The Lopsided Universe

By Sean Carroll | June 8, 2008 2:55 pm

Here’s a new paper of mine, with Adrienne Erickcek and Mark Kamionkowski:

A Hemispherical Power Asymmetry from Inflation

Abstract: Measurements of temperature fluctuations by the Wilkinson Microwave Anisotropy Probe (WMAP) indicate that the fluctuation amplitude in one half of the sky differs from the amplitude in the other half. We show that such an asymmetry cannot be generated during single-field slow-roll inflation without violating constraints to the homogeneity of the Universe. In contrast, a multi-field inflationary theory, the curvaton model, can produce this power asymmetry without violating the homogeneity constraint. The mechanism requires the introduction of a large-amplitude superhorizon perturbation to the curvaton field, possibly a pre-inflationary remnant or a superhorizon curvaton-web structure. The model makes several predictions, including non-Gaussianity and modifications to the inflationary consistency relation, that will be tested with forthcoming CMB experiments.

The goal here is to try to explain a curious feature in the cosmic microwave background that has been noted by Hans Kristian Eriksen and collaborators: it’s lopsided. We all (all my friends, anyway) have seen the pretty pictures from the WMAP satellite, showing the 1-part-in-100,000 fluctuations in the temperature of the CMB from place to place in the sky. These fluctuations are understandably a focus of a great deal of contemporary cosmological research, as (1) they arise from density perturbations that grow under the influence of gravity into galaxies and large-scale structure in the universe today, and (2) they appear to be primordial, and may have arisen from a period of inflation in the very early universe. Remarkably, from just a tiny set of parameters we can explain just about everything we observe in the universe on large scales.

The lopsidedness I’m referring to is different from the so-called axis of evil. The latter (in a cosmological context) refers to an apparent alignment of the temperature fluctuations on very large scales, which purportedly pick out a preferred plane in the sky (suspiciously close to the plane of the ecliptic). The lopsidedness is a different effect, in which the overall amplitude of fluctuations is a bit different (just 10% or so) in one direction on the sky than in the other. (A “hemispherical power asymmetry,” if you like.)

What we’re talking about is illustrated in these two simulations kindly provided by Hans Kristian Eriksen.

Untilted CMB

Tilted CMB

I know, they look almost the same. But if you peer closely, you will see that the bottom one is the lopsided one — the overall contrast (representing temperature fluctuations) is a bit higher on the left than on the right, while in the untilted image at the top they are (statistically) equal. (The lower image exaggerates the claimed effect in the real universe by a factor of two, just to make it easier to see by eye.)

What could cause such a thing? Our idea was that there was a “supermode” — a fluctuation that varied uniformly across the observable universe, for example if we were sampling a tiny piece of a sinusoidal fluctuation with a wavelength many times the size of our current Hubble radius.

The blue circle is our observable universe, the green curve is the supermode, and the small red squiggles are the local fluctuations that have evolved under the influence of this mode. The point is that the universe is overall just a little bit more dense on one side than the other, so it evolves just slightly differently, and the resulting CMB looks lopsided.

Interestingly, it doesn’t quite work; at least, not in a simple model of inflation driven by a single scalar field. In that case, you can get the power asymmetry, but there is also a substantial temperature anisotropy — the universe is hotter on one side than on the other. There are a few back-and-forth steps in the reasoning that I won’t rehearse here, but at the end of the day you get too much power on very large scales. It’s no fun being a theoretical cosmologist these days, all the data keeps ruling out your good ideas.

But we didn’t give up! It turns out that you can make things work if you have two scalar fields — one that does the inflating, cleverly called the “inflaton,” and the other which is responsible for the density perturbations, which should obviously be called the “perturbon” but for historical reasons is actually called the “curvaton.” By decoupling the source of most of the density in the universe from the source of its perturbations, we have enough wiggle room to make a model that fits the data. But there’s not that much wiggle room, to be honest; we have an allowed region in parameter space that is not too big. That’s good news, as it brings the hope that we can make relatively precise predictions that could be tested by some means other than the CMB.

One interesting feature of this model is that the purported supermode must have originated before the period of inflation that gave rise to the smaller-scale perturbations that we see directly in the CMB. Either it came from earlier inflation, or something entirely pre-inflationary.

