The future of the universe

By Sean Carroll | January 26, 2006 11:08 am

This month’s provocative results on the acceleration of the universe raise an interesting issue: what can we say about our universe’s ultimate fate? In the old days (like, when I was in grad school) we were told a story that was simple, compelling, and wrong. It went like this: matter acts to slow down the expansion of the universe, and also to give it spatial curvature. If there is enough matter, space will be positively curved (like a sphere) and will eventually collapse into a Big Crunch. If there is little matter, space will be negatively curved (like a saddle) and expand forever. And if the matter content is just right, space will be flat and will just barely expand forever, slowing down all the while.

Fate of the universe This story is wrong in a couple of important ways. First and foremost, the assumption that the only important component of the universe is “matter” (or radiation, for that matter) is unduly restrictive. Now that we think that there is dark energy, the simple relation between spatial curvature and the ultimate fate of the universe is completely out the window. We can have positively curved universes that expand forever, negatively curved ones that recollapse, or what have you. (See my little article on the cosmological constant.) To determine the ultimate fate of the universe, you need to know both how much dark energy there is, and how it changes with time. (Mark has also written about this with Dragan Huterer and Glenn Starkman.)

If we take current observations at face value, and make the economical assumption that the dark energy is strictly constant in density, all indications are that the universe is going to expand forever, never to recollapse. If any of your friends go on a trip that extends beyond the Hubble radius (about ten billion light-years), kiss them goodbye, because they won’t ever be able to return — the space in between you and them will expand so quickly that they couldn’t get back to you, even if they were moving at the speed of light. Meanwhile, stars will die out and eventually collapse to black holes. The black holes will ultimately evaporate, leaving nothing in the universe but an increasingly dilute and cold gas of particles. A desolate, quiet, and lonely universe.

However, if the dark energy density actually increases with time, as it does with phantom energy, a completely new possibility presents itself: not a Big Crunch, but a Big Rip. Explored by McInnes and by Robert Caldwell, Marc Kamionkowski, and Nevin Weinberg, the Big Rip happens when the universe isn’t just accelerating, but super-accelerating — i.e., the rate of acceleration is perpetually increasing. If that happens, all hell breaks loose. The super-accelerated expansion of spacetime exerts a stretching force on all the galaxies, stars, and atoms in the universe. As it increases in strength, every bound structure in the universe is ultimately ripped apart. Eventually we hit a singularity, but a very different one than in the Big Crunch picture: rather than being squashed together, matter is torn to bits and scattered to infinity in a finite amount of time. Some observations, including the new gamma-ray-burst results, show a tiny preference for an increasing dark energy density; but given the implications of such a result, they are far from meeting the standard for convincing anyone that we’ve confidently measured any evolution of the dark energy at all.

So, it sounds like we’d like to know whether this Big Rip thing is going to happen, right? Yes, but there’s bad news: we don’t know if we’re headed for a Big Rip, and no set of cosmological observations will ever tell us. The point is, observations of the past and present are never by themselves sufficient to predict the future. That can only be done within the framework of a theory in which we have confidence. We can say that the universe will hit a Big Rip in so-and-so many years if the dark energy is increasing in density at a certain rate and we are sure that it will continue to increase at that rate. But how can we ever be sure of what the dark energy will do twenty trillion years from now? Only by actually understanding the nature of the dark energy can we extrapolate from present behavior to the distant future. In fact, it’s perfectly straightforward (and arguably more natural) for a phase of super-accelerated expansion to last for a while, before settling down to a more gently accerated phase, avoiding the Big Rip entirely. Truth is, we just don’t know. This is one of those problems that ineluctably depends on progress in both observation and theory.

Of course, it’s thoroughly remarkable that we can even think about these possibilities in a scientific way, even if we haven’t yet isolated the ultimate answer. Before the dynamical spacetime of Einstein’s general relativity replaced Sir Isaac Newton’s view of absolute space and time, we couldn’t have been having this conversation. Newtonian spacetime is there once and for all, fixed and unchanging in its structure, only permitting the matter within it to evolve. It’s really quite difficult to come up with any sensible long-term history of the universe within Newtonian cosmology; in any finite region of space, the matter will ultimately settle down to some equilibrium — so why is evolving now, if spacetime is infinitely old? In Einstein’s universe, spacetime can evolve and change, and we have grounds for speculating about where it came from and where it’s going. In the last ten years we’ve learned an amazing amount about the universe that bears directly on this question.

