Hubble Constant Refined
and
Positive Cosmological Constant Postulated

by Hill Roberts

Editor's Note: One of the key issues in cosmological evidence for the existence of God involves the shape of space and how things are moving within space. We have mentioned recently that there is new evidence that the universe is accelerating. The age of the cosmos and its future are also tied into these questions. One of our consultants, Hill Roberts of Huntsville, Alabama, has written a great deal on this, and the following article will help expain these issues. We hope you will find it interesting and challenging.

The following is my lame attempt to explain a very complex suite of inter-related concepts central to the cosmology of today. Hopefully this will help someone attempting to distinguish the facts (data) from interpretations of the data.

These 1999 findings are based on a mix of data and current cosmological assumptions about how the universe “ought” to be. It is supposed that it “ought” to be flat (of a critical density to critically dampen the expansion — that is, to just slow it to dead stop in an infinite time). The primary basis for this supposition is simply that it is so close to this critical value, it must actually be this value. Before we consider these ideas we need to get some basics of general relativity under our belts.

Einstein had predicted cosmic expansion and a cosmic beginning from his theories about gravity and space/time. Actually the idea is fairly simple. His brilliant insight was that gravity was simply a manifestation of the curvature of space/time, like a funnel spinning a marble ever faster into its center. (We see direct evidence of this in pictures of distant space showing gravitational lensing where galactic light is bent as it passes by intervening galaxies.) If no force opposed gravitational space/time, then space/time would expand forever. If that were the case, then setting time equal to zero in the equations produced the result that the volume of space contracts to zero, while the mass remains constant. This produces an infinite mass density at the beginning of space/time. In mathematical jargon, such an infinity is called a singularity. An infinite mass density would be so hot or energetic that all the mass is converted to energy per E = mc². Einstein originally so much disliked the implications of his theory of general relativity which predicted the cosmic beginning that he put a “fudge factor” in the equations to counteract the unbounded expansion and the resultant singularity at T = 0. This factor is called the cosmological constant. Later he removed the constant, or set it to zero, to be in accord with Hubble's galactic expansion data, which did imply a singular beginning, or a T = 0. Hubble developed an estimate for the rate of the observed expansion of space. This is now called Hubble's constant, which is just the measure of the expansion rate (and not to be confused with the cosmological constant of Einstein's equations). The inverse of Hubble's constant is proportional to the size of the universe. The cosmological constant is a factor indicating a repulsive (anti-gravity) force when positive, no force when zero, and an attractive force when negative. This unknown postulated force is separate from the force of gravity, which is just the effects of the curvature of space. Hence the terminology of a flat or curved universe. The nature of the curvature, if curved, is another hot area of current research, both empirical and theoretical. Is space generally curved or only locally curved but flat overall? The usual supposition has been that it is flat overall.

The flat supposition is the impetus for the inflation model (see below for explanation) of early expansion with a positive cosmological constant. If even a roughly-flat state is assumed in the current epoch, one gets a flat universe to about 60 decimal places prior to the assumed inflation phase. However, the empirical data indicates that only 40% of the mass required to halt expansion exists, consisting of 1 part visible matter and about 3 parts invisible matter. In other words, only about 10% of the mass needed to halt the current expansion can actually be seen with telescopes. The remainder of the 40% is “invisible.” That invisible matter is still seen albeit somewhat indirectly, through its gravitational effects on visible galactic objects. (Some estimates have it as only 5% being visible, the rest being invisible.) But all in all, we can see evidence of only about 40% of enough mass to halt the expansion. The universe appears designed to expand until the end of time. But it might still be a flat expansion. In fact an expansion that goes on forever, “oughter” be flat according to the math of general relativity.

Given that the universe “ought” to be flat, then that means 60% of the mass is of a type that “ought” to be weird. This weird mass “ought” not to interact gravitationally, else it would be observed. So this weird mass is not mass at all, it “ought” to be its negative equivalent in energy — a negative energy. Negative energy “ought” to have the effect of opposing gravity, hence leading to cosmic acceleration at some point. In the past, the mass density dominated so the universe was decelerating. But now the negative energy density dominates (60%) so acceleration is observed. Whence cometh all this negative energy? Well, it “ought” to come from quantum mechanical vacuum fluctuations in the energy fields of empty space/time. Although such a phenomenon is observed in high energy particle accelerators for fleeting instants, there is no indication that such is happening throughout space. This seems to violate the uncertainty principle for such a large mass/energy (the observable mass of the universe) to persist for such a long time (billions of years). It is this same uncertainty principle that argues for vacuum fluctuations in the first place, but the larger the mass/energy that “fluctuates” into existence, the shorter that mass/energy should be able to persist. Hence the only observations for such phenomena are for very small subatomic particles produced in high energy accelerators and which only persist themselves for very short times much less than a second.

