Neutrino Mass, Inflationary Cosmology, and the Fine-tuning Argument

Loren D. Haarsma,

University of Pennsylvania, Philadelphia, PA

and Deborah B. Haarsma, Haverford College, Haverford, PA

From: PSCF 50 (September 1998): 160-161.

Recent results from the Super Kamiokande Collaboration provide the strongest evidence to date that some neutrinos have non-zero mass.1 Contrary to the implications of some popular press reports, most physicists have been expecting such results for several years. Non-zero neutrino mass can be accommodated by fairly straightforward extensions of the "standard model" of particle physics. Earlier measurements of neutrinos produced in the sun, in the atmosphere, and by accelerators2 suggested that neutrinos might oscillate from one "flavor" (electron-, muon-, and tau-) to anotheróan expected consequence of non-zero mass. Neutrino mass gives additional data in constructing the Grand Unified Theory (GUT) of physics. It also provides additional data for cosmologists.

The neutrino mass measurement should cause a revised estimate of Omega, the mass density of the universe. Omega is defined such that if it is greater than 1, the mass in the universe is large enough to cause its eventual collapse, and if Omega is less than 1, the mass of the universe cannot prevent it from expanding forever. Observations of the galaxy clusters dynamics currently place Omega at about 0.3. If neutrinos (or other Weakly Interacting Massive Particles [WIMPS]) have even a small amount of mass, their high density throughout the universe would add significantly to this value. Since the actual values of the neutrino masses are not known (only that at least two are non-zero), their contribution to Omega is not yet known.

The cosmological constant lambda is also an important parameter. It is also referred to as "vacuum energy," "quintessence," and (recently in the press) "anti-gravity." It is an energy density associated with empty space and has a constant value throughout the universe. Lambda and Omega in various combinations determine the current acceleration or deceleration of the universal expansion, the curvature of the universe, and its ultimate fate (whether it will contract or expand forever). There are several types of observations being made to determine lambda and Omega. Recent distance measurements to supernovae have found that the universal expansion may actually be accelerating, which is only possible if lambda is non-zero. Observations of the curvature of the universe limit the sum of Omega + lambda to less than about 1.5. Standard inflation theory predicts that the curvature of the universe will be precisely flat, or Omega + lambda = 1. There are also variations of inflation theory that allow a curved universe.3

Cosmology and particle physics are closely related. The values of the fundamental constants of physics (particle masses, coupling constants of the various forces, etc.) are integral to both fields. It has been known for some time that only very narrow ranges within the fundamental constants allow for human life. This fact is sometimes used apologetically, as evidence that the laws of nature were designed for life. However, several scientific theories have been proposed to account for this apparent fine-tuning without reference to a Designer. Three theories which have attracted the most attention are the "many-worlds" interpretation of quantum measurement theory, "many-universes" quantum cosmology (in which quantum fluctuations in a hypothetical high-dimensional space-time can produce Big Bang-like events), and inflation theory. The first two, while intriguing, are not widely accepted by physicists. It is unclear whether they resolve the problems they claim to resolve, nor do they seem to make any observable predictions different from "standard" interpretations of quantum mechanics and standard cosmological theories.

Inflation theory, although still speculative, is given a fair bit more credence because it solves a few problems in noninflationary cosmology.4 Three problems in particular are: (1) Magnetic monopoles are scarce, yet predicted in abundance in noninflationary cosmology. The exponential expansion of inflation would push monopoles and other relics beyond the edge of the observable universe. (2) Observations (see above) indicate that the universe is nearly flat, but noninflationary cosmology has no mechanism to set Omega + lambda between 0.3 and 1.5. The exponential expansion would cause any initial curvature to be smoothed out so that Omega + lambda is precisely 1.5 (3) The cosmic microwave background is very nearly in thermal equilibrium everywhere we observeóincluding parts of the sky which should be causally disconnected from each other. In noninflationary big-bang cosmology, we know of no particular reason why different parts of the universe which never had a chance to interact with each other should be at the same temperature. In inflation, the different parts of the universe were in causal contact before the exponential expansion and the observed thermal equilibrium is expected.

Another prediction of inflation theory is that the universe is much larger than the observable universe, containing other regions in which the fundamental constants of physics may be different. These different regions are thought to arise in the following manner: Immediately after the Big Bang, gravity, electromagnetism, and the strong and weak nuclear forces operate as a single, unified force described by what is often called the "theory of everything" (TOE). As the universe cools, gravity uncouples from the other three forces, which are now described by the GUT. As the universe cools further, the mathematical symmetries which GUTs have at higher energies break down. The strong nuclear force uncouples from the weak nuclear force and electromagnetism. The exact details of this "symmetry breaking" are not understood because we do not yet know the details of the GUT, but it is known that those symmetry-breaking details set the values of many particle masses, coupling strengths of the forces, etc.

The inflationary epoch is thought to happen after the TOE separates into gravity and GUT, at the time of the spontaneous symmetry breaking of the GUT into strong force + electro-weak force. If inflation theory is correct, space expands (and matter cools) exponentially during the inflationary epoch. The spontaneous symmetry breaking happens at slightly different times in different regions of space. Each region becomes its own "island universe," each much larger than our observable universe. Since the symmetry-breaking happened differently in each region of the universe, each could have somewhat different strong-force, weak-force, and electromagnetic coupling constants, particle masses, etc.

It is unknown how different the fundamental constants could be. All parts of the universe would have the same TOE and the same GUT. Since we do not yet know what the correct GUT is, we do not know how much variability there could be in the fundamental constants set by symmetry breaking. Even supposing that inflation would produce many different regions of the universe with a great variety of fundamental constantsósome of them "naturally" falling into ranges suitable for lifeóit still begs two important questions. First, how "finely-tuned" is the GUT and the TOE? It is impossible to speculate on the answer to that question until more details are known about the GUT. Second, why should the universe, with its particular TOE, exist at all? Inflation, or for that matter any scientific theory, cannot answer why something should exist rather than nothing.

Whether inflation theory is true or not, we can praise the Creator for an amazing creation. As for using the apparent "fine tuning" of the laws of nature as an apologetic argument, it would seem that wise use is cautious use.





3For a recent overview of alternatives to standard inflation, see "Inflation is Dead; Long Live Inflation" by George Musser, Scientific American 279 (July 1998): 19ñ20.

4For a recent popular overview by the originator of inflation, see The Inflationary Universe: The Quest for a New Theory of Cosmic Origins by Alan Guth and Alan Lightman (Reading, MA: Addison Wesley, 1997).

5George Musser, "Inflation is Dead; Long Live Inflation."