But the old picture of collapse vs. perpetual expansion is wrong in another way, too: it takes a feature of our observable universe, namely that it is homogeneous and isotropic, and extrapolates it to the entire universe, even the unobservable bits. This is a reasonable first guess on grounds of simplicity, at least if you didn’t have any reason to suspect that the ultra-large-scale structure of the universe were wildly different from place to place. But these days we do have such a reason: eternal inflation. The idea of cosmic inflation invokes a period of rapidly accelerated expansion in the very early universe, that takes a tiny patch of space and blows it up to fantastic size. Eternal inflation is simply the realization that this phase doesn’t end everywhere at once: inflation typically stops in some part of the universe, but continues on somewhere else — forever! In other words, somewhere far away, inflation is still going on. And this idea isn’t some baroque kind of model that requires a handful of miracles to set in motion; to the best of our current understanding, it’s very easy for inflation to be eternal once it begins at all. That means that the ultimate expansion or contraction of our meager patch of universe is just a tiny part of the big picture — so we shouldn’t take the fate of our little neighborhood too seriously.

Meanwhile, of course, there’s the issue of the distant past of our universe, as well as the distant future. It’s becoming more and more popular to contemplate the idea that the Big Bang wasn’t the start of it all, but simply a dramatic moment in a much larger picture. For a long time now, Gabrielle Veneziano and others have been investigating the idea of a pre-Big-Bang phase in the context of string theory. Steinhardt and Turok have suggested that the universe is cyclic, repeating an infinite pattern of expansions and collapses. And of course Jennie Chen and I have been arguing (following the exhortations of Huw Price about the arrow of time) that the far past should look like the far future, only backwards.

Thinking about what happened before the Big Bang is precisely as respectable as, although admittedly more difficult than, thinking about what the ultimate future of our universe will be. In each case we have to extrapolate into unknown territory, relying on a combination of observational clues and theoretical predictions. And in each case the current state of the art isn’t nearly good enough for us to make any definitive statements. But no need to invoke the God of the Gaps just yet! The amazing thing is not that these questions are hard, but that they are legitimate scientific issues, and that we are increasingly able to address them in the context of established (or at least plausible) physical theories. Stick around, we’ll figure it out.

CATEGORIZED UNDER: Science, Time
  • http://feynman137.tripod.com/ Science

    It is good that people are applying the cosmological constant to evolving dark energy problem. It does seem to make the theory ever more complex. Each failed prediction in cosmology is fixed by a new adjustment in the theory.

    I wonder if you think there should be freedom to work on alternatives, within general relativity and the big bang? The “dark energy” was inserted to stop gravity decelerating the universe. An alternative theory is that the gravity has a physical mechanism within the universe and fades out at great distances.

    The force mechanism dynamics show that the big bang early time dynamics run the same, because weaker gravity at 3 minutes also involves weaker electromagnetism, and fusion rate falls if gravity is weaker, but rises if electromagnetism is weaker (Coulomb repulsion of charges).

    Feel free to delete this if you find it annoying…

  • http://astromalte.blogspot.com/ Malte

    I think it’s interesting that the content of the future has changed from ‘same as now’ through ‘same as now but a bit more’ to ‘immeasurably more than now’ to ‘anything can happen, and it could be disastrous’. This progression seems to me to parallel the way people talk about capitalism, globalisation and the threats it involves. I wonder if we could talk about dark energy and the fate of the universe in a less terrifying way if we felt more comfortable with politics here on Earth.

  • fh

    Hmmm… I always thought that a finite universe was rather appealing philosophically, we can always ask the question “where” the universe comes from, wether it’s eternal or finite, with a finite universe we know though that only so much can have happened in it. In a sense we know the border of scientific inquiry, and have a clear line that all things beyond that border do not matter within this universe. Ideally we’d of course have natural initial conditions as well…
    Seems like eternity wont be easily put to rest though.

  • Nicholas

    Incredible post from an Expert in the field–this is why I come to this site :)

    Cheers,

    NM

  • spyder

    I am with Nicholas on this one. This is a great post, that brings the abstractions of cosmological theories into language constructs that make them accessible and understandable to the laymen, such as myself. What a great read to ponder some of the imagineering ponderables. Thanks Sean!!! I like the notion of the BigRip as you expressed it.