There are several observational problems in all this in addition to the metaphysical “oughts.”

1. The measurements of distant type 1a supernovas is the basis of the acceleration rate; but distant supernovas are indicative of the past when decelerating expansion supposedly dominated, not accelerating expansion. If acceleration is to be observed it should be observed in nearby galaxies, not the most distant (earliest) galaxies. Unfortunately, nearby galaxies are bound to us in our local group, and hence useless for making such observations. So I must confess I do not understand how measuring such distant galaxies tells us anything about the cosmological constant today. Then maybe, but not today. But that is not what is being claimed by the cosmologists.
2. The ~10% difference in the 60 to 70 km/s/mps values for the Hubble constant reflects a priori assumptions about whether it is a decelerating or accelerating expansion, but that is what is being claimed as the result. Seems a bit circular, but it is mostly just a self-consistency argument.
3. The database for these computations is still relatively small, less than two dozen galaxies. But this is many more than available only two years ago.

One previously held “ought” now seems to be defunct. It is now reasonably assured both from theoretical studies (Hawking-Penrose) and empirical data (Freeman-Sandage) that the universe will never be able to contract or oscillate eternally. The “space/time” is infinite idea is essentially dead. In Science News, January 1, 2000, P. Weiss discusses an idea for time reversal based on space contraction, but finally acknowledges that the idea of a “big crunch” is pretty well dead. So I consider this some degree of metaphysical progress toward my own set of cosmological “oughts.”

The state of current cosmological affairs is illustrated in a debate before an audience of astronomers between two cosmologists who differ in their “oughts.” Cowen of Science News observed, “At the end of the debate between Turner and Peebles, moderator Margaret J. Geller of the Harvard-Smithsonian Center for Astrophysics in Cambridge, Mass., took a straw poll. She asked the listeners if they thought that a century from now, the basic concepts exciting astronomers this year would be cornerstones of understanding. Most of the audience thought the concepts would be substantially different” (Cowen, Science News, Jan. 3, 1998).

The expansive nature of the universe seems to indicate a beginning of space/time in the distant past. How the first moments of that beginning occurred seems to be highly ellusive to our current physical insight, and some aspects of quantum mechanics indicate such is forever out of reach of knowing. After all is said and done, there is nothing better to be said than, “In the beginning God created the heavens and the earth.” That's my “oughter”

The Inflation Model proposed by Alan Guth in the early 1980s was developed to resolve a cosmological enigma — maybe. That is, today as we observe the universe, it seems that on the large scale of galactic distances, galaxies widely separated from one another do not interact. Although mass is distributed in “lumps” (galaxies), the average mass density is about the same everywhere on a large scale, and the thermal background is astonishingly uniform in all directions of empty space. In other words, they are further apart than can be traveled in the available time even if moving at the speed of light. If we can see objects in one direction that are 13 billion light years away and can see similar objects in the opposite direction which are 13 billion light years away, it would take 26 billion years for a signal from one to reach the other. But it appears that the universe is too young for that, at only 13 billion years. That is the problem — coming up with an explanation for how those galaxies got so far apart in the first place if they all started from the same singular event. Well maybe at an earlier time, when they were closer together, they could have interacted? Unfortunately that does not help. For example when they were only half as far apart, the universe was only half as old and only half as much time was available to travel the distance between them, so the problem stays exactly the same. There is another problem here as well: we have no clue how far apart these galaxies are today because we are not seeing them as they “are” but only as they were. This is just another way of saying they no longer interact. It is the fundamental paradox of relativity. The only way anyone has come up with a naturalistic explanation for the non-interaction situation is to propose that sometime right after matter condensed from the hot singularity, the then very small universe went through a period of un-natural expansion or inflation. In other words, space/time expanded at a rate significantly higher than the limiting speed of light. (We tend to overlook this little detail, which violates the sacred cosmological principle.) This continued until all the clumps of matter became too far apart to ever interact, thus forming little “island universes” as galaxies were once called. This rapid expansion phase would homogenize or smooth out both the mass and the radiation background in a manner similar to what is actually observed. So inflation is consistent with a smooth universe, but a smooth universe does not necessarily require inflation to become smooth. Thus the whole inflationary premise sits on a view of how the universe “ought” to be.

