Guest Post: Max Tegmark on Cosmic Inflation

Max TegmarkMost readers will doubtless be familiar with Max Tegmark, the MIT cosmologist who successfully balances down-and-dirty data analysis of large-scale structure and the microwave background with more speculative big-picture ideas about quantum mechanics and the nature of reality. Max has a new book out — Our Mathematical Universe: My Quest for the Ultimate Nature of Reality — in which he takes the reader on a journey from atoms and the solar system to a many-layered multiverse.

In the wake of the recent results indicating gravitational waves in the cosmic microwave background, here Max delves into the idea of inflation — what it really does, and what some of the implications are.


Thanks to the relentless efforts of the BICEP2 team during balmy -100F half-year-long nights at the South Pole, inflation has for the first time become not only something economists worry about, but also a theory for our cosmic origins that’s really hard to dismiss. As Sean has reported here on this blog, the implications are huge. Of course we need independent confirmation of the BICEP2 results before uncorking the champagne, but in the mean time, we’re forced to take quite seriously that everything in our observable universe was once smaller than a billionth the size of a proton, containing less mass than an apple, and doubled its size at least 80 times, once every hundredth of a trillionth of a trillionth of a trillionth of a second, until it was more massive than our entire observable universe.

We still don’t know what, if anything, came before inflation, but this is nonetheless a huge step forward in understanding our cosmic origins. Without inflation, we had to explain why there were over a million trillion trillion trillion trillion kilograms of stuff in existence, carefully arranged to be almost perfectly uniform while flying apart at huge speeds that were fine-tuned to 24 decimal places. The traditional answer in the textbooks was that we had no clue why things started out this way, and should simply assume it. Inflation puts the “bang” into our Big Bang by providing a physical mechanism for creating all those kilograms and even explains why they were expanding in such a special way. The amount of mass needed to get inflation started is less than that in an apple, so even though inflation doesn’t explain the origin of everything, there’s a lot less stuff left to explain the origin of.

If we take inflation seriously, then we need to stop saying that inflation happened shortly after our Big Bang, because it happened before it, creating it. It is inappropriate to define our Hot Big Bang as the beginning of time, because we don’t know whether time actually had a beginning, and because the early stages of inflation were neither strikingly hot nor big nor much of a bang. As that tiny speck of inflating substance doubled its diameter 80 times, the velocities with which its parts were flying away from one another increased by the same factor 2^80. Its volume increased by that factor cubed, i.e., 2^240, and so did its mass, since its density remained approximately constant. The temperature of any particles left over from before inflation soon dropped to near zero, with the only remaining heat coming from same Hawking/Unruh quantum fluctuations that generated the gravitational waves.

Taken together, this in my opinion means that the early stages of inflation are better thought of not as a Hot Big Bang but as a Cold Little Swoosh, because at that time our universe was not that hot (getting a thousand times hotter once inflation ended), not that big (less massive than an apple and less than a billionth of the size of a proton) and not much of a bang (with expansion velocities a trillion trillion times slower than after inflation). In other words, a Hot Big Bang did not precede and cause inflation. Instead, a Cold Little Swoosh preceded and caused our Hot Big Bang.

Since the BICEP2 breakthrough is generating such huge interest in inflation, I’ve decided to post my entire book chapter on inflation here so that you can get an up-to-date and self-contained account of what it’s all about. Here are some of the questions answered:

  • What does the theory of inflation really predict?
  • What physics does it assume?
  • Doesn’t creation of the matter around us from almost nothing violate energy conservation?
  • How could an infinite space get created in a finite time?
  • How is this linked to the BICEP2 signal?
  • What remarkable prize did Alan Guth win in 2005?
This entry was posted in Guest Post, Science. Bookmark the permalink.

51 Responses to Guest Post: Max Tegmark on Cosmic Inflation

  1. kashyap Vasavada says:

    Max: My understanding is that BICEP2 ( assuming it is correct) shows that one can get by with classical general relativity and quantum field theory , separately, until about 10^16 GeV. But it seems that some prominent physicists like Guth and Wilczek are saying that it proves quantum gravity. What is your opinion? In what sense it says anything about QG and perhaps string theory?