    “”And of course Jennie Chen and I have been arguing (following the exhortations of Huw Price about the arrow of time) that the far past should look like the far future, only backwards.””

    This makes far too much sense from my philosophical perspective.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Thanks, folks. None of us here is above the occasional bits of flattery, I assure you.

  • Dumb Biologist

    I got thinking about this once, in relation to the potential Big Rip…

    The aptly-named Rip will reportedly even tear atoms apart once it really gets going. I suppose next goes nuclei. So now you’ve just got electrons and nucleons flying apart from each-other. And after that? Supposedly you can’t rip an electron to bits, but you can disrupt a baryon. That said, you can’t get a free quark. Pull them apart and you pump enough energy into the system to make quark-antiquark pairs. Try to pull a meson apart, and you just get more mesons.

    Perhaps I’m wrong, but it seems to me that, insead of space approaching a total vacuum during the rip, it might become filled with mesons, as their numbers should blow up during the phase when even hadrons of one form or another feel the Rip. In that case, could it be that the “dark energy” stretching space would get converted into quarks and gluons, which, being ordinary matter/energy, would try to curve space negatively, not positively like quintessence? Would the Rip poop itself out this way? Seems if you really can’t isolate a quark, period, then the Rip might smack into quark confinement at some point, and then…well, I have the foggiest clue what then.

    I dunno, just a thought.

  • http://countiblis.blogspot.com Count Iblis

    Isn’t it to be expected that the universe on ultra large scales is (statistically) stationary?

  • Dumb Biologist

    Whoops, you get the Big Rip with “phantom energy” not “quintessence”…I DID read the post, I swear, and I liked it a lot too.

  • James Graber

    Amazing paper on Astro-ph tonight, astro-ph/0601581.
    If this is true, I think it’s game over for dark matter, MOND wins.
    I appologize for putting this dark matter comment in a dark energy thread,
    but I think this result is too important to ignore.
    Jim Graber

  • Aaron Bergman

    This “First Crisis in Cosmology” conference doesn’t lend itself towards confidence, at least based on a quick googling.

    I also found this paper responding to an earlier paper of the authors. Not my field, though.

  • Science dragon

    Einstein’s relative conclusions only present a barrier not a limit. The effects of light, time and space around a black hole prove this. Just as the sound barrier was broken the light barrier is continually broken. Mass driven through a black hole is projected at different past light speeds. It is my hypothesis that although at the speed of light, mass becomes infinite, mass traveling faster doesn’t. Just as we have little clue as to the nature of dark mass besides it’s weight. It could be regular mass traveling at some positive and negative multiple harmonic of speeds far beyond light. Because of our inability to see things beyond this barrier called light, mass manifests itself as dark, at least to us.

  • James Graber

    Hi Aaron,
    Not really my field either, but close to it.
    All three authors at ESO, which impresses me.
    Also over 25 papers each, some with fairly famous coauthors.
    Further, they say further cases are being tested.
    I said, “if it is true”, and it needs to be confirmed,
    but the current evidence looks pretty persuasive to me,
    YMMV.
    The real clincher is the coincident numeric value of the flattening.
    First Zwicky and clusters, then Rubin and spirals, now globular clusters.
    Jim

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    DB (#7): this is a hard question, actually. You would need to do some quantum field theory in the dramatically curved spacetime of the Big Rip to figure out what precisely happens to bound states of quarks. But it likely wouldn’t “slow down” the acceleration in any way, although we can’t say for sure without a reliable theory of the dark energy.

    Count Iblis: I’m not sure what’s “expected.” In some models of eternal inflation, the relative abundance of certain phases of spacetime should approach an equilibrium distribution. But this is far outside what we really understand at this point.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    James: that’s an interesting paper, although the link Aaron found tends to cast serious doubt on the conclusions. You should know, though, that both galaxy clusters and the CMB provide strong evidence against MOND-like theories (something I hope to post about someday…). Even MOND supporters admit that you need dark matter to make sense of clusters. See a talk I gave here: http://pancake.uchicago.edu/~carroll/talks/mond05/ .