So, to make a bit of a segue here, this Wednesday I gave a plenary talk at the summer meeting of the American Astronomical Society in St. Louis. I most discussed the origin of the universe and the arrow of time — I wanted to impress upon people that the origin of the entropy gradient in our everyday environment could be traced back to the Big Bang, and that conventional ideas about inflation did not provide straightforward answers to the problem, and that the Big Bang may not have been the beginning of the universe. I was more interested in stressing that this was a problem we should all be thinking about than pushing any of my favorite answers, but I did mention my paper with Jennie Chen as an example of the kind of thing we should all be looking for.

To an audience of astronomers, talk of baby universes tends to make people nervous, so I wanted to emphasize that (1) it was all very speculative, and (2) even though we don’t currently know how to connect ideas about the multiverse to observable phenomena, there’s no reason to think that it’s impossible in principle, and the whole enterprise really is respectable science. (If only they had all seen my bloggingheads dialogue with John Horgan, I wouldn’t have had to bother.) So I mentioned two different ideas that are currently on the market for ways in which influences of a larger multiverse might show up within our own. One is the idea of colliding bubbles, pursued by Aguirre, Johnson, and Shomer and by Chang, Kleban, and Levi. And the other, of course, was the lopsided-universe idea, since our paper had just appeared the day before. Neither of these possibilities, I was careful to say, applies directly to the arrow-of-time scenario I had just discussed; the point was just that all of these ideas are quite young and ill-formed, and we will have to do quite a bit more work before we can say for sure whether the multiverse is of any help in explaining the arrow of time, and whether we live in the kind of multiverse that might leave observable signatures in our local region. That’s research for you; we don’t know the answers ahead of time.

One of the people in the audience was Chris Lintott, who wrote up a description for the BBC. Admittedly, this is difficult stuff to get all straight the very first time, but I think his article gives the impression that there is a much more direct connection between my arrow-of-time work and our recent paper on the lopsided universe. In particular, there is no necessary connection between the existence of a supermode and the idea that our universe “bubbled off” from a pre-existing spacetime. (There might be a connection, but it is not a necessary one.) If you look through the paper, there’s nothing in there about entropy or the multiverse or any of that; we’re really motivated by trying to explain an interesting feature of the CMB data. Nevertheless, our proposed solution does hint at things that happened before the period of inflation that set up the conditions within our observable patch. These two pieces of research are not of a piece, but they both play a part in a larger story — attempting to understand the low entropy of the early universe suggests the need for something that came before, and it’s good to be reminded that we don’t yet know whether stuff that came before might have left some observable imprint on what we see around us today. Larger stories are what we’re all about.

  • Alison Kemper

    I read about this on the BBC website and was extremely thrilled.

    Who knew that anisotropy would become one of the most important concepts in our scientific array?

    As well, the research features a remarkable young woman, Adrienne Erickcek. How on earth can anyone so young be so very accomplished?

  • Pingback: Not Even Wrong » Blog Archive » Hints of ‘time before Big Bang’()

  • Sam Cox


    This is just excellent! I heartily agree that if a multiverse, or phylogenically developing repeating similarverse exists, we WILL be able to detect it.

    The math has been around for years. Some pretty direct evidence (mass distribution) not related to the CMB is available and we understand the engineering necessities related to the existence of complex information and structure in the universe. Considering these circumstances, the fact the the CMB contains evidence for possible pre- big bang existence should really not be a surprise at all.

    You are not ready to be assertive about the connection of this CMB observation and your work on time direction and process, and it is easy to understand why…it is much too early to make speculative assertions.

    Still, for the reasons I listed above, I believe personally that the nature of time process in the universe is linked to this observation and its pre-big bang implications…

    Very Exciting!

  • Pingback: Chris Lintott’s Universe » In his own words()

  • grbiersema

    It’s good to note though that the claimed hemispherical asymmetry is not yet convincingly
    statistically signitficant. Eriksen et al point that caveat out quite nicely in their paper – the significance is 99 percent, which is simply not very convincing yet.
    To convince an observational astronomer like me (I have seen my fair share of 3 sigma results that failed to materialize with better datasets), it will probably take the Planck dataset; or a
    more thorough foreground-analysis of the WMAP data.

  • Hiranya

    Hi Sean,

    I was really taken aback by this BBC article saying that you claimed a connection between a large scale asymmetry and testing the “multiverse”! Perhaps there is some very tenuous connection to what happened before inflation but nothing like what is implied in that article. Your post has made things a bit clearer.