Let me try to explain this from a different direction. In principle, inflation springs from a common sense presupposition against coincidence. The apparent coincidence is that the cosmos appears to be following the same “plan” for how mass is distributed in any region or epoch of the universe. The unspoken presupposition is that this coincidence could not be the result of some intentional design. If not by design, then somehow these regions must share some common “ancestry,” to borrow an idea from the biologists. For objects of mass, the common ancestor must be the ability to interact, to exert forces on each other, or for all elements to be subjected to the same common force. Hence, Guth gave birth to the idea of inflationary expansion. Prior to the postulated inflation phase, all matter interacted in a common radiation field. After the inflation the pieces of the primordial cosmos were so widely separated that they no more interacted. Hence, the original interactions and distribution patterns prior to inflation became fixed for all time. At least that is the idea.

In the early 1960s Arno and Penzias of Bell Labs (1978 Nobel) detected the 3K isotropic (uniform in all directions) microwave radiation in the sky. This thermal data fit very nicely with the idea of expansion from a primordial hot “fireball” as predicted by Einstein's general relativity, and propounded by George Gamow in the late 1940s.

How so? By extrapolating the temperature back in time as the universe began from the singularity, it is possible to predict the initial temperature. Answer: really hot, so hot all matter “evaporates” into pure energy. Take a cosmic “gas” that is hot and dense, and expand it to the size of the universe. Voila, it cools off to about 3K. That is three degrees above absolute zero, or minus (-) 459.67°F! However, there was a conceptual problem with this nice smooth cold radiation background. Since the universe is obviously slightly “lumpy” with all the galaxies scattered about, the radiation field should likewise be slightly lumpy as a reflection of the early non-uniformity that corresponded to galaxy condensation. Unfortunately, technology was not available until 1992 to make such sensitive measurements of the uniformity of the background radiation. That is where the Cosmic Background Explorer (COBE) satellite (and a bunch of other measurements since) come in. COBE was able to detect very slight “lumps” in the radiation field that would be consistent with a slight lumpiness in the distribution of matter throughout the universe. However, this does not really prove inflation one way or the other. It does, however, lend strong evidence that the universe is the result of a long process of expansion in both the mass and energy distribution. Two very different ways of measuring the universe (background radiation and visible matter) yield results consistent with each other and consistent with a universe expanding from some primordial beginning. However, as inflation hypothesis shows, the nature of things in the earliest phases of that beginning appears to transcend known natural laws. The radiation variations only show that all mass and the radiation field seem to share a period of common origin, whereas now cosmic masses are non-interacting. The data does not indicate the process whereby the mass and radiation became non-interacting. That points to inflation only by reason of default, or lack of other naturalistic explanations at the current time. That is not a particularly satisfying situation so inflation has come on a bit of hard times both metaphysically as well as observationally (Musser 1998).

My own “oughter” in all this is that the transcendent aspect of the beginning of the universe is very nicely summed up by the statement, “In the beginning God created the heavens and the earth.”

End Matter

Reference: Cowen, “Hubble Telescope Dates the Universe” Science News (May 29, 1999).

The latest round of measurements in 1999 indicate a currently accelerating expansion rate — a positive cosmological constant- (with a Hubble constant of 60-70 km per second per mparsec), whereas in the past history of the universe the expansion was slowing — or had a zero or even negative cosmological constant. This also refines the estimate of the age of the universe to be 12-13.5 billion years old.

Other articles from 1998 and 1999 that give some good background:
Cowen, “The Greatest Story Ever Told,” Science News, Dec. 19, 1998.
Cowen, “The Cosmos' Fate: World Without End” Science News, Jan. 3, 1998.
Freeman, “The Expansion Rate and Size of the Universe,” Scientific American, March, 1998.
Landy, “Mapping the Universe,” Scientific American, June, 1999.
Musser, “A 100 Billion Years of Solitude,” Scientific American, May 1999.
Musser, “Inflation is Dead, Long Live Inflation,” Scientific American, July, 1998.
Introduction to Cosmology, (Microware Anisotropy Probe - MAP), NASA website.