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Our Runaway Universe and Einstein's Cosmological Constant

by John G. Cramer

Alternate View Column AV-95
Keywords: accelerating expansion universe Big Bang Einstein's cosmological constant quintessence cosmology
Published in the May-1999 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 11/11/98 and is copyrighted ©1998 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


    Much of what you thought you knew about the universe and its expansion may be wrong. That expansion appears to be speeding up rather than slowing down. This column is about recent astronomical evidence for a positive cosmological constant, suggesting that space itself has mass-energy (E = mc2).

    In 1913 Albert Einstein developed the general theory of relativity, which today remains the standard model of gravity. A few years later, beginning in 1917, he turned to cosmology, applying his theory to the universe itself, and he discovered a vexing problem. His equations were unable to describe a universe in an unchanging steady-state. Every model universe he considered that contained matter would collapse on itself because of the pull of gravity unless it was expanding. Einstein decided that he must have left something out. He proposed that the empty vacuum must have intrinsic mass-energy, and he added a term WL (Greek Omega-sub-Lambda) called the cosmological constant to reflect this energy density.

    Contrary to what one might expect, general relativity a mass-energy for empty space produces a repulsive force instead of gravitational attraction. If a volume of gas expands or contracts, the mass density changes, producing a positive pressure that, in the simplest case, follows the Ideal Gas Law (p = nRT/v). However if a volume of mass-containing vacuum expands or contracts, the mass-energy density remains constant, and the pressure in this case is negative. The gravitational effect of this negative pressure overwhelms gravitational attraction of the mass and results in a net repulsive force. That force grows linearly with distance, becoming very strong at large distances and balancing the tendency of model universes to collapse. Einstein's introduction of WL thus made general relativity compatible with a steady-state universe.

    Later Edwin Hubble studied the red-shifts of distant galaxies and discovered that the universe was expanding. Einstein then decided that he had not needed to introduce WL into general relativity. He became convinced that WL = 0 and that space has no intrinsic mass-energy. He referred to the cosmological constant as "my biggest mistake".

    Fred Hoyle attempted to save the steady-state idea, even in the presence of Hubble expansion, by proposing that new hydrogen atoms are spontaneously generated out of the vacuum, continuously refueling the universe and preserving it in a steady state of constant density. This became the standard model of the 1950s. Innovators like George Gamow had other ideas and extrapolated universal expansion backward to a primordial explosion. They talked about a Big Bang at the beginning of the universe and explored its consequences, but few took them seriously.

    In the mid-1960s Arno Penzias and Robert W. Wilson accidentally discovered the microwave background radiation left behind by the Big Bang. Gamow had predicted that up to about 400,000 years after the Big Bang the universe was filled with charged particles and therefore "black", because the particles immediately absorbed all light as soon as it was produced. However, at 400,000 years the universe became cool enough that the charged particles, protons and electrons, could pair off to form neutral hydrogen, so that the universe abruptly went from black to transparent. The many photons of light present at that time were liberated into the now-transparent universe. Penzias and Wilson had detected the remnant of that primordial light flash. Their discovery triggered a revolution. Hoyle's steady-state universe model was declared dead and Gamow's Big Bang ideas were transformed from fringe speculation to the standard model of cosmology almost overnight.

    Alan Guth later modified the Big Bang model with his "inflationary scenario", which assumes that in the very early stages of the Big Bang, for reasons not well understood, the universe expanded at an exponentially increasing rate under the influence of a strong repulsive force, its radius growing much faster than the speed of light. After inflation subsided the universe continued to expand at a more modest pace, with the expansion rate slowly diminishing under the influence of gravity. This is the currently accepted standard model of cosmology.

    But there are new observations that may be in the same class with the discovery of Penzias and Wilson. There is now evidence that the universe is expanding at an ever-increasing rate, that Einstein's cosmological constant WL, far from being a mistake, is needed to explain the behavior of the universe, and that space itself may have a net mass-energy. If these observations are confirmed with better data, the standard model must be modified.

    Modern cosmology addresses questions related to the Big Bang model with five related parameters: the Hubble constant or expansion rate of the universe (H0), the mass density of the universe (WM), the previously mentioned cosmological constant (WL), the deceleration parameter of the universe (q0), and the age of the universe (t0). Up to now, the cosmological constant WL has been taken to be zero, implicitly assuming that the vacuum contains no net energy. The deceleration parameter q0 has been assumed to be positive, with the expansion rate of the universe progressively slowing down under the pull of gravity. Actually measuring q0 requires a comparison of the observed red-shifts of the most distant visible galaxies with their absolute distances from the Earth. Unfortunately, the determination of absolute astronomical distances is extremely difficult.

    Now astronomers have devised a new technique for making distance measurements, using Type Ia supernovas as distance indicators. A Type Ia supernova is a burned-out star in a binary orbit around another star, from which it receives gas that builds up on its surface. After enough gas has accumulated, it suddenly detonates in a thermonuclear explosion that shines with extraordinary brilliance for about a month, then fades away. Such supernovas occur in all galaxies and can be observed (during their 30-day period of brilliance) in our galactic neighbors and also in galaxies that are half way across the universe. Since the brightness of the supernova a distance r away will fall off as 1/r2, a measurement of the light intensity of the supernova implies a distance. If one makes a "Hubble plot" of red shift against inferred distance for Type Ia supernovas, one finds considerable scatter around the expected straight-line behavior, indicating that all Type Ia supernovas are not of identical brightness and are unsuitable as distance indicators.

