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The Big Rip at the End of Time

by John G. Cramer

Alternate View Column AV-126
Keywords: general, relativity, dark, energy, cosmological, constant, runaway, expansion, catastrophe  
Published in the March-2005 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 9/22/2004 and is copyrighted ©2004 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


This column is about the end of the universe and of time itself, as implied by a new variant of the standard model of Big Bang cosmology.  But before considering the destruction of the universe-as-we-know-it, we will need to review the most startling development in modern cosmology, the discovery that the expansion of the universe is increasing due to “dark energy” contained in space itself.  The best evidence for dark energy comes from studies of Type Ia supernovas.

A Type Ia supernova is a burned-out star that is in a binary orbit around another star, from which it receives a flow of hydrogen gas that builds up on its surface.  After enough hydrogen has accumulated, it suddenly detonates in a thermonuclear fusion explosion.  The detonating star shines with extraordinary brilliance, brighter than the rest of the galaxy, for a period of up to a month and then fades away.  Such supernovas occur in all galaxies and can be observed (during their period of brilliance) in our galactic neighbors and also in galaxies half way across the universe.   Since the brightness of a supernova a distance r away will be diminished by 1/r2, a measurement of light intensity gives information about distance.  However, a plot of the red shifts of nearby supernovas against the distances inferred from observed brightness shows considerable scatter around average straight-line behavior.  This demonstrates that Type Ia supernovas are not all of identical brightness, and therefore that supernova brightness cannot be used directly as a distance indicator.

However, two groups, one led by Australian astronomer Brian P. Schmidt and the other by Saul Perlmutter of the Lawrence Berkeley Laboratory, found a cure for this problem.  They tracked the "light curve", the intensity vs. time of nearby Type Ia supernovas as observed through blue and violet filters, and found 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 brought nearby Type Ia supernovas of the same red-shift to the same intensity.  When they plotted red shift against distance using the corrected intensities, the scatter was gone and all of the Type Ia supernovas fell nicely on the same straight-line curve, demonstrating their value in establishing an astronomical distance scale.

The groups then extended the plot to more distant supernovas, where the plot was expected to fall below straight line behavior because of the expansion rate of the universe was expected to slow due to the pull of gravity, modifying the red shift.  But instead of the distant supernova points falling below the expected straight-line, the points were elevated above the straight line.  Conclusion: the expansion rate of the universe is not decreasing with time, it is increasing .

But how could the expansion of the universe be accelerating?  It turns out that Albert Einstein’s general theory of relativity, our present standard model for gravity, contains a built-in answer to this question.  Einstein, in order to accommodate model universes that did not collapse on themselves under the pull of gravity, included the possibility that the empty vacuum itself might have an intrinsic mass-energy, which we now refer to as “dark energy”.  He added to his equations a term L (Greek capital Lambda) which he called “the cosmological constant”.  Einstein’s cosmological constant L puts dark energy in the vacuum itself.

In universes described by general relativity, adding mass-energy to the vacuum has a different effect from adding mass-energy in the form of matter.  Dark energy, in addition to the expected gravitational attraction, also produces a negative pressure that is three times bigger than the gravitational attraction and acts in the opposite (antigravity) direction.  The repulsive force associated with dark energy grows linearly with distance, becoming very strong between objects separated by large distances and balancing or overcoming the tendency of universes to collapse due to the pull of gravity.  The groups measuring the accelerated expansion of the universe have concluded that 70% of the total mass-energy of the universe is in the form of dark energy.

The unresolved issue is whether the repulsion of dark energy is constant, growing, or shrinking with time.  Einstein assumed that his cosmological constant L was truly constant with time.  That implies that any unit volume of space contains the same fixed amount of dark energy (rL » 6.7 ´ 10-10 joules per cubic meter).  An alternative called “qunitessence” suggests that the density of dark energy is produced by a primordial scalar field that permeates the universe and depends on the size of the universe, so that the dark energy density rL was larger in the early universe and will become smaller as the universe continues to expand and evolve.  All such cosmologies can be described by assuming that rL is proportional to a(t)-3(1+w), where a(t) is the time-dependent scale-factor (i.e., radius) of the universe and w is the so-called “equation-of-state” parameter.

