CMB History - a brief introduction
(copyleft) Tim Gebbie 1999

Histories are by there very nature revisionist and a function of time and place. Science is not free of vested interest. However, what makes science very different from political, social, economic and religious endeavours is that it is the natural enemy of vested interest including those of the scientific establishment itself. I attempt to outline the History of the development of our understanding of temperature anisotropies.

The first theoretical estimates of the radiation temperature were based on a theory of element synthesis worked out by George Gamow in the 1940's (Gamow 1948). The first observational detection leading to the calculation of the background temperature seems to have been made by Andrew McKellar in 1940, Dominion Observatory, British Columbia ( Dominion Astrophysics Observatory Journal (Victoria B.C.) Vol VII, No 15, 251 (1941)). It is unlikely that he had any idea of the cosmological implications of what he had uncovered, he was however able to quote an average bolometric temperature of $T_{R0} = 2.3 ^{\circ}$ K -- based on the study of interstellar absorption lines. He was prompted to try and find the average temperature of the interstellar medium given the then recent spectral work of Adams from the Mount Wilson Observatory. He computed "a temperature for molecules in interstellar space", the "rotational" or "effective" temperature that governed the population of the lowest states of the molecules giving rise to the "interstellar molecular lines". This was nevertheless a remarkable and sophisticated achievement.

In the 1950's a somewhat more detailed theoretical analysis of present radiation temperature as an artifact of some early hot era where undertaken by Alpher and Herman. The idea that the individual photons arising from an era with temperatures of the order of $10^9$ K would have been absorbed long before today. It was realized that because the photon entropy per baryon is very large that the matter temperature would relax as $a^{-1}$ in such a manner so as to give on the idea that the photons emitted as the universe was becoming transparent would have has the same value of $T_{R} a$ as during the element synthesis; a consequence of an expanding FRW cosmology. The remarkable prediction of a 5K black-body radiation was attained. These results where allowed to sink into obscurity.

It was only in the mid sixties that the problem of determining the radiation temperature was once again taken up. The argument of Dicke, Peebles, Roll and Wilkinson was that the early universe was hotter than $10^{10}$ K because it either expanded from a singularity with $a=0$. Or there where cyclic oscillations between finite values of $a$; it would get hot enough to dissociate the heavy elements left over from previous cycles. They suggested that the energy density of the CMB would be such that $T_{R0}$ is somewhere less than or close to $40$ K; the predictions of the previous decade had been significantly better. At last the CMB was being taken seriously again. An experiment by Roll and Wilkinson was prepared to measure the radiation temperature. In order to detect the temperature a radiometer designed by Dicke in the mid forties was to be used -- the Dicke switching radiometer which jumped between two recievers a hundred times per second; one pointed at the sky the other at a liquid Helium bath. Before Roll and Wilkinson could complete a measurement of the radiation temperature they learned that Penzias and Wilson had already made the observations.

Penzias and Wilson observed a weak background signal from a Horn antenna at Holmdel, New Jersey; though McKellar actually had the additional a priori intent of calculating this temperature from observations he did not have anyone to tell him about its cosmological source. For Penzias and Wilson it was a trully serendipidous, well placed and beautifully timed discovery; with a temperature detection of $T_{R0} \approx 3.5 \pm 1$ K resulting from an antenna intended to track the Echo satellite. It was at one frequency only, so made very little impact with regards to the expectation of a blackbody spectrum. The impact on cosmology and the public perception of cosmology was immence.

This observation, published in 1965, along with the work of Dicke, Peebles, Roll and Wilkinson was to hail the beginning of the moden CMB physics in cosmology.

The key point was that at wavelengths in the range of centimeters to millimeters the extraterrestrial electromagnetic radiation is dominated by a nearly isotropic component the, Cosmic Microwave Background (CMB). The closeness to isotropy suggests that the CMB uniformly fills space, meaning that an observer in another galaxy would see almost the same intensity of radiation -- this is the consistent with the copernican principle. The spectrum is close to black-body, in fact the best example of a black body known. It has a thermal plankian form at a temperature near 3K. This suggests that the radiation has almost completely relaxed to thermodynamic equilibrium. This could not have happenend recently as the universe is currently optically thin to radiation -- we can see distant galaxies and stars. The CMB can move across the present universe on scale of the hubble length with little change beyond that caused by expansion.