  • Indiana Jones

    Okay, so this is something I don’t understand. When you say “the super-accelerated expansion of spacetime exerts a stretching force on all the galaxies, stars, and atoms in the universe”, how is it the expansion of spacetime has any effect on bound objects? Do the force carriers get redshifted by the expansion? Doesn’t this mean that (say) the ground state of hydrogen is different depending on the expansion rate of the universe? thanks for tolerating my ignorance.

  • Dumb Biologist

    Thanks for the answer!

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Indiana– depends on what is causing the expansion. In an ordinary universe made of matter, here in the Solar System the expansion is precisely zero, and there’s no effect, not even an infinitesimal one. But if there is dark energy, it’s probably here even in the Solar System, and yes indeed the ground-state energy of hydrogen is just a bit different. Spacetime is accelerating even locally, and that exerts a tidal force on all the objects in spacetime. Completely unobservable in practice, but it would become important if we were to approach a Big Rip.

  • http://opiniondominion.blogspot.com Steve W

    No mention of Frank Tipler’s Omega Point ideas in this thread yet, which is a pity. I found recently that the apparent acceleration of the expansion of the universe has not caused him to give up on the idea (that the Universe will eventually contract into a big crunch guided by super evolved intelligence of the future that is effectively the same as “God”.) See the interview here: http://transhumanism.org/index.php/th/more/312/

    I assume that maybe 90% of cosmologists think his ideas are just nuts. His papers are very hard for a layman like me to follow (as indeed was much of “The Physics of Immortality”,) but I get the feeling that some of his basic ideas behind the wilder speculations are more ignored than contested. Any comments?

  • http://eskesthai.blogspot.com/2006/01/drawing-venn-diagram-entanglement.html Plato

    Cyclical processes had to make sense in the over all picture and drawing to a close this “whole process” has to have geometrical inclinations housed in different regions of our universe, to propell further dark energy productions.

    Is this right?


    If held to current technologies and pre producable themes held in context of our cosmo, can we take such levels of “dark energy production” to be from the cause of strange quark productions?

  • Paul Valletta

    There are so many if’s and but’s?.. but what has been known for some time is, that if the future has some point, where the total MATTER content, is not comprable to the total SPACE content of the then Universe, then all of matter will be dynamically guided and acted upon by the Vacuum of space.

    Its the reverse of Einsteins Field Equations, and consequently leads to a very high rate of dimensional flatness?

    Matter tells space which way to curve?

    In one of sean’s collaborated papers, he deals with the problem thus, the future of Time’s Arrow evolves into a singularity, that could be detached from its past, at a LATE cut-off time.

    The big-rip, which is in the future, but can also have an history pertaining to a cyclic past, Big-Bang>>Big-Crunch>>Big-Rip>>Big-Crunch…

    What is not known is the make-up of the Spacetime/Vacuum ratio? If all of Spacetime is being acted upon by Dark Energy emminating from the Vacuum, then all of matter will, in the future, be constrained into a density that cannot allow structure to communicate by visible energy, all of radiative energy will lose its ability to communicate from Atom to Atom with Photons that is.

    From an observers point of view, that is looking out into the cosmos, we would NOT see light from our Galactic neigbours(the expansion of Dark Energy would be forcing Galaxies apart exponentionally).

    It would appear to us(at a time of first evidence) that all Galactic Blackholes, would be taking in local light at an increased rate.

    Visable Energy would be offset by the Dark Energy, and theoretically, the Dark Energy would be in effect, PUMPING energy into Galactic Blackholes(Because this is where all of 3-D matter occurs) to such a rate that there occurs a change in Phase, a Collapse of Spacetime.

    Where this is the Singularity of an eventual future civilization, is where the Cyclic models come into their own.

    To eleviate any fears, the very first sight of evidence of an oncoming, big-rip/big-bang/big-crunch, would still be of the order of magnitude wherby our everyday lives would not be effected in any way at all, except philosophically.

    Some see it like this:
    http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?1995ApJ%2E%2E%2E445%2E%2E%2E%2E7R&nosetcookie=1Vacuum%20Zero-Point-Field%20Pressure

    but is this Zero Point Energy another way of stating singularity?

  • http://eskesthai.blogspot.com/2006/01/drawing-venn-diagram-entanglement.html Plato

    Paul,

    but is this Zero Point Energy another way of stating singularity?

