An interesting paper on the arXiv yesterday gave me a prod to expand a little on one of the cosmic anomalies I’ve blogged about before.

Before explaining what this is all about, let me just briefly introduce a bit of lingo. The pattern of variations fluctuations in the temperature of the cosmic microwave background (CMB) across the sky, such as is revealed by the *Wilkinson Microwave Anisotropy Probe* (WMAP), is usually presented in terms of the behaviour of its spherical harmonic components. The temperature as a function of position is represented as a superposition of spherical harmonic modes labelled by two numbers, the degree *l* and the order* m*. The degree basically sets the characteristic angular scale of the mode (large scales have low *l*, and small scales have high *l*). For example the dipole mode has *l=1* and it corresponds to variation across the sky on a scale of 180 degrees; the quadrupole (*l=2*) has a scale of 90 degrees, and so on. For a fixed* l* the order *m* runs from *-l* to *+l* and each order represents a particular pattern with that given scale.

The spherical harmonic coefficients that tell you how much of each mode is present in the signal are generally complex numbers having real and imaginary parts or, equivalently, an *amplitude* and a *phase*. The exception to this are the modes with *m=0*, the zonal modes, which have no azimuthal variation: they vary only with latitude, not longitude. These have no imaginary part so don’t really have a phase. For the other modes, the phase controls the variation with azimuthal angle around the axis of the chosen coordinate system, which in the case of the CMB is usually taken to be the Galactic one.

In the simplest versions of cosmic inflation, each of the spherical harmonic modes should be statistically independent and *randomly distributed* in both amplitude and phase. What this really means is that the harmonic modes are in a state of maximum statistical disorder or entropy. This property also guarantees that the temperature fluctuations over the sky should be described by a Gaussian distribution.

That was perhaps a bit technical but the key idea is that if you decompose the overall pattern of fluctuations into its spherical harmonic components the individual mode patterns should look completely different. The quadrupole and octopole, for example, shouldn’t line up in any particular way.

Evidence that this wasn’t the case started to emerge when WMAP released its first set of data in 2003 with indications of an alignment between the modes of low degree. In their analysis, Kate Land and Joao Magueijo dubbed this feature *The Axis of Evil*; the name has stuck.They concluded that there was a statistically significant alignment (at 99.9% confidence) between the multipoles of low degree (*l=2 and 3*), meaning that the measured alignment is only expected to arise by chance in one in a thousand simulated skies. More recently, further investigation of this effect using subsequent releases of data from the WMAP experiment and a more detailed treatment of the analysis (including its stability with respect to Galactic cuts) suggested that the result is not quite as robust as had originally been claimed. .

Here are the low-*l* modes of the WMAP data so you see what we’re talking about. The top row of the picture contains the modes for *l=2* (quadrupole) and l=3 (octopole) and the bottom shows *l=4* and *l=5*.

The two small red blobs mark the two ends of the preferred axis of each mode. The orientation of this axis is consistent across all the modes shown but the statistical significance is much stronger for the ones with lower *l*.

It’s probably worth mentioning a couple of neglected aspects of this phenomenon. One is that the observed quadrupole and octopole appear not only to be aligned with each other but also appear to be dominated by *sectoral* orders, i.e those with *m=l*. These are the modes which are, in a sense, opposite to the zonal modes in that they vary only with longitude and not with latitude. Here’s what the sectoral mode of the quadrupole looks like:

Changing the phase of this mode would result in the pattern moving to the left or right, i.e. changing its origin, but wouldn’t change the orientation. Which brings me to the other remarkable thing, namely that the two lowest modes also have correlated phases. The blue patch to the right of Galactic centre is in the same place for both these modes. You can see the same feature in the full-resolution map (which involves modes up to *l*~700 or so):

I don’t know whether there is really anything anomalous about the low degree multipoles, but I hope this is a question that Planck (with its extra sensitivity, better frequency coverage and different experimental strategy) will hopefully shed some light on. It could be some sort of artifact of the measurement process or it could be an indication of something beyond the standard cosmology. It could also just be a fluke. Or even the result of an over-active imagination, like seeing Elvis in your local Tesco.

On its own I don’t think this is going to overthrow the standard model of cosmology. Introducing extra parameters to a model in order to explain a result with a likelihood that is only marginally low in a simpler model does not make sense, at least not to a proper Bayesian who knows about model selection…

However, it is worth mentioning that the Axis of Evil isn’t the only cosmic anomaly to have been reported. If an explanation is found with relatively few parameters that can account for all of these curiosities in one fell swoop then it would stand a good chance of convincing us all that there is more to the Universe than we thought. And that would be fun.