The interpretation is that the CMB is left over from an earlier time when the expanding universe was dense and hot, interaction rates between particles were rapid enough to have allowed a relaxation to thermal equilibrium. Thus filling space with a sea of black-body radiation. Furthermore, when the interaction is negligible, cooling is due to expansion, preserving the thermal spectrum. When the radiation interacts with the matter, because the heat capacity of the radiation is very much larger than that of the matter, the spectrum will still tend to remain close to blackbody.

A nearly thermal spectrum of blackbody radiation is thus an expected signature of an expanding universe in which the radiation is that left over from a early hot dense era.

There is however structure in the universe, we see galaxies and super-cluster of galaxies, stars and other interesting objects and phenomena, here on earth and elsewhere. If the CMB was perfectly isotropic one would have expected there to have been no deviations from isotropy and homogeneity in the early universe, where then would the structure come from?

In the Big Bang Model, complex structures arise from primodial perturbations, the perturbations grow by gravitational instability as a result of the expansion. Even though the CMB was expected to be an artifact of and earlier less structural complex phase the fluctuations should be between the $10^{-6}$ to the $10^{-5}$ level in order to be consistent with the simplest gravitational instability models.

The detection of anisotropies in the CMB, by the COBE team, in 1992, was thus a most auspicious moment in the history of cosmology. It brought in to play an era of precision cosmology, both on the theoretical and observational fronts. It vindicated the idea that there should be small fluctuations in the early universe that would seed the formation of structure and promised to provide a testing ground for the physics describing the nature of the primordial fluctuations and hence large scale structure of the observable universe.

Launched on November 18, 1989, the COBE satellite carried three experiments : the Far Infrared Absolute Spectromphotometer (FIRAS) to compare the spectrum of the CMB with a precise blackbody, a Differential Microwave Radiometer (DMR) to create an all sky map of the cosmic radiation, and a Diffuse Infrared Background Experiment (DIRBE) to search for the Cosmic Infrared background radiation. The COBE satelite revealed the CMB with an almost perfect thermal spectrum (from the FIRAS experiment) of a temperature $T_{R0} = 2.726 \pm 0.010K ( 95 \% CL )$ with a maximum deviation of $3 \times 10^{-4}$ (Mather et al) and noise weighted deviations of its peak intensity of under $5 \times 10^{-5}$. It was also to show that the CMB had temperature anisotropies (from the DMR experiment) near to one part in $10^5$ (Smoot et al 1992).

It is because of these developments that the careful calculation of temperature anisotropies as arising from primodial perturbations has become an important aspect of modern cosmology. It is only since April 1992 that CMB anisotropies have taken up there place with spectral distortions, BBN element abundances and large scale structure constraints. The DMR experiment made a map of the sky with a resolution set by a $7^{\circ}$ FWHM beam which meant that only low-order multipoles were accessible to the experiment; DMR probes the pure Sachs-Wolfe effect. This makes it straight-forward to relate the DMR detection limits to those of the power spectrum (Peacock). It also provides sufficient data (the dipole, quadrupole and octupole limits) in order to place observation limits directly on the geometry using the almost-EGS theorem (Maartens-Stoeger-Ellis), the so called COBE-Copernican limits (Stoeger-Arajou-Gebbie).

The future of the subject is anticipate to be rich given that the American MAP satelite, which promises to obtain precision all-sky small-scale and polarization maps of the CMB by 2002, and the European PLANK satelite, which will have even higher precision maps by the end of the next decade. In this regard the two outstanding issues in astrophysical cosmology are those of the foregrounds and nonlinearity. While the issues of astrofundamental cosmology, those pertaining to the nature and formation of the primordial anisotropies, are still open. I would recommend the excellent Phd thesis of Wayne Hu for a broad summary of the canonical treatment of theoretical CMB anisotropies (astro-ph/9508126).

