The Friedmann-Robertson-Walker (FRW) models of general relativistic cosmology represent the spatial universe to be homogeneous and isotropic. This means, respectively, that each point in space is indistinguishable from any other, and at each point all the spatial directions are indistinguishable. Up to now, astronomical observations have suggested that the FRW models are correct. The distribution of galaxies appear to be isotropic on sufficiently large length-scales, and, at first sight, the temperature variations in the cosmic microwave background radiation (CMBR) also appeared to be isotropic.

However, in the past few years, detailed analysis of those temperature variations have revealed some anomalies. In particular, it appears that there is a preferential axis to those temperature variations, dubbed the '

Axis of Evil'. The temperature variation in the CMBR is expressed as a function upon the inner surface of our celestial sphere, δT(θ,φ). θ and φ are the angular coordinates upon the sphere, of which the temperature variation δT is a function. Like any function upon a sphere, it can be decomposed into a sum of the 'spherical harmonics' Y

^{m}_{l}(θ,φ). The spherical harmonics are essentially trigonometric functions upon the sphere.

Physicists tend to refer to the terms in a spherical harmonic decomposition as 'modes'. The term corresponding to

*l*=0 is referred to as the monopole term,

*l*=1 terms are called dipole terms,

*l*=2 terms are quadrupole terms, etc. A dipole anisotropy in the temperature of the CMBR is a periodic variation which completes 1 cycle around the sky; it has one 'hot' pole and one 'cold' pole. A quadrupole anisotropy is a periodic variation in the temperature of the CMBR which completes 2 cycles around the sky. Mode

*l* anisotropies complete

*l* cycles around the sky. Higher

*l* modes correspond to temperature fluctuations on smaller angular scales. After subtracting the effects of the Earth's diurnal rotation, its orbit around the Sun, the motion of the Sun within the Milky Way galaxy, and the motion of the Milky Way within the Local Group, we observe from the Earth a dipole anisotropy in the CMBR upon the celestial sphere. This is a dipole anisotropy upon our own private celestial sphere due to the proper motion of the Local Group of galaxies towards the Virgo supercluster at approximately 600kms

^{-1}. This dipole temperature anisotropy is subtracted from the CMBR to leave a temperature pattern which should be isotropic in a statistical sense.

Unfortunately, it appears that the quadrupole and octopole modes (the

*l*=2 and

*l*=3 modes) are less than isotropic. Their respective cycles of hot and cold spots are only present in a particular plane of the sky, and the axes of these two planes are closely aligned. Intriguingly, these axes point in the general direction of the Virgo supercluster. If these alignments have occurred by chance, then they constitute 1-in-66 and 1-in-20 flukes, respectively.

Moreover, Michael Longo of the University of Michigan has now analysed 1660 spiral galaxies from the Sloan Digital Sky Survey, and found that their rotation axes mostly line up with the Axis of Evil. Longo estimates the probability of this happening by chance to be less than 0.4 per cent.

The fluctuations in the CMBR on the largest angular scales are purported to be the remnants of the primordial density fluctuations. These primordial fluctuations were purportedly stretched to the length scales necessary for the formation of galaxies and clusters of galaxies by inflation, the hypothesized period of exponential expansion which occurred early in the history of the universe. The Axis of Evil is potentially, therefore, a serious problem for inflation.

However, it should be noted that general relativistic cosmology is perfectly capable of embracing a non-isotropic spatial universe. Whilst the FRW models are spherically symmetric about each point in space, there is another class of spatially homogeneous models which are merely rotationally symmetric about each point. These models include the Kantowski-Sachs class of models. Whereas the spatial isotropy group at each point of a FRW model is SO(3), the spatial isotropy group of a rotationally symmetric model is SO(2). These rotationally symmetric models are still homogeneous, so each point in space is rotationally symmetric about some axis.

So far, attempts to explain away the Axis of Evil as the consequence of contamination of the CMBR data by foreground processes have been unsuccessful. Nevertheless, the fact that the Axis of Evil points towards the Virgo supercluster also seems to be a remarkable coincidence if it occurred by chance. Perhaps local processes, related to the motion of the Local Group towards the Virgo supercluster, have altered the dipole anisotropy from its calculated form. The consequence may be that we have not correctly subtracted the dipole anisotropy from the CMBR, thereby leaving a remnant in the quadrupole and octopole modes.