  2. Max Tegmark says:

    Good question, Kashyap. The point is that the BICEP2 signal is due to quantum fluctuations not in any old quantum field, but in the *gravitational* field, which proves that gravity is in fact quantized. Most researchers had of course assumed this to be the case, but it’s important to test our assumptions, and this is the first experimental evidence of this fact. So now we know that there is in fact such a thing as quantum gravity.

  3. John Gordon says:

    The only Google hits today on “Hawking/Unruh quantum fluctuations” are to this article. Is this a new term? Can you explain relationship of those quantized gravity fluctuations to Hawking and Unruh?

  4. Nice article. 🙂

    I am one of those alternative-opinion voices that Sean has so-far allowed to comment in his interesting Blog.

    I was surprised when problems were openly recognized with the Big Bang model that eventually led to the Inflation Hypothesis since the problems of “Flatness” and “Horizon” were just a couple of the recognized problems at that time that Inflation tried to fix.

    The biggest of these remaining problems with the model, in my opinion, is the observed density of the universe. As far back as we can see the universe appears to have the same density, or appears to have less density, than the close-by universe. In an expanding universe model the past density of the universe should have been greater. After Inflation, expansion was somewhat consistent, according to theory, therefore such increased densities (looking backward in time) should be observable. Considering an average expansion rate of the universe, for instance, 7 billion years ago the universe should accordingly have had 8 times the present observed density based upon the volume of an expanding sphere or other expanding 3D volume. To my knowledge nobody has ever made such an observational claim.

    Dark Matter and Dark Energy are also ad hoc explanations to keep the BB model aligned with observations that would otherwise contradict the model’s physics.

    I do like the way this article is written and its use of such qualifying words such as “in my opinion,” “assumptions,” etc. Sean uses such qualifying words and phrases also, to his credit, which I think are very appropriate for a blog, but even for a technical paper where needed.

    regards Forrest

  5. Max Tegmark says:

    Here you go, John: http://en.wikipedia.org/wiki/Unruh_effect
    Stephen Hawking realized that black holes evaporate, because quantum fluctuations cause radiation to emerge from its event horizon. Bill Unruh realized that analogous radiation emerges from *any* event horizon, not merely the kind surrounding black holes. During inflation, you have an event horizon around you that you find yourself inside, and the Unruh radiation from it includes the gravitational waves seen by BICEP2.

  6. Agron says:

    You know what? If you accept the origin of universe from the tiny elementary particle, which after big banged that means that you put yourself in the role of God. So you are the God that created universe. That’s to create the model of universe as you wish. The technology on Earth is not able to find out where the Boing 370 with 229 people on board (Malaysian Airline) disappeared here on Earth, which is a tiny particle of universe, instead you are talking for the existence of Big Bang and universe inflation. The creation of universe from nothing. This is what religion says. The same as you predict, but you sophisticate things with allegedly math and physics, while the religion tells such bull sheet through predictions.

  7. Pingback: Congratulations, you are a Science Nerd

  8. Nick says:

    Hi,

    I read the article, it was very interesting.

    But my question would be, is the theory of eternal inflation almost certain to be true if inflation is true? Are there models of inflation without internal inflation?

    In other words have we discovered the origin of the universe??

    Thank you,
    Nick

  9. MeOldChina says:

    Squeezing an infinite amount of space into a finite space is a neat trick!

    Are we causally connected to the other volumes of space kicked off by other inflation ending events? Are we screened off by our event horizon or can the radiation coming off that horizon carry information about them?

    Would these other volumes of space have the same fundamental parameters as ours?

    Can we possibly tell, and would it be interesting to know, which generation of inflation decays our local volume of space came from?

    Cheers!

