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.