    By the way (in case some readers are interested in some background), the idea of a spontaneous breaking of isotropy by a “supermode” was first proposed by Chris Gordon et al (here and here). The difficulty with testing such ideas lies not only with the low significance of the observation, but the a posteriori nature of the way that significance was inferred.

    Fortunately, if the temperature anisotropy is indeed telling us that there is an asymmetry, it makes a prediction for the polarization pattern of the microwave background anisotropies. Cora Dvorkin, a grad student at Chicago, did some nice work last year which shows how we can test whether this observation is telling us that there is a significant anomaly in the first place. This can be applied to much better polarization data that’s coming in the next couple of years.

    The larger stories draw in the crowds, but sometimes its nice to mention the smaller stories, the careful studies that sort out the wheat from the chaff of observations, because it’s on the basis of these analyses that the big ideas live or die.


  • Sean

    The extra field certainly participates in re-heating, and contributes to the local density; that’s where perturbations come from. No affect on nucleosynthesis, as everything is completely thermalized long before you get there.

    Hiranya, thanks, I should have done a better job of referring to the earlier work in the blog post. They are referenced in the paper, but even there we were up against a word limit and didn’t go into any detail. Chris’s work is certainly right on topic; we went further in connecting the supermode to inflation.

  • Mike

    I’ll take care to look at your paper later. For the moment, are you saying that this “lop-sidedness” cannot be explained by Gaussian statistics? What I mean is, if I ask two people to flip a coin 100 times, I’m not surprised if one gets heads 10% more frequently than the other one (in fact, I think the differences will typically be larger than that… but of course this relates to whether we flip the coin 100 times, 1000 times, or 10,000 times… in the latter case I agree a 10% difference is quite an anomoly) .

  • Mike

    Nevermind… I only had to glance at your paper to see my point is addressed in your references.

  • Albatross

    For a fun time, align the two images rotated 90 degrees (either way) on your monitor, then view them 3D ala the “Magic Eye” images. For additional fun, alternate visualizing the image as being convex and concave.

    As for the universe, unless it were to be completely homogenous, wouldn’t it then necessarily be lopsided? Or is the lopsidedness greater than the standard deviation to be expected from a random distribution?

  • Mike

    Albatross (#13): this is what I was getting at in the post above yours, but apparently it has been checked that the difference is statistically significant. An initial concern of mine was, how is this check performed? Sometimes this is harder to do than you’d guess, because its tempting to calculate the probability to obtain a certain imbalance (pointing in a given direction) when really there’s no reason for us to care about one direction more than another, so you should account for the possibility for the imbalance to point in any direction. You can account for this by thinking carefully, but I prefer an empirical approach, where one simply runs a huge number of simulations and sees how many have the peculiar feature one is looking for. From how Sean and his collaborators describe the work they cite, it appears this was done, and anisotropies like what is observed occur in less than 1% of the sample.

  • Sean

    The statistical significance is obviously an important issue. Straightforwardly, it’s a 3-sigma result, which is pretty good if you really think you understand all of the systematic errors. Maybe you don’t, of course. (Certainly they do take into account the fact that you could find an anisotropy in any direction a priori, thus raising the chance of a random effect.) The WMAP folks were skeptical of the initial claim, but the seem to admit that it’s there, even in subsequent years’ data. One of the reasons why it’s important to get explicit theoretical models is that we can then ask what other tests can be done, besides the CMB.

  • Az

    Sean, check your email 😛 or email me at the address here please

  • Sean

    Okay, one last time: we’re not here to discuss Peter, his blog comment policies, his notions of etiquette, or his sex life. I’ve deleted a bunch of things, and will continue to do so, so why bother?

  • Hans Kristian Eriksen

    Just a few comments:

    First of all, as several of you have noted already, the question of statistical significance is of course the over-shadowing question in all of this. And here there are some different schools of thoughts around. On the one hand, if you take a frequentist approach, you simply ask “Given this particular model, how often does the a particular data set have such or such properties?” In this particular case, we would ask “Given that the underlying model is indeed homogeneous and isotropic, how often would we see a *more* asymmetric universe than the one we actually observe?” The answer to this question is easily answered using massive computer simulations, and turns out to be <~ 1%. So it’s not very likely — but it could be due to “bad luck”.

