stenger

For Skeptical Briefs March 1999

Revised April 3, 1999 11:31 am

He called it his greatest blunder, but Einstein's cosmological constant refuses to go away. When Einstein first wrote down his equations of general relativity in 1915, he saw that they allowed for the possibility of gravitational energy stored in the curvature of empty space. Furthermore, the force that resulted on a particle placed in this field would be repulsive if the constant were positive. The gravitational force between material objects is always attractive.

At the time, Einstein and most others thought that the stars formed a fixed "firmament," like it says in the Bible. This is not possible with attractive forces alone, so Einstein at first thought that the repulsive term might balance things out.

A decade latter, Hubble discovered that the universe was expanding and the cosmological term was no longer needed. Until recently, all the data gathered by astronomers has fit very well to models that set the cosmological constant equal to zero.

The cosmological constant resurfaced in 1980 with the inflationary model of the early big bang. This model assumes an original empty universe that is a tiny empty sphere containing a small amount of energy in the cosmological term. That energy did not have to come from outside. It could have been just the zero point energy, the minimum energy any finite volume must always contain according to quantum mechanics.

If energy resides in the curvature of space, that is, in a cosmological constant, then the empty sphere would have expanded exponentially. The energy inside the sphere would also have increased exponentially, without violating the first law of thermodynamics. Then, by a kind of frictional process, the first round of elementary particles that eventually evolved into the ones we see today would have been generated. As inflation was brought to a halt by the loss of curvature energy, the conventional big bang, which resembles a simple explosion, then took over.

Inflation solved a number of cosmological problems for which no other viable solutions have been suggested. It explained why the visible universe today is so "flat," that is, its geometry close to if not exactly Euclidean. With inflation, what we can see with our telescopes is just a tiny patch of rubber on a much larger balloon. Inflation also explained why the universe is so isotropic. The cosmic microwave background is almost the same temperature, 2.7 degrees Kelvin, in all directions. In the big bang without inflation, the regions of space opposite one another, as viewed from a single point like the earth, were never in causal contact with one another. So they could not have been in thermal equilibrium. With inflation, all of visible space, and much more that is beyond our horizon, was once all together as a uniform hot gas.

Still, the primordial gas could not have been completely uniform. Some non uniformity was necessary for the hydrogen and a few other light elements in the gas to coalesce into galaxies. Calculations indicated that this would have to show up today as a small anisotropy in the cosmic microwave background, about one part in 100,000. When a few years ago the COBE satellite, and other observations shortly thereafter, confirmed this prediction, the inflationary model emerged triumphant.

Or did it? The conventional inflationary model requires that the universe be absolutely flat. Any tiny deviation from flatness would have been magnified by many orders of magnitude during the inflationary epoch. Nevertheless, observations from other branches of astronomy continued to find insufficient matter to provide a flat universe. These measurements, like those on the microwave background, continued to improve and now indicate, not a flat universe, but a negatively curved (like a potato chip), open one. Even including indirect evidence on the still undetected dark matter that is believed to be all around us, only about 40 percent of the mass needed for a flat universe is indicated, with about 10 percent "visible." As a result, in the last year or so inflation has seemed to be in great trouble--at least if you go by reports from the media which, as I have said before, frequently over-hype what scientists tell them.

Now, it seems, the cosmological constant has galloped to the rescue of inflation. Two independent and fiercely competing groups have been studying distant supernovae and using them as new standard candles for the calibration of cosmic distance scales. Each has reported strong evidence for a slight acceleration to the universe. The universe seems to be falling up!

The only known explanation for an acceleration is the presence of a repulsive cosmological term, and the amount is just about what is needed to flatten out the universe so that inflation is safe. As an added bonus, this result also implies a slightly older universe than we thought, one that expanded slower in the past. This helps bring into line the marginal discrepancies between different age estimates, where some objects appeared to have lifetimes longer than the universe. You have undoubtedly read in the media how this discrepancy has brought into question the whole notion of a big bang. That was never the case, but it made for good headlines.

Now the jury is still out on cosmic acceleration. A poll of participants at a recent cosmology meeting showed one in two still moderately to strongly skeptical (all scientists should always be a little skeptical). And, a serious theoretical problem remains. Vacuum energy is found, sure enough, in modern theories of elementary particle and forces. The trouble is, that energy is about 120 orders of magnitude higher than the value implied by the tiny, if not zero, cosmological constant we observe today. If space were so highly curved, you could not see your hand in front of your face as the light was bent away.

Two terms actually contribute to vacuum energy and an effective cosmological constant that yields a smaller curvature. One is the bare curvature of spacetime, the energy of a completely empty universe. The other is the energy contributed by the virtual particle-antiparticle pairs that can exist for short periods of time according to the quantum uncertainty principle. These have effects that have been measured to high precision. The particle energy can be negative and a fine tuning of 120 orders of magnitude is necessary for these two terms to cancel, or almost cancel. This is an outstanding problem, but it's a problem whether we have a cosmological constant or not.

Many remain skeptical of the inflationary model, and a few knowledgeable people still question the big bang. However, none can recommend an alternative that provides a small fraction of the explanatory power of these theories. It may appear to outsiders that what is going on is a process of propping up a failing theory by adding new features. However, this betrays a gross misunderstanding of the scientific process. As data get better and better, most theories are fleshed out with more details. In a recent column I explained how this worked with the new evidence that the neutrino has mass. The standard model of elementary particles and fields had assumed zero neutrino mass for simplicity, but not required it as the logical consequence of any of the hypotheses of the theory.

Sometimes the cosmological constant is called a "fudge factor" that Einstein supposedly inserted into his equations to "save the appearances." This is also wrong. Einstein's equations call for a cosmological constant and conventional general relativity says nothing about its value. A value of zero would be less parsimonious than an arbitrary value, requiring one or more additional hypotheses to eliminate it in the theory. Time and again we find that the universe seems to be only as complex as it has to be.