  10. Max Tegmark says:

    Hi Nick,
    > is the theory of eternal inflation almost certain to be true if inflation is true?
    As I explain in the chapter (linked above), Alex Vilenkin and others have shown that inflation is generically eternal, in the sense that that’s what typical inflation models predict. The basic reason is that for inflation to work in the first place, the amount of inflating substance has to double faster than its half-life (the time it takes half of it to stop inflating), so the total volume of inflating stuff just keeps growing forever.

    > have we discovered the origin of the universe?
    No: We’ve discovered what caused our Big Bang, but we still haven’t figured out what, if anything, caused inflation to start.

  11. Gordon D. Munro says:

    Among “elite” theoretical physicists what percentage still believe “mutiversality” of any kind is “not even wrong?”

  12. Max Tegmark says:

    Squeezing an infinite amount of space into a finite space is a neat trick!

    Hi MeOldChina,

    > Are we causally connected to the other volumes of space kicked
    > off by other inflation ending events?
    No, we’re no longer causally connected to those other volumes, because space between here and there is still inflating, stretching faster than we could ever pass through them.

    > Would these other volumes of space have the same
    > fundamental parameters as ours?
    Inflation alone can’t answer that question. It depends on whether the fundamental theory of physics, whatever it is (string theory, loop quantum gravity, something we haven’t yet thought of, etc.) has one or more solutions for homogeneous space. If it has many solutions (like the equations governing homogeneous water has the three solutions ice, steam and liquid), then inflation will create volumes realizing each of these solutions, and some parameters describing measurable properties can then differ. If there’s only one solution, then the parameters will be the same everywhere.

  13. Ben Goren says:

    Max,

    Thanks much for taking the time to help us mere mortals get a better understanding of this amazing Cosmos we happen to find ourselves in.

    This would seem to be a good place to ask a couple questions I’ve been wondering about. I haven’t yet read the book excerpt, so feel free to tell me to just go read it if you’ve already answered these there.

    First, it seems to me that, especially with the Fermi-LAT (yet-to-be-confirmed) discovery of ~35 GeV WIMPs, we now have all the major empirical pieces of the puzzle that were missing just a short while ago: the Higgs, quantum gravity, inflation, and dark matter — and with specific value ranges (some very precise, others not so) for all. What, if anything else, do you theorists need from the experimentalists to finally crack the big nuts of quantum gravity, cosmogenesis, and perhaps a GUT? (And quite likely, of course, they’re a package deal.) Are you making any bets on when those will be solved?

    Next…well, without even reaching for the envelope, it would seem to be safe to suggest that the Schwarzschild Radius of the mass of the entire universe is just a wee bit larger than the radius of our own Sun (which is what I get from that envelope as the initial conditions of the post-Inflation Big Bang). I’m guessing that the obvious types of confusion that would naïvely arise from this sort of observation mostly don’t apply. For example, it seems clear that you can’t use the same approach to describe the Universe as an whole as you would to stuff within it, and I think you’ve already indicated that Inflation is an ongoing process, continuing to this day. Still, could you perhaps spare a moment or two to elaborate on what it means for so massive a Universe to be so small, and how that differs from compressing parts of the universe to such densities today?

    Thanks again!

    b&

  14. Nick says:

    “Hi Nick,
    > is the theory of eternal inflation almost certain to be true if inflation is true?
    As I explain in the chapter (linked above), Alex Vilenkin and others have shown that inflation is generically eternal, in the sense that that’s what typical inflation models predict. The basic reason is that for inflation to work in the first place, the amount of inflating substance has to double faster than its half-life (the time it takes half of it to stop inflating), so the total volume of inflating stuff just keeps growing forever.

    > have we discovered the origin of the universe?
    No: We’ve discovered what caused our Big Bang, but we still haven’t figured out what, if anything, caused inflation to start.

    Thank you for the explanation Doctor Tegmark.

    I was wondering because I had heard Lawrence Krauss say that the universe may have started from absolutely nothing, yet with an inflation. If I understand correctly what Krauss says, he is talking about just our universe, not an eternally inflationary universe.