    IN context of the “quantum harmonic oscillator,” you would have to make certain deductions about how you interpret that?

    Is the universe never ever really flat? :)

  • Paul Valletta

    The dynamic condition of the Universe is calibrated by its dimensionality? Flat=2-D..Curved=3-D a mix of both is where exchange and interactions occur?

    I have no doubt that the blackhole at our Galactic core, plays an important part in protecting/sheilding my atomic structure, if there is a future of Big-Rip, Iam certain I would not feel a thing!

    The Universe varies in Time, not all “times” are equivilent.

  • http://eskesthai.blogspot.com/2006/01/spacetime-101.html Plato

    The dynamic condition of the Universe is calibrated by its dimensionality?

    Do You mean, degrees of freedom?

    People are afraid to approach this subject?

    ASa layman this perspective is troubling, since it is not fully understood.


    In physics, the fifth dimension is a hypothetical dimension which would exist at a right angle to the fourth dimension

    If the “debate” is held, would this help move the ideas in context of Sean posts ahead for consideration? I dunno:)

  • Jim

    “The point is, observations of the past and present are never by themselves sufficient to predict the future. That can only be done within the framework of a theory in which we have confidence.”

    I’d say the same could be said about inferring the past as well as predicting the future, which is why I find the usual retorts of scientists to the creationist/ID/… types (on this site and others) so hollow. Many of these people basically don’t believe that the same scientific laws held X thousand years ago. And of course it’s impossible to disprove that, or even the statement that God snapped his fingers and created the universe at noon yesterday. So it seems to me that really the only way of countering is by philosophically out-flanking them: You can believe whatever you want, but I’ll be better at finding diamonds in the ground, curing diseases, … because I’m going to use standard theories of geology, evolution, … And then tell them that they can still apply these theories successfully without believing that they’re ‘really’ true, only that they ‘appear’ to be true.

    I feel like I’m committing a double sin by posting an mostly off-topic tautology, but I think I’ve seen objections on this site to the point of view behind what I just wrote and the remark I quoted above, and I didn’t want to let the moment go without saying something.

    Great post, by the way.

  • http://eskesthai.blogspot.com/2006/01/spacetime-101.html Plato

    ….or look at current experimental processes…..how you got there.:)

    For such wide speculation on the stringevangislistic views, it is not done without recognizing experimental basis, like a everyone saids, “does not exist.”

    They never considered how they might handle it in extra dimensions, and such. It is just called a fantasy for some so a “real debate” is needed by the experts to help us lay people contend with letting our minds run amuck.:).

    Maybe that’s an Edge question that John Brockman could handle?

  • Indiana Jones

    thanks for clearing that up Sean!

  • Shantanu

    Sorry again to change the subject., talking about provocative papers (since Jim
    mentioned astro-ph/0601581), Sean (and others) any comments on gr-qc/0511160?
    (however it hasn’t yet been published).

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Shantanu is referring to http://arxiv.org/abs/gr-qc/0511160, “Indications for a preferred reference frame from an ether-drift experiment.” Like any other completely unexpected and difficult-to-explain experimental result, I would advise waiting to see if anyone can confirm it.

  • http://feynman137.tripod.com/ Science

    What I want to know is how a paper got on to arXiv.org with ether in the title? They deleted my paper in 2002 and I had to change the title to get it on CERN doc server.

  • http://countiblis.blogspot.com Count Iblis

    Science, if they deleted your paper from the arXiv, then that speaks volumes about the content of your paper. :)

  • http://feynman137.tripod.com/ Science

    They didn’t have time to read it, which speaks volumes about you. ;)

  • http://feynman137.tripod.com/ Science

    Sent: 02/01/03 17:47
    Subject: Your_manuscript LZ8276 Cook
    {MECHANISM OF GRAVITY}
    Physical Review Letters does not, in general, publish papers on alternatives to currently accepted theories…. Yours sincerely, Stanley G. Brown, Editor, Physical Review Letters

    ‘… the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new. This coolness arises partly from fear of the opponents, who have the laws on their side, and partly from the incredulity of men, who do not readily believe in new things until they have had a long experience of them. Thus it happens that whenever those who are hostile have the opportunity to attack they do it like partisans, whilst the others defend lukewarmly…’ – http://www.constitution.org/mac/prince06.htm

    ‘(1). The idea is nonsense. (2). Somebody thought of it before you did. (3). We believed it all the time.’ – Professor R.A. Lyttleton’s summary of inexcusable censorship (quoted by Sir Fred Hoyle in ‘Home is Where the Wind Blows’ Oxford University Press, 1997, p154).