    The other line of thought is the Bayesian approach, in which you rather ask “Given this particular observed data set, which model is more likely?” A common tool to compare such models is the Bayesian evidence, which is nothing but the average likelihood over the prior volume. The nice thing about this is that it implements Occam’s razor in a quantitative approach, and so it addresses Hiranya’s “a-posteriori concerns” in a natural way — if it was just an effect of “noticing something odd in the data”, it would get heavily penalized by the larger prior volume.

    As it turns out, the Bayesian evidence ratio between the anisotropic and the isotropic models comes out to be roughly 6-to-1 in favour of the anisotropic model, even after taking into account “Occam’s razor”, which conventionally is considered “substantial evidence”. It’s not decisive, but it’s most definitely interesting.

    So that’s the current situation regarding statistical significances.

    A second issue concerns systematic errors. In this respect, one is well adviced to be cautious. However, one should also note that a major advantage of the large-scale CMB temperature measurements is that they are extraordinarily clean. For an astronomer who is used to Lyman alpha measurements, or a CERN particle physist who spends his time worrying about the train schedule between Paris and Geneva, it would be like entering into a completely different world when going to large-scale CMB temperature measurements. On the one hand, the signal-to-noise ratio of ~5 degree scales in WMAP is like three or four orders of magnitude. So it doesn’t matter what your noise is — it’s irrelevant on these scales. (As far as large scales goes, WMAP is a perfect imager.) On the other hand, WMAP measures on five different frequencies, and this gives us a pretty good image of the foreground composition of the data. We (and, by now, many other independent groups) have also done lots of other tests with respect to these issues, and the tests always come out negative — the asymmetry is very robust with respect to foregrounds or systematic issues.

    The way to think about this is this: If the asymmetry disappears when Planck arrives, then the entire WMAP *picture* we are so used to looking at, is just plain wrong. It could of course happen — but then the asymmetry would be the smallest of our concerns. In that case, WMAP couldn’t be trusted at all, and all the stuff we’ve been talking about for the last five years or so would pretty much have been a waste of time.. :-)

    So I think it’s fair to say that, from an image analysis point of view, the asymmetry is definitely there: The picture is what it is. The question is just what it means: Is it a ~1% statistical fluke? Or is it a signature of new physics? For now, that remains uncertain. But fortunately, Planck will tell us a whole lot more about this in just a few years. However, right now I think it’s very fun indeed to see that theorists pick up on this issue in a serious way, and come up with new ideas, like this new one presented by Adrienne, Sean and Marc :-)

  • Az

    temperature anisotropy occurs in instances where whats generating (or has generated) the heat isnt a “constant” or has partial obscurity. (cookers hotplate half covered with metal sheet will display temperature anisotropy when viewed from far above)

  • Az

    Though i wonder in laymens terms, does the temperature anisotropy evident there “shift” alittle during long-term observation of the CMB?

  • Tim Eby

    Sean, and excellent discussion, thank you: and also thanks for the discussion of the origin of the universe and the arrow of time. In my unsophisticated way I have long been intrigued by the arrow of time. Sorry if I digress from the topic of your article.

    I may be simply verifying an old cliché – to paraphrase: “It is better to lurk and let the world think I’m a fool then to comment and remove all doubt” – I (possibly foolishly) speculate as follows and find myself in an apparent contradiction.
    If we view the universe as the ultimate information processor and invoke Landauer’s Principle, then, if entropy is at a minimum at the instant of the “big bang”, information is a maximum at that instant. If the universe then evolves towards a point where eventually entropy reaches a maximum value (near infinite) then the universes information content evolves towards zero. Here I am assuming that time, necessary for the universe to “evolve”, is associated with entropy increasing.

    At the risk of wandering into metaphysics, I make the assumption that “information” may be equated in some way with “existence”. I.e. For an entity to exist, that entity must be associated with information: otherwise we have no way of knowing that it exists. An entity that contains zero information then cannot exist. Thus the universe could be said to evolve from a state of “maximum existence” towards a state of “non-existence”. If I may stretch an analogy, this situation appears to be similar to the evolution of a virtual particle and time would be a variable used to describe the evolution of the wave function

    If I now apply the uncertainty principle to the “virtual universe”, i.e. d(energy) x d(time of measurement) is greater than (h/2pi), and assume that at any instant the total energy of the universe is zero hence d(energy) must also be zero. Then in this greater space time, d(time) must be arbitrarily large: i.e. I arrive at a steady state universe which would seem to indicate that no information is being lost and entropy cannot be increasing. In addition if for a computational operation in which 1 bit of logical information is lost, the amount of entropy generated is at least k ln 2, and so the energy that must eventually be emitted to the environment is E ? kT ln 2. (The environment here is the spacetime that the universe inhabits as a virtual entity.) However, if the total energy of the universe is zero at every instant, it cannot emit energy into its environment, and information cannot be lost and entropy cannot be increasing!

