And another paper! Will the science never end?
Superhorizon Perturbations and the Cosmic Microwave Background
Adrienne L. Erickcek, Sean M. Carroll, Marc Kamionkowski (Caltech)Abstract: Superhorizon perturbations induce large-scale temperature anisotropies in the cosmic microwave background (CMB) via the Grishchuk-Zel’dovich effect. We analyze the CMB temperature anisotropies generated by a single-mode adiabatic superhorizon perturbation. We show that an adiabatic superhorizon perturbation in a LCDM universe does not generate a CMB temperature dipole, and we derive constraints to the amplitude and wavelength of a superhorizon potential perturbation from measurements of the CMB quadrupole and octupole. We also consider constraints to a superhorizon fluctuation in the curvaton field, which was recently proposed as a source of the hemispherical power asymmetry in the CMB.
This is a followup to our paper on the lopsided universe, although the question we’re tackling is a little different. Remember that the point there was that we imagined some sort of ultra-long-wavelength perturbation, much larger than the size of the visible universe, and we asked how that would change the amplitude of small-scale perturbations in one direction of the sky as compared to the other.
In the new paper, we actually address a more basic question: what about the induced temperature anisotropy itself? So instead of looking at the power asymmetry (how does the amplitude of fluctuations in one direction compare to that in the opposite direction), we’re looking at the temperature asymmetry (how does the temperature in one direction compare to the temperature in the other). In fact, we’re looking at the “dipole” asymmetry — not small-scale fluctuations, but the large-scale hemispherical pattern.
Ordinarily, we simply ignore the dipole asymmetry, for a good reason: you get a dipole just from the ordinary Doppler effect, even if there are no intrinsic fluctuations in the CMB. If you have both, it’s hard to disentangle one from the other. But we were considering a supermode that was pretty substantial, and it became an issue — if the predicted dipole was much larger than what we actually observe, it would be hard to wriggle out of.
Except — it exactly cancels. That’s what the new paper shows. (And another paper the next day, by Zibin and Scott, comes to the same conclusion.) We were surprised by the result. There are clearly competing effects: we do have a peculiar velocity, so there is a Doppler effect, and there is an intrinsic anisotropy from the primordial density perturbation (the Sachs-Wolfe effect), and there is also something called the “integrated Sachs-Wolfe effect” from the evolution of the gravitational field between us and the CMB. And they all delicately cancel. We came up with a plausible hand-waving explanation after the fact, but it was the grungy calculations that were more convincing.
Nevertheless, the supermode idea is still constrained — the dipole cancels, but there are higher-order effects (quadrupole and octupole) that are observable. Karl Popper would be proud.
Never let the science end!!
Just a quick question : I have always thought that superhorizon modes, especially those very very long ones like the one you considered, would just look like the “background” to short wavelength modes inside the horizon. One can think of the “separate universes” argument. In a way, once can think of it as a “field renormalization” in the field theory sense. This way, I guess I would be surprised if we see some kind of dipole effect coming out of it.
Are you looking for a different kind of effect? I have briefly skimmed through the paper but since this is a blog, I can actually ask questions instead!
Addenda : The above argument does not rely on how big the superhorizon modes are (in terms of amplitude). The superhorizon mode can do whatever it wants, but since short wavelength modes are simply ‘modulation’ on top of it, it wouldn’t matter.
I’m enjoying the blog Sean! How about multiverses. Each expands from its own big bang. Sometimes they are close enough to each other that they expand into each other
Eugene, in the infinite-wavelength limit you are certainly right (if I understand you correctly). But we are imagining that there is a dipole modulation of the power, so a modulation of the temperature is not completely crazy. You could easily get one, in fact, in models with isocurvature perturbations; only in the adiabatic limit does it cancel.
wdjohns, I’m not sure what you are thinking. There is only one spacetime, so it can’t bump into itself. There can be “bubbles” of spacetime in different phases, but that’s not what we’re talking about here.
Hi Sean, this is completely off-topic but I thought fellow bloggers and readers might be interested in a simple puzzle concerning Hubble’s law that I’ve posted on my blog at
http://coraifeartaigh.wordpress.com
The prize is a guest post for the correct answer in simple language!
Congrats on the paper Sean, published in the nick of time by the sound of it!
Talking about ultra-long wavelengths, I was wondering the other day what would happen to a photon that appeared during inflation if space was expanding sufficiently fast to reduce its frequency to 1 Planck unit, which is obviously the minimum.
If that notion makes sense, might not “maximally stretched” photons like this oppose further increases in the cosmic expansion rate, and even slow it? Or would their existence in the first place be ruled out for some reason, such as the background temperature being so high at that stage, above the electroweak unification temperature for example?
Thanks for the reply Sean. How do we know there is only one spacetime? Why could there not be multiple big bangs in a universe that is (much) bigger than the “universe” produced by our own big bang?
I’m interested in the idea of other big bangs because I understand that there is not enough matter and energy in the product of our own big bang to cause it all to eventually collapse on itself. If it all goes outward forever, then “where do babies come from?” 😉 that is, what precipitated our big bang? and why is it the only one?
P.P.S.: Sorry for the multiverse multipost. My comment is specific to your post on Groeneboom, Eriksen, and the CMB anomaly.
My question then is could the observed polarity reflect mass and energy pulled in from the product of two previous big bangs?
And I wonder if you could look out through the blue spots (lower radiation areas) and see the product of other big bangs.
Thanks for the discussion space, and praise for your work!
wdjohns– there’s not much that we “know” about spacetime beyond the observable universe; we can only talk about what a certain model says, and that’s what I’m doing here. I know of models where there are disconnected bubbles of spacetime, but those bubbles would never collide, as they are not embedded in some bigger spacetime.
John– I’m not sure what you have in mind. Frequency is 1/time, so “Planckian” frequency would be 1/(Planck time), which is a maximum (if anything), not a minimum. I think what you have in mind is a photon whose wavelength is stretched beyond the Hubble radius. That’s no problem — it’s just an electromagnetic field, which dilutes away as the universe expands.
Sean,
You mean it only cancels when the supermode is adiabatic? I am not sure I understand a superhorizon adiabatic mode though. Are you saying that if the supermode is evolving outside the horizon (hence is effectively isocurvature when it reenters the horizon eventually), the dipole doesn’t cancel?
I should go read the paper…
This is clearly a complex paper to read. I have only read the first two pages. The cancellations between dipole CMB temperature and amplitude in the adiabatic assumption means that any difference between them thermalized or went into equilibrium. So the Sach-Wolfe amplitude variations and any DT/T variation had sufficient time to cancel out. Since the two are determined by the same gravitational potential I presume the two are likely to deviate in the early universe by a small enough amount so as to be cancelled out if these deviations are adiabatic or sufficiently small.
I figure if I display my relative ignorance I will be corrected and learn something.
Lawrence B. Crowell
I’m still amazed at how many cool new ideas CMB cosmology stimulates! Very much looking forward to the Planck data coming along (once ESA finally launch it; space missions seem to take for *ever*)
Does this mean the dipole that is measured is actually due to our peculiar velocity alone, and does not have a contribution from fluctuations in the inflaton? I think it’s pretty cool just to know our peculiar velocity!