  • http://feynman137.tripod.com/ Science

    1. Feynman diagrams, the physics behind the maths of quantum field theory, show that forces arise from the exchange of gauge bosons (coming from distances at light speed, hence coming from times in the past).

    2. The big bang mass has an increasing speed, in our observable spacetime, from 0 toward speed of light c with times past of 0 toward 15 billion years (or distances of 0 to 15 billion light-years), giving outward force by Newton’s 2nd empirically based law: F = ma = m.dv/dt = m(c – 0) / (age of universe) = mcH, where H is Hubble’s constant (based on v = HR, where R is distance).

    3. Newton’s 3rd empirically based law suggests equal inward implosion force, carried by gauge bosons, which shielded by mass, proves gravity and electromagnetism to within 1.65% (proof below). This mechanism also predicts particle masses and other observables, and eliminates most of the unobserved ‘dark matter’ speculation and the need for a cosmological constant / dark energy (the latest data suggest that the ‘cosmological constant’ and dark energy epicycle would need to vary with time!

    These are all existing accepted facts; the Feynman diagrams are widely accepted, as is the spacetime, the big bang, Newton’s laws of motion. The result, that apples fall at the measured acceleration, is apparently ‘only a personal pet theory that should be suppressed from arXiv.org and ignored’. Drs Lee Smolin and Peter Woit could sit under an apple tree to verify that existing ‘string theory’ gravity is ‘speculative gibberish': it is an effort to destroy science using untestable hocus pocus ‘string theory’!

    Update: Lee Smolin has now kindly acknowledged the possibility of using this type of argument (that quantum field theory gauge boson exchange process predicts magnetic moments and Lamb shift, so an attempt to unify the spacetime fabric with Feynman path integrals is an empirically defendable physical reality, unlike ‘string theory’ speculation). This applies for some kind of spin foam vacuum in loop quantum gravity, as mentioned on Peter Woit’s blog. Smolin is committed to the very difficult mathematical approach, but was decent enough say:

    Nigel Says: January 14th, 2006 at 2:18 pm

    Some kind of loop quantum gravity is going to be the right theory, since it is a spin foam vacuum. People at present are obsessed with the particles that string theory deals with, to the exclusion of the force mediating vacuum. Once prejudices are overcome, proper funding of LQG should produce results.

    Lee Smolin Says: January 14th, 2006 at 4:41 pm

    … Thanks also to Nigel for those supporting comments. Of course more support will lead to more results, but I would stress that I don’t care nearly as much that LQG gets more support as that young people are rewarded for taking the risk to develop new ideas and proposals. To go from a situation where a young person’s career was tied to string theory to one in which it was tied to LQG would not be good enough. Instead, what is needed overall is that support for young scientists is not tied to their loyalty to particular research programs set out by we older people decades ago, but rather is on the basis only of the quality of their own ideas and work as well as their intellectual independence. If young people were in a situation where they knew they were to be supported based on their ability to invent and develop new ideas, and were discounted for working on older ideas, then they would themselves choose the most promising ideas and directions. I suspect that science has slowed down these last three decades partly as a result of a reduced level of intellectual and creative independence avaialble to young people.

    Thanks,
    Lee

  • machs

    This guy right here used Occam’s Razor and came up with a simple and elegant model of tthe accelerating universe. Check it out.

  • Tasmania

    Sean said
    “First explored by Robert R. Caldwell, Marc Kamionkowski, and Nevin
    Weinberg”….
    No, it wasn’t first explored by these gentlemen. See for example

    http://arxiv.org/abs/hep-th/0112066

    Which, in fact, they cite. Note too [from this paper] that phantom
    cosmologies *do not* have to be singular.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    My mistake; fixed.

  • Kate

    I was describing this post to my roommate, to relate to her my favorite quote in it:

    the far past should look like the far future, only backwards.

    Quoth my roommate: “And in heels.”

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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