    This speculation would seem to indicate that either the total energy of the universe is non zero, that Landauer’s Principle cannot be applied to the universe and hence the universe is not a “computing machine”, or that time cannot be associated with increasing entropy (or, more likely, that I have made some gross logical error)!
    Have I erred?

  • sn

    >Okay, one last time: we’re not here to discuss Peter,
    >his blog comment policies, his notions of etiquette,
    >or his sex life. I’ve deleted a bunch of things, and
    >will continue to do so, so why bother?

    Hmmmm…. so that means that there is no safe haven for people who try to criticize Woit – because he deletes them all if you try that on his blog. I am sorry, but I was really getting sick of nobody willing to hear our side of the story. I apologize if I was a bit brutal with him here.

    Anyway, thanks for answering my silly questions about reheating, Sean.

  • Lawrence B. Crowell

    I don’t know if this will help, but this might not be due to other universes and the like, but due to the structure of the quantum spacetime in the preinflationary period.

    We might imagine (imagine — an important word) that the four dimensional spacetime of the early universe is defined on an ADM “sandwich,” where one spatial surface contains the initial conditions of the universe and the other is a “slice” taken at the onset of inflation. This four dimensional volume contains all the quantum information of the universe. We might think of it as a set of all quantum fields, including gravity, and is a space or superspace described by a lattice system, say the E_8 group. The E_8 contains the Clifford Cl(8), or the “120” the system of roots given by the 120-cell, plus the “128.” We will focus on the 120, which are a representation of quaternionic fields.

    The 120 cell contains 120 dodecahedra, three for each three dimensional face. For the 120-cell the boundary space is SO(3)/A_5 for A_5 the alternating group of the dodecahedral group. This then defines the boudning three sphere of the four volume a Poincare homology sphere. By the Rokhlin theorem a region of a four dimensional space that is bounded by a homology 3-sphere is a spin manifold. We then can embed the exceptional group F_4 in the Cl(8), which is by Musin’s theorem the minimal sphere packing configuration of a 4-dim space. The “spheres” we might think of as Planck units of volume. For the four volume restricted to the 24-cell the bounding space is then given by the quotient space SO(3)/I, where I is the binary icosahedral group given by the cyclotomic field on F_9.

    This binary discrete structure might then impose a “dipole” configuration on the spacetime. I emphasize the word “might.” Yet this strange configuration to the CMB might be a signature of the quaternionic structure of the universe in the inflationary or pre-inflationary phase. If so then this would mean this can be understood entirely from the observed nature of the universe, with no need for unobservable “other universes.”

    Lawrence B. Crowell

  • Lawrence B. Crowell


    I forgot to include that the breaking up of the 120 to the 24-cell, the breaking of Cl(8) to the smaller exceptional group F_4, might physically be associated with the transition of the universe from a quantum wave functional over all (or many) possible metric configurations to a classical or semi-classical spacetime.

    Tim Eby on Jun 9th, 2008 at 5:14 pm WROTE:

    However, if the total energy of the universe is zero at every instant, it cannot emit energy into its environment, and information cannot be lost and entropy cannot be increasing!

    I think the existence of entropy might not be due to the outright destruction of information, but rather its concealment. In fact I will use the term encryption, where quantum information is transformed in ways that an observer who lack the appropriate “key” is unable to cypher. In our physics classes we coarse grain things or do “sums over states” and other things which are a way of burying away things we can’t tractably work with.

    Lawrence B. Crowell

  • Plato

    As to the image, “is what it is “and then to think “genus figures could be allocated to the description of the universe” may actually be then be held relevant?

    WMAP has produced a new, more detailed picture of the infant universe. Colors indicate “warmer” (red) and “cooler” (blue) spots. The white bars show the “polarization” direction of the oldest light. This new information helps to pinpoint when the first stars formed and provides new clues about events that transpired in the first trillionth of a second of the universe.