The canonical calculation of temperature anisotropies in universes with small deviations from perfect isotropy and homogeniety can be divided into the study of : primary sources (projected) and secondary sources (integrated). The primary sources arise due to the effects at the time of recombination, there are three important contributions. The Sachs-Wolfe effect, where photons climb out of potential wells which induces a redshift (Sachs-Wolfe 1967). The intrinsic photon temperature at last scattering due to acoustic oscillations, where the photons have been glued to the baryons by thompson scattering off electrons such that the coupled radiation-baryon fluid can compress the radiation leading to a higher temperature. Below the horizon but above the photon diffusion scale the radiation-baryon fluid evolve adiabatically leading to acoustic oscillations as the photons pressure resists gravitational compression (Peebles-Yu 1970). The plasma has a non-zero velocity at recombination which leads to Doppler shifts in the frequency and hence becomes brighter (Sunyaev-Zel'dovich 1970). The secondary sources are generated by scattering along the line of sight. These are characterized by differential gravitational redshifts, the Integrated Sachs-Wolfe effects (Sachs-Wolfe 1967). Additionally it was realized that diffusion damps out the intrinsic temperature fluctuations, meaning that the acoustic oscillation will be damped in strongly reionized models as well as during an era of slow decoupling (Kaiser 1984). In the reionized case other sources arising from fluctuations in the matter are important. These sources can yield strong contributions if last scattering occurs after the matter has been released from Compton drag (Vishniac 1987). A good code, CMBFAST (Seljak-Zaldariagga 1996), is avaliable for the calculation of linear-FRW temperature anisotropies (it is avaliable from http://www.sns.ias.edu/~matiasz/CMBFAST/cmbfast.html). Software, HEALPix, is avaliable with which to create, display and statistically analyse discrete full sky-maps, on a sphere, at a high angular resolution, http://www.tac.dk/~healpix/).

The approach of Sachs-Wolfe was that of integrating the photons down the null-cone. This was appropriate when the photons were either free-streaming or tightly-coupled to the matter. In the situation of interest, particularly for the primary sources, the photons are not perfectly coupled to the matter, nor is decoupling instantaneous. A kinetic theory description of the physics of temperature anisotropies, by being more fundamental than the fluid approach, became necessary. Particularly when dealing with reionization and other foreground physics. The line-of-sight code, CMBFAST, is a compromise between these two approaches and is only relevant to the linear regime. The Sachs-Wolfe approach forms a literature of its own. It is however the kinetic theory approach that is of interest here -- being physically more interesting.

In order to give one a sense of the two different traditions that developed with regards to understanding the CMB and it implications within the kinetic theory approach. I list some of the key papers in each tradition, first, the astrophysical cosmology approach and , second, the relativistic cosmology approach. The intention is of contrasting them -- this is not definative nor complete, merely my understanding of the key papers in the chronological development of the subjects theoretical foundations. The intention is to make clear how I view the development of the subject, along two distinct branches.

The first, as an artifact of the Astrophysical Cosmology approach : (acoustic sources) Peebles-Yu (1970), (gauge invariant perturbation theory of linearized metrics) Bardeen (1980), (relativistic kinetic theory and its mode decomposed formulation) Wilson-Silk (1981), Wilson (1983), (diffusion damping and second order scattering corrections) Kaiser (1983), (calculating realistic temperature anisotropies and fixing the cosmological parameters) Hu-Sugiyama (1995a,1995b) - they favoured metrics and the explicit use of coordinates and mode functions.

Second, that of Relativistic Cosmology : (relativistic kinetic theory in the 1+3 lagrangian formulation of GR) Ehlers (1971), (Exact RKT and the PSTF representations) Ellis-Matravers-Treciokas (1983) and Thorne (1980), (covariant and gauge invariant perturbation theory) (Ellis-Bruni 1989), (almost-EGS) Stoeger-Maartens-Ellis (1995), (the exact temperature anisotropy equations) Maartens-Gebbie-Ellis (1998) -- they favoured a dynamical treatment using coordinate free representations.