6.3 Anisotropies in the Universe itself
Having subtracted the dipolar anisotropy due to the motion of the Earth relative to the 3 K radiation, we are left with radiation that is exceedingly isotropic. So, we have to ask whether there are any residual variations that would point to a departure from isotropy of the radiation itself? This is a crucial question. Although it was gratifying to have the radiation so isotropic that there could be little doubt of its cosmic origins, nevertheless a completely isotropic distribution would bring troubles of its own.
The reason for this is that, although the matter distribution is isotropic on a large enough scale, it is clearly not so on smaller scales. It is clumped together in galaxies, the galaxies are preferentially to be found in clusters of galaxies, and even the clusters are loosely associated in superclusters. In fact, the matter distribution somewhat resembles a gigantic sponge; it has enormous holes in it, with the superclusters arranged around the boundaries of these voids. Presumably this distribution came about as a result of inhomogeneities in the original distribution of matter coming from the big bang. If a particular region happened to have by chance a somewhat greater density of matter than its neighbours, its increased gravity would tend to attract matter away from the less densely populated regions and towards itself. This would enhance the inhomogeneity, leading to this particular region gaining an even stronger pulling power, and attracting yet more material to itself. The initial inhomogeneities, which in themselves may have been slight, would over the course of time have become magnified.
That is thought to be the process whereby we have our present-day distribution. Having said that, it is not at all clear yet in what order the hierarchy of structures formed. Perhaps the matter first assembled to form superclusters; these then broke down into their component clusters, which in their turn later separated out into galaxies. Finally, the individual stars condensed. Alternatively it could all have happened the opposite way round, with stars forming first, these being attracted into galaxies, which later gathered into clusters and superclusters. Or indeed it could have been some other mix of aspects drawn from both these scenarios. But whichever was the correct sequence of events, one thing is clear: there had to be density inhomogeneities on some scale or other.
From this we infer that there should also be anisotropies in the 3 K radiation. The reason is that when gas collects together and is squashed down by its mutual gravity, potential energy is converted into kinetic energy leading to a temperature rise. It is such temperature increases that can ignite nuclear reactions and result in the birth of a new star (assuming sufficient gas has been collected originally). Gas collecting to form a primordial galaxy or a cluster of galaxies will similarly undergo a temperature rise, this rise being reflected in the type of radiation it emits. The angular distribution of this radiation, as we receive it today, should show a degree of anisotropy because it originates in matter that was not itself entirely homogeneous. Inhomogeneities must have already been present in matter when it was emitting what is now the 3 K radiation. Thus we should expect the 3 K radiation to manifest some degree of anisotropy; it should not be wholly uniform.
This is not to say that we should necessarily expect to detect ‘hot spots’. The situation is somewhat more subtle than that. We have to recall that when we are dealing with galaxies or with clusters, a great deal of matter is involved. The gravitational potential energies are enormous. Radiation emitted from the depths of one of these conglomerations of matter has to escape the gravitational field of the matter producing it. This will lead to a gravitational redshift, i.e. a cooling of the radiation. The interesting question then becomes whether the hot radiation from the interior is still ‘hot’ when it escapes, or whether it will now have lost so much energy through redshift that it emerges cooler than the ambient temperature of the surrounding matter. We might therefore observe ‘cold spots’ rather than ‘hot spots’.
So, although the theoretical analysis is complicated, there have to be anisotropies of one kind or another in the 3 K radiation at some level of sensitivity, and definite predictions have long been made about the angular scale on which such anisotropies ought to appear. The refinement of these predictions and the effort to detect the anisotropies observationally have become major themes in the recent development of cosmology.
There was a great stir, which even the popular press recognised, when in 1992, the COBE satellite succeeded in detecting the anisotropies, albeit at the extremely low level of 1 part in 100 000. Figure 29 shows a picture of the measured intensity distribution across the sky.
This first detection of the intrinsic anisotropies in the cosmic microwave background had to be interpreted with great care since the signal being detected was of the same order of magnitude as the background noise fluctuations. However, since that first detection many other studies have been carried out and the angular distribution of the anisotropies has been characterised with greatly increased precision.
The characterisation of the angular distribution of anisotropies is usually expressed through a plot of the angular power spectrum of the observed radiation. Such a plot indicates the relative strength of intensity (or temperature) fluctuations as a function of the angular scale of those fluctuations. A recent determination of this angular power spectrum, based on results obtained by COBE's successor, the Wilkinson Microwave Anisotropy Probe (WMAP), is shown in Figure 30.
The details of the angular power spectrum need not concern us here, but the following points should be noted.
The points and vertical ‘error bars’ represent the results of observation. The smooth line represents a ‘best fit’ to the data based on specific theoretical assumptions.
The shaded band represents the unavoidable uncertainty (known as cosmic variance in this case) associated with trying to determine a ‘cosmic’ quantity from observations made at one (typical) point in the Universe, i.e. from the neighbourhood of the Earth.
The COBE data were limited to angular scales of 10° or more. The WMAP data reveal anisotropies on much finer scales and tell us much about the angular distribution of those anisotropies.
The anisotropies are particularly powerful on a scale of about 1°. This is just the angular scale at which the inhomogeneities associated with the formation of superclusters are expected to leave their imprint on the 3 K radiation.
Theoretical explanations for the peaks and troughs seen in the data depend on the assumed values of various cosmological parameters such as the current value of the Hubble parameter. Thus the process of ‘fitting’ predictions to the data provides a method of determining the values of those cosmological parameters. We shall return to this point later.
In conclusion, we can say that the extreme degree of isotropy of the 3 K radiation points to its cosmic origin in the big bang, and justifies us in regarding it as powerful confirmatory evidence that there was indeed a big bang. Nevertheless, it is perhaps the exceedingly weak inhomogeneities that will ultimately prove to be of the most lasting value for cosmology. These give us what may be a unique snapshot of a stage in the early development of galaxies/clusters/superclusters – the stage reached at the time of decoupling, 4 × 105 years after the big bang.