    Might it then not be as if “holes exist in the universe” with which such calculations made in terms of Lagrangian’s that allow satellites to traverse this universe given space in the simplest energy configuration. So over all, such polarizations would ultimately show an outcome which does rest in the valley, as that WMAP. It reminded me of Wayne Hu’s polarization map.

    B-modes retain their special nature as manifest in the fact that they can possess a handedness that distinguishes left from right. For example here are two polarization fields with the same structure but in the E-mode on the left and the B-mode on the right:

  • Lawrence B. Crowell

    Plato on Jun 9th, 2008 at 8:35 pm

    As to the image, “is what it is “and then to think “genus figures could be allocated to the description of the universe” may actually be then be held relevant?


    Topology might indeed play a role here. The question is what topology, and what physics does it imply?

    Lawrence B. Crowell

  • Gary Bridgewater

    This sort of thing usually leads to a new theory. Are there other whole-sky observation sets that show any such striking asymmetry? Visible light? IR? Any correlation with them?

  • holo

    I want to know that does such lopsidedness anything to do with the uncertainty (maybe larger than 3 sigma) in the polarization spectra from WMAP at the small angular scale which corresponding to the large scale anisotropy of the CMB?

  • Hans Kristian Eriksen

    Gary Bridgewater:

    It’s probably not what you were thinking about, but COBE, WMAP’s predecessor, shows similar structures, although at lower significance because of its much lower signal-to-noise. But I don’t know about any other full-sky maps which are deep enough to be relevant to this issue, really. But of course, even limited sky data sets such as 2dF or quasar catalogs may eventually be interesting.


    I’m afraid that WMAP’s polarization maps are too noisy to be useful for this, really. They barely have enough signal-to-noise to constrain a very few full-sky multipoles at the very largest scales, and not much more than that. They are useful for foreground studies, though, but for proper full-sky CMB polarization information, we’ll just have to wait for Planck..

  • Plato

    Lawrence B. Crowell:Topology might indeed play a role here. The question is what topology, and what physics does it imply?

    The “landscape “is a dirty word now? So too, is Witten ready to discard it?

    I have yet to read Sean’s and their group effort work, but to go by the news reports that are selective released through his blog here.:) Oh, and the “other news source” he had identified.

    So we are getting straight from the….. and as a layman how can I assess and give anything of value here, while there are better minds at work?

    So let’s see.

    The group is using a phenomenological approach to the theory they are expounding? So in this case, we know the hesitancy that censorship “can elevate” or “distort a view” that is vacuous in it’s explanation and reveal a distast to multiverse hypothesis and such, how so then to think that such “reverse arrow of time” can be of help to this current view? It is progressive I must admit from my perspective.

    So we have a universe, a WMAP to look at, and to this extent(genus relations), how far had Mandelstam taken the mathematical of a “genus three construct?”

    This then would be a layman mistake on my part if such an associative value of the universe can be made in relation to the Genus figure, yet, I would not have all my facts in place from my inexperience?

  • John R Ramsden

    Plato, do you use a computer to help with your composition? If so I’d stop, or get an upgrade, because it makes your meaning very obscure.

    Also, with bloggers here putting so much time and effort into explaining their ideas and those of fellow experts, for you to ask “As a layman how can I assess and give anything of value here, while there are better minds at work?” sounds not only rude but foolish.

    How can you expect to find an infallible oracle anywhere, when everyone knows there’s no universal agreement on speculative models and how best to interpret and explain new observations?

    Oh, and calling yourself “Plato” – Do us a favour!

  • Lawrence B. Crowell

    Plato on Jun 10th, 2008 at 10:15 am WROTE:

    The “landscape “is a dirty word now? So too, is Witten ready to discard it?

    String theory might be said to be too unconstrained. LQG is too constrained. :) To me these things are really math-methods more than being theories in a proper sense. They both have interesting things to say, but it is best not be believe either — belief is for religion and politics.

    you wrote:

    how far had Mandelstam taken the mathematical of a “genus three construct?”

    I could fill this with a lengthy essay, but I will keep this short. I think the issue is with the moduli of gravity or quantum gravity/cosmology. In particular how does one get a matching conditions on the moduli space for the instanton state “pre-tunneling state” and the tunneling state. Mandelbrot geometry in spacetime has some interesting issues with the separability of moduli. My suggestion of the Poincare homology sphere is in part meant to address this issue.