    However, a group of astronomers and astrophysicists led by Brian P. Schmidt of the Mount Stromlo Observatory in Australia (Riess, et al, 1998) have found a way around this problem. They track the "light curve", the intensity of nearby Type Ia supernovae with time, as observed through blue and violet filters, and they find that there are significant differences in falloff times of the light from one object to another, from falloff in about 10 days to over 30 days. They used these light-curve differences to generate a correction that brings nearby Type Ia supernovas of the same red-shift to the same intensity. When they made a Hubble plot of red shift against distance using the corrected intensities, the scatter was removed and all of the Type Ia supernovas fell on the same straight line, demonstrating their value in establishing an astronomical distance scale.

    They then collected data from 10 very distant supernovas that were studied between 1995 and 1997 using the Hubble Space telescope and ground-based telescopes in Chile, Australia, and Hawaii. They extended the Hubble plot into the distance region where it would be expected to fall below a straight line because of the expected decrease in the expansion rate of the universe due to the pull of gravity, inferring the deceleration parameter q0.

    The result was a surprise. Instead of the supernova points falling below the Hubble straight-line behavior as expected, the points for the most distant supernovas were elevated above the straight line. The implication of this is that the expansion rate of the universe is not decreasing. Instead, it is increasing, and the deceleration parameter is negative. Another group led by Saul Perlmutter of the Lawrence Berkeley Laboratory has reached similar conclusions (Perlmutter, et al, 1997).

    In a previous AV column (Analog 8/95) I reported the "state of the universe" as viewed from the 1994 "Texas" Symposium held in Munich, Germany, listing estimates of cosmological parameters as of 1994. They were H0 = 66±30 km/sec per megaparsec, WM = 0.1 to 2, and t0 = 8±5 × 109 years. These values imply a value for q0 between about +0.05 and +1.0. At the Symposium there was concern about "the age crisis", the fact that the estimated age t0 of the universe appeared to be less than the ages of the oldest stars in it. Stars in globular clusters had estimated ages of up to 11.5±2 × 109 years and thorium and europium abundances in stars implied ages of up to 15.2±3.7 × 109 years.

    Symposium speakers generally assumed WL= 0 for the cosmological constant, but at the time I felt uneasy about that assumption. In my 8/95 column I predicted that a non-zero cosmological constant would soon be discovered. My prediction seems to have been proven correct.

    In contrast to the 1994 values, the analysis of Riess, et al leads to a negative value of the deceleration parameter of q0 = -1.0±0.4, a mass density of about WM = 0.24, and a positive value for the cosmological constant of about WL= 0.72. Because the expansion rate of the universe is increasing, the extrapolation back to time zero which gives the age of the universe is radically changed, and the universe is older than previously estimated. The revised age value is t0 = 14.2±1.5 × 109 years, almost double the 1994 value. This provides a solution to the age crisis mentioned above. The new analysis gives the value for the product H0t0 to be about 0.93, a bit outside the range 0.7 to 0.9 preferred by theorists.

    The result may resolve part of the Dark Matter problem. Inflationary cosmology requires that the total mass-energy density of the universe is exactly WTotal = 1.0. Adding the energy density of normal mass to that of the vacuum gives WTotal = WM + WL = 0.96, i.e., equal to unity within the analysis uncertainties, solving the inflation part of the Dark Matter problem. There remains, however, the problem of the nature of the Dark Matter that appears to be clumped around galaxies, speeding their rotation rates.

    What are the implications of these new results for science fiction? The 1998 results carry the message that the universe is not just expanding, it's expanding at an ever-increasing rate, and it will continue to expand forever. Therefore, SF stories, novels, and speculations that are based on a universe that recollapses, e.g., Poul Anderson's Tau Zero and Paul Preuss' Re-Entry, and Frank Tipler's speculations in The Physics of Immortality have been rendered somewhat contra-factual by the new observational data.

    Another SF implication of the 1998 analysis is that WL= 0.72 implies that empty space has a positive energy density, with the negative pressure anti-gravity action of this mass-energy accelerating the expansion of the universe. Many SF stories and novels by authors, including Isaac Asimov and Robert L. Forward, suggest that the vacuum abounds with energy that could be used as a free and abundant energy source for space drives, etc. These new results tend to support that idea, although the implied energy density is very low. It remains to be seen whether the vacuum can be persuaded to give up its treasure trove of free energy.

    It is also interesting to speculate on whether there could be some connection between the strong repulsion that produced the initial inflation of the universe and the weaker repulsion that seems to persist even 14 billion years later. Perhaps the cosmological constant is not really a constant at all.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


"Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant", Adam G. Riess, et al., submitted to Astronomical Journal, preprint astro-ph/9805201 in the LANL Archive, (May 15, 1998).

"Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications", S. Perlmutter, et al., Nature, 1/1/98 issue, preprint astro-ph/9712212 in the LANL Archive, (December 16, 1997).

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