1. BACKGROUND

Figure 1 gives an overview of information on background radiation in the Universe. The reason to plot I is so that it is possible to read off the relative contributions to total energy density. What can be seen is that the Cosmic Microwave Background (CMB) is by far the dominant background. The CMB corresponds to an energy density of 0.260 eV cm^-3, or a number density of 410 cm^-3, corresponding to about 2 billion photons per baryon in the Universe today. On the figure, the next biggest background - almost two orders of magnitude down in energy contribution - is in the far-IR/sub-mm part of the spectrum, and believed to come from distant, dusty, star-forming galaxies. A little below that is the near-IR/optical background, coming from the sum of the emission of all the stars in all the galaxies we can observe. Then much lower are the X-ray and -ray backgrounds, which come predominantly from active galactic nuclei.

Figure 1. A compilation of recent constraints on extragalactic diffuse background radiation. In terms of total energy the CMB dominates, with the Far-Infrared and Optical Backgrounds about a factor of 100 lower. These data are based upon the older compilation of primarily from Ressell & Turner 1990 [1], supplemented with more recent data from: Smoot 1997 [2] for the CMB; Lagache et al. 1999 [3] and Hauser et al. 1998 [4] for the FIB; Leinert et al. 1998 [5] for a near-IR to near-UV compilation; Dwek & Arendt 1998 [6] for the near-IR; Pozzetti et al. 1998 [7] for the optical; Miyaji et al. 1998 [8] and Gendreau et al. 1995 [9] for the X-ray; and Sreekumar et al. 1998 [10], Kappadath et al. 1999 [11] and Watanabe [12] for the -ray. In the colour version lower limits are shown in red and upper limits in blue.

Apart from the CMB, there is no evidence for background emission arising from anything other than known sources of radiation: stars, gas and dust within galaxies. In other words, there is no reason to believe that decaying particles, for example, distributed throughout the Universe, are contributing much to the background, and hence these sorts of data can place constraints on exotic particles (e.g. [1]). The CMB is different, however. Its spectral shape is spectacularly well-fit by a blackbody [13, 14, 2], over more than 4 decades in frequency. The current best estimate of the CMB temperature is

(1)

[15]. The fact that the CMB is such a good blackbody is one of the pillars of the standard Big Bang model. The argument is that, since we can't even make such a good blackbody in the lab, the CMB needs to have originated from something in extraordinarily good thermal equilibrium. The only known source is the entire Universe, during an earlier epoch when it was very much hotter and denser. Together with the Hubble law for distant galaxies, this leads to a robust model in which the Universe used to be hot and dense, and has been cooling and expanding since then.

Since we know that the Universe consists mainly of hydrogen, we can calculate (see [16] for a recent update) that the Universe was ionized when it was hotter than about 4,000K (a lower temperature than you might have first guessed, because of the high photon-to-baryon ratio). Since the radiation redshifts just like T (1 + z), then that means the Universe recombined ⁽¹⁾ at z 1500. This was the time when the radiation last interacted with the matter (through electron scattering), and most CMB photons have been travelling freely since then. In models with typical parameters, this epoch corresponds to a time of around 300,000 years. The spectrum is thermalised (by double Compton and Bremsstrahlung) for times earlier than about 1 year, corresponding to z ~ 10⁷. Hence particle decays, or other energy emitting processes, occurring over the redshift range 10³ < z < 10⁷, could leave an observable signature on the CMB spectrum (see e.g. [17]).

Although all measurements are currently only upper limits, there is some prospect of detections of spectral distortions from planned spectral experiments [18]. For example, at low frequencies it seems feasible to detect Bremsstrahlung emission from the reionized gas in the inter-galactic medium at moderate redshifts [19]. However, progress in constraining other realistic physical effects will require considerably greater improvements in experimental sensitivity.

As well as distortions to the spectrum, the CMB also contains cosmological information in the variations in temperature across the sky [20]. After the detection of CMB anisotropy by the COBE satellite in 1992 [21] attention has been focussed almost exclusively on these anisotropies. This is partly because it became clear that detection was easily within reach of state-of-the-art detectors, but also because theoretical calculation showed that precise measurements of the anisotropy power spectrum would provide detailed information about fundamental cosmological parameters [22].

Figure 2. Most of the experiments published to date. See Smoot & Scott (1997) [17] for full references, supplemented with more recent results from: OVRO Ring [25], QMAP [26], MAT TOCO [27], CAT [28], Python V [29] and Viper [30]. The error bars (these are 1 except for the upper limits which are 95%) have generally been symmetrised for clarity, and calibration uncertainties are included in most cases. The horizontal bars represent the widths of the experimental window functions. The dotted line is the flat power spectrum which best fits the COBE data alone. The dashed curve is the prediction from the vanilla-flavoured standard Cold Dark Matter model.

Since COBE there have been around 20 separate experiments which have detected temperature fluctuations which are most likely to be primordial. These are summarized in Figure 2. Here the x-axis is the spherical harmonic multipole, l. The temperature fluctuation field on the sky can be decomposed into an orthogonal set of modes:

(2)

Since there is no preferred direction on the sky (e.g. [23]) the individual ms are irrelevant, and so the important information is contained in the power spectrum

(3)

Indeed if the perturbations are Gaussian, then this contains all the information. The conventional amplitude of the quadrupole is given as

(4)

A `flat' spectrum means one in which l(l + 1) C_l = constant, and we can therefore define that constant in terms of the expectation value for the equivalent quadrupole Q_flat - which is what is plotted as the y-axis in Figure 2.

Each experiment quotes one (or in the best cases several) measures of power over a range of multipoles, and these can be quoted as `band powers' or equivalent amplitudes of a flat power spectrum through some `window function'. The horizontal bars on the points are an indication of the widths of these window functions.