    Beyond mathematics there are also physical issues, which are really more important. In particular we need to discard what might be called excess baggage. Physically this amounts in part to a generalization of the equivalence principle where non-inertial and inertial frames are treated on the same basis.

    These is a possible related issuewith Shean’s paper. This data might be related to gravitons stretched out an imprinted on the post inflationary universe. In the paper:

    there appears noise in the LIGO detectors which ound like the gravitational analogue of the CMB. Maybe we are getting signals from the decoupling of gravity & gauge fields analogous to the deionization phase of the universe about 380,000 years after the big bang. This might be data from the universe from within some 10^10 Planck times into the “shebang.” Maybe in time we will get data on the full spectrum, but all so the anistoropic distribution. That will tell us something about the scaling of the universe at large. This gravity wave noise might then be from the universe at a distance so that z ~= lambda/lambda_0 ~= 10^{40}! That is rather impressive given that the most distant galaxies have z ~ 7 and the CMB is z ~ 1000.

    So are we getting some data which is related to an anisotropy of gravitons? We don’t know, but we can be certain that the future holds many surprises.

    Lawrence B. Crowell

  • Plato

    Lawrence B. CrowellMy suggestion of the Poincare homology sphere is in part meant to address this issue.

    I am currently trying to learn to understand the Poincare Conjecture and the lessons in this are amazing to me. Going to a universe in a three manifold description I made the link when it referred “the set in which every point that belongs to a region could be mapped to every point in the box or clear Aquarium.”

    That such a logic leading from Euclid’s element could have ever gotten to something so abstract as seeing “routes in space” as I have detailed them in “satellite travel above” and in terms of Lagrangian points Is an amazing thing for me to grasp, as much, “the departure from the fifth postulate, to non-euclidean geometries. For a layman like me, this is exciting way to think.

    A bulk perspective now instead of “an anisotropy of gravitons?” Well my views are suppose to be telling when I write the way I do and I am glad some people do get them, or bother to ask.

    Thank you Lawrence for the courtesy and helpful information.

    John Ramsden,

    I meant it John, when I said there are better minds then mine here because I am truly at a disadvantage and it is to mean nothing more then, “I have a lot of work to do to catch up sometimes.” Some will be able to read more into what I am saying then others.

    It’s true, I am enamoured with Plato and everything about him.:) But yes, I know he’s dead physically, but not in, what remains of him. Those who write about him. Those who speak of the Solids.

    Even people like Coexeter who represent a new stage in my view of taking geometries to amazing new spaces or Banchoff. Garret Lisi model and E8 complexity are attempts, are they not of modelling of our universe? Or maybe even Tegmarks fascination?

    Anyway, back to the post of Sean’s here.

  • Plato

    The idea to me of” time reversals” had to have some inclination to include Gr at the inception of a new universe, or, of connecting the “beginning and end” in the very nature of this universe now.

    Where is Zero point entropy? Does it exist in any positions in our universe that would be considered the place where such beginning and ends make then self known?

    What would be the physics of this place?

    I am thinking in my layman mind that it is contained in the “moment of the collision process” where we are experimentally moving to words a “supersymmetrical view.” Navier Stokes equations are then considered and the viscosity then provides for this opening to “time reversal and such?”

    Of course I am all over the map:) But to me such a concentration of of gravity in my views of the universe belong to the idea that a gravity perspective is now contained in the “bulk view.”

  • John R Ramsden

    Plato wrote:
    > I said there are better minds then mine here

    Ah. Sorry, I misinterpreted your question to mean are there better minds (on other blogs or forums for example) than the blog authors here!

    I must say it did seem a somewhat implausible thing to ask, and perhaps I should have read between the lines; but it just shows how easily a “discursive” writing style (using as nice a word as possible) can be misunderstood 😉

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  • Jonathan Vos Post

    Re: #8 ” that this ‘lop-sidedness’ cannot be explained by Gaussian statistics?”

    Recent observations and analysis by Benjamin Wandelt indicate (just below the level where they announce “detection” in the forthcoming Phys Rev Letters but instead say “evidence for”) “non-gaussianity” in the CMB.

    This earlier paper by Yadav and Wandelt claims ‘detection’:

    * Amit P. S. Yadav and Benjamin D. Wandelt, Detection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence.