The parameter w is not well determined by observational data.  It should be exactly -1 for Einstein’s unchanging cosmological constant.  It could be anywhere between -1/3 and -1 for quintessence models.  Combined observational data from type Ia supernovas, galactic cluster abundances, gravitational lensing, and the apparent age of the universe favor a value of w that is more negative than about -0.8, tending to support Einstein’s assumption of a constant time-independent rL.

However, a recent paper written by Robert P. Caldwell of Dartmouth College and Marc Kaminowski and Nevin Weinberg of Cal Tech has raised the question of whether w can be more negative than -1.0.  This concept has been called “phantom energy” because an expanding universe with w less than -1 would have a rapidly increasing net energy.  In the phantom energy scenario, rL, the dark energy content of a cubic meter of vacuum, increases with time as the universe expands.  The observational data showing that w is less than -0.8 can also be interpreted as allowing negative w values as negative as about -1.5.

If w is less than -1, the energy density rLincreases as the universe expands.  The growing energy density increases the negative pressure, driving the acceleration of the expansion harder, leading to more volume and more energy, etc.  This produces a “runaway” feedback loop that makes the universe expand explosively.  The accelerated expansion of the universe itself accelerates and reaches an “end of time” limit that the authors call trip.  Assuming w = -1.5, available data would put is value at about trip = 22 billion years from now.

About a billion years before trip, the growing negative pressure will rip apart galactic clusters.  At 60 million years before trip the Milky Way galaxy will be dispersed.  At about 3 months before trip the gravitational pull of the Sun is countered by negative pressure and the Solar System disperses, first the outer planets and then the inner planets. At 30 minutes before trip negative pressure explodes the Earth.  At 10-19 seconds before trip the negative pressure dissociates all atoms.  A short time later the negative pressure dissociates nuclei into neutrons and protons.

What the negative pressure does at the quark-level is an interesting question, because the color force should grow as neutrons and protons are pulled apart into their constituent up and down quarks.  The authors say that at this point they expect some new physics, in the form of spontaneous particle production or extra-dimensional effects or string or quantum-gravity effects to kick in.  In any case, time has effectively ended.  The resulting universe has no structure, and all point-like particles, electrons, neutrinos, and quarks, are isolated as the only particle in their event horizon, with all other particles receding at superluminal velocities.  The implication is that the universe may not end with a bang or a whimper or by fire or by ice or with a Big Crunch, but by a ripping apart of all structure.  How likely is this picture of the ultimate fate of the universe?  As I said above, present observational data (which will improve in the next few years) tells us that w is roughly between -0.8 and -1.5 or so, allowing plenty of room for a Big Rip scenario. 

However, the phantom energy scenario does violate a cherished tenet of general relativity called “the dominant energy condition”, a principle that keeps energies positive and imposes energy conservation on a global scale.  It is the dominant energy condition that helps to rule out some manipulations of general relativity that would permit things like wormholes, warp drives, and time machines.  If the phantom energy scenario has any validity, the dominant energy condition can only be satisfied by broadening the picture, so that the phantom energy would have to be supplied from some phantom source “outside” the universe.  The present work assuming w<-1 cosmologies does not address this issue.

What are the science fictional implications of the Big Rip and phantom energy cosmology?  There would seem to be no immediate consequences, in that the entire evolution of the universe so far has taken us only about 1/3 of the way from the Big Bang to the Big Rip.  The rate of growth of the energy present in the vacuum, presently about 6.7 ´ 10-10 joules of dark energy in each cubic meter of vacuum, is not large enough to represent any significant source of energy for SF applications like spaceship drives.  Therefore, the implications of the scenario apply mainly to SF works set in the very far future or in other universes where the parameter w is much more negative than seems to be the case in our universe.

Therefore, the implications are mainly philosophical.  The ripping apart of the universe is a dismal picture.  There may be a true End of Time that is approaching at a steady pace.  And no matter haw hard we seek to achieve some immortality by creative acts that are preserved for posterity, the Big Rip promises to erase everything, without even the satisfaction of ultimate recycling implicit in the cycling Big Crunch or Big Clap scenarios.  Perhaps the only escape from the inevitable Big Rip would be to create some extra-dimensional wormhole passage to a universe with less hostile parameters.

Perhaps we should be working on that, as a long-term goal.


Phantom Energy Cosmology

Robert R. Caldwell, Marc Kamionkowski, and Nevin N. Weinberg, Physical Review Letters 91, 071301 (2003).

SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : .

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