    I don’t know whether Lawrence Krauss’s ideas could be relevent to explain the start of an eternal inflation.

    Nick.

  15. MeOldChina says:

    Hi Max,

    Thanks for the response.

    So, the quantum fluctuations give rise to volumes with slightly different initial conditions, differences that then get amplified, but does eternal inflation predict the different volumes of space all initially having low entropy, like own observable region? If so, is this because the initial inflationary patch is low entropy?

    Cheers!

  16. Antonio Sanchez says:

    Max, many thanks for sharing the chapter of your new book. I am going to buy it and read it anyway. As you mentioned in several interviews, I agree that math, laws, physical patterns… are not just useful tools to describe reality, they constitute reality itself.

  17. Pingback: Max Tegmark posts his chapter on cosmic inflation online | SelfAwarePatterns

  18. @Forrest: “As far back as we can see the universe appears to have the same density, or appears to have less density, than the close-by universe. “

    Simply not true. No-one claims this, except you, as far as I know.

  19. @Ben Goren: “it would seem to be safe to suggest that the Schwarzschild Radius of the mass of the entire universe is just a wee bit larger than the radius of our own Sun”

    Why?

  20. Ben Goren says:

    Phillip, the Schwarzschild Radius of Sagittarius A* is about a tenth of an AU, more than an order of magnitude bigger than the Sun’s radius and about a third of the way to Mercury’s orbit. I don’t think I need a calculator to know that the mass of an hundred billion such black holes plus all the visible matter is going to have just a wee bit larger Schwarzschild Radius still.

    Cheers,

    b&

  21. UncleMonty says:

    Max, thanks – a couple of things clicked for me that never clicked before, when reading your chapter. Could you tell me, if inflation is still going on in some regions of the universe, and if during inflation the density of the initial blob does in fact get smeared out a little with each doubling, then when inflation ends in those regions will they necessarily have very different properties from ours because the ur-stuff had time to get more diluted before inflation came to an end? Or is it thought instead that the “trigger” for inflation coming to an end occurs when the density is sufficiently smeared out, so that in fact all regions will be similar when their own “hot big bang” begins–they just took a different amount of time during inflation to reach that critical density?

  22. ” I don’t think I need a calculator to know that the mass of an hundred billion such black holes plus all the visible matter is going to have just a wee bit larger Schwarzschild Radius still.”

    Right. So what is the point of your original comment?

  23. Ben Goren says:

    Phillip, my point was that, at least naïvely, it would seem that the Universe is a black hole. And pursuing that line with similarly naïve reasoning leads to questions such as, “If we’re in a supermassive black hole, why haven’t we been crushed into oblivion?”

    As I noted in my original question, that’s clearly not the way things actually are and the naïve approach fails spectacularly. I was hoping Max or Sean or somebody could expand upon why that should be so.

    Cheers,

    b&

  24. Joan Hendricks says:

    Dr. Tegmark, Thank you for this blog. I read all of the Chapter 5 you included the link to. Reading that chapter almost blows my mind. It seems very different from other things I have read about the Big Bang. Significantly, the Big Bang after inflation. Positive and negative gravity sound like the ultimate perpetual motion machine if we could capture that energy. And, you are writing this without detailed mathematical formulas that I probably couldn’t comprehend.

    Guess I’d better get your book and not be satisfied with just one chapter!

  25. @Ben Goren:

    The universe is not a black hole. A black hole is a static solution of Einstein’s equation in a background metric while the universe is expanding and has no background as such. Yes, if you plug in the numbers, the radius of curvature of the universe is of the order of its Schwarzschild radius, but that is essentially just dimensional analysis.

    However, even if we were inside a large black hole, we wouldn’t necessarily be crushed to oblivion (although, in the context of GR, it is inevitable that someday we will be). The larger the mass of a black hole, the larger the radius and the lower the density. With a really large black hole, one wouldn’t even notice crossing the horizon.

    I still don’t get why you equate the Schwarzschild radius of the Sun with that of the universe.