    Their abstract finishes with: “We conclude that the WMAP 3-year data disfavors canonical single field slow-roll inflation.”

    This may be the start of the collapse of Alan Guth’s “inflation” – the unifying principle of Cosmology since Big Bang.

    What, Dr. Sean Carroll, should we focus on in relating your theories and this data interpretation?

  • Lawrence B. Crowell

    Plato on Jun 11th, 2008 at 12:51 am

    I am currently trying to learn to understand the Poincare Conjecture and the lessons in this are amazing to me.

    … as I have detailed them in “satellite travel above” and in terms of Lagrangian points

    The Poincare homology sphere is related to his conjecture. Yet the homology sphere is a sphere with the rotational group SO(3) “modulo” a discrete set of rotations which describe a polytope or polyhedra. The homology sphere is a boundary of a region of four dimensions with a quaterionic structure. If the four manifold is a 4-sphere then the 3-homology sphere bounds both of then and there is then a quaternionic structure in the whole 4-space. At the time Poincare worked on these matter, in the late 19th century, quaterions were a “hot item.” Indeed Maxwell originally formulated his EM equations according to quaterions.

    Lagrange points are regions where the Newtonian gravitational forces from two main bodies and centripetal force on a third “test mass” cancel out. For the Earth and sun alone these are fixed points. The L_1, L_2 and L_3 points have potential functions (in the accelerated frame) which are saddle point configurations, and are thus not stable, but quasistable. Another problem is that there is a perturbation due to the moon, so the Lagrange points are not fixed points, but wobble around in Lissajous orbit.

    So to get there is tricky. The craft is placed in a highly elliptical orbit that approaches the Lagrange point. The RTG on the craft then after 3 passes nudges the craft into the Lagrange points. Also, since the Lagrange point is a saddle potential one needs to perform station keeping to maintain a “trim” on the orbit. This requires occassional rocket burns. This will continue until Sept 2009, after which WMAP will go silent and become “lost in space” as space junk. The Planck spacecraft will be launched later this year and will provide better data, including measurements of B-mode polarizations.

    Astro-navigation is a bit like golf, you have a certain par for a mission and the objective is to get the ball in the hole, craft to its orbit, libration point, planet etc.

    Lawrence B. Crowell

  • Plato


    Thanks again.

    “I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered.”Harold Scott Macdonald (H. S. M.) Coxeter

    Moving to polytopes or allotrope seem to have values in science? Buckminister Fuller and Richard Smalley in terms of allotrope.

    I was looking at Sylvestor surfaces and the Clebsch diagram. Cayley too. These configurations to me were about “surfaces,” and if we were to allot a progression to the “projective geometries” here in relation to higher dimensional thinking, “as the polytope[E8]”(where Coxeter[I meant to apologize for misspelling earlier] drew us to abstraction to the see “higher dimensional relations” toward Plato’s light.)

    As the furthest extent of the Conjecture , how shall we place the dynamics of Sylvestor surfaces and B Fields in relation to the timeline of these geometries? Historically this would seem in order, but under the advancement of thinking in theoretics does it serve a purpose? Going beyond “planck length” what is a person to do?

    Thanks for the clarifications on Lagrange points. This is how I see the WMAP.

    Diagram of the Lagrange Point gravitational forces associated with the Sun-Earth system. WMAP orbits around L2, which is about 1.5 million km from the Earth. Lagrange Points are positions in space where the gravitational forces of a two body system like the Sun and the Earth produce enhanced regions of attraction and repulsion. The forces at L2 tend to keep WMAP aligned on the Sun-Earth axis, but requires course correction to keep the spacecraft from moving toward or away from the Earth.

    Such concentration in the view of Sean’s group of the total WMAP while finding such a concentration would be revealing would it not of this geometrical instance in relation to gravitational gathering or views of the bulk tendency? Another example to show this fascinating elevation to non-euclidean, gravitational lensing, could be seen in this same light.

    Such mapping would be important to the context of “seeing in the whole universe.”

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  • A dumb christan


    The earth is flat and is 6000 years old.
    The sun, which is 1/2 the size of the earth orbits in a perfect circle around the earth.
    The moon which is 1/2 the size of the sun orbits the sun and the earth.

    Oh, yeah and in the end of days a giant seven headed snake will come out of noware and brand 666 on everyones head! :-)

    Watch out for Poes Law!

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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] .


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