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The current model for structure formation in the expanding universe has been remarkably successful. Indeed it has recently been argued that we have resolved the principal issues in cosmology. 1 However the lessons of history prescribe caution. There have been more oscillations in the values of the Hubble constant, the deceleration parameter and the cosmological constant over the working life of a cosmologist than one cares to recall. As the quality of the data has improved, one can be reasonably confident that the uncertainties in parameter extraction have decreased. But have we really converged on the definitive model?

I have selected seven of the key paradigms in order to provide a critical assessment. To set the context I will first review the reliability of the fundamental model of cosmology, the Big Bang model, in terms of the time elapsed since the initial singularity, or at least, the Planck epoch, 10-43 s.

Galaxies are well studied between the present epoch, ~ 14 x 109 yr, and ~ 3 x 109 yr (z approx 3). One can examine the distribution of Lyman alpha clouds, modelling chemical evolution from the gas phase metal abundances, 2 and find large numbers of young, star-forming galaxies back to about 2 x 109 yr (z approx 4). 3 Beyond this are the dark ages where neither gas nor evidence of galaxy formation has yet been detected. Strong circumstantial evidence from the Gunn-Peterson effect, indicating that the universe is highly ionized by z = 5, suggests that sources of ionizing photons must have been present at an earlier epoch.

Microwave background fluctuations provide substantial evidence on degree angular scales for an acoustic peak, generated at 3 x 105 yr (z = 1000), when the radiation underwent its last scatterings with matter. 4 The blackbody spectrum of the cosmic microwave background, with no deviation measured to a fraction of a percent and a limit on the Compton y parameter Deltay < 3 x 10-6 (95% CL) on 7 degree angular scales, 5 could only have been generated in a sufficiently dense phase which occurred during the first year of the expansion. Light element nucleosynthesis is an impressive prediction of the model, and testifies to the Friedmann-like character at an epoch of one second. At this epoch, neutrons first froze out of thermal equilibrium to subsequently become incorporated in 2H, 4He, and 7Li, the primordial distribution of which matches the predicted abundances for a unique value of the baryon density. 6

Thus back to one second, there is strong observational evidence for the canonical cosmology. At earlier epochs, any observational predictions are increasingly vague or non-existent. One significant epoch is that of the quark-hadron phase transition (t ~ 10-4 s, T ~ 100 MeV), which while first order cannot have been sufficiently inhomogeneous to amplify density fluctuations to form any primordial black holes. 7 The electro-weak phase transition (t ~ 10-10 s, T ~ 100 GeV), was even more short-lived but may have triggered baryon genesis. Before then, one has the GUT phase transition (t ~ 10-35 s, T ~ 1015 GeV), and the Planck epoch (t ~ 10-43 s, T ~ 1019 GeV), of unification of gravitation and electroweak and strong interactions. Inflation is generally believed to be associated with a strongly first order GUT phase transition, but is a theory that is exceedingly difficult, if not impossible, to verify. 8 A gravitational radiation background at low frequency is one possible direct relic of quantum gravity physics at the Planck epoch, but we are far from being able to detect such a background.

In summary, we could say that our cherished beliefs, not to be abandoned at any price, endorse the Big Bang model back to an epoch of about one second or T ~ 1 MeV. One cannot attribute any comparable degree of confidence to descriptions of earlier epochs because any fossils are highly elusive. Bearing this restriction in mind, we can now assess the paradigms of structure formation. The basic framework is provided by the hypothesis that the universe is dominated by cold dark matter, seeded by inflationary curvature fluctuations. This does remarkably well at accounting for many characteristics of large-scale structure in the universe. These include galaxy correlations on scales from 0.1 to 50 Mpc, the mass function and morphologies of galaxy clusters, galaxy rotation curves and dark halos, the properties of the intergalactic medium, and, most recently, the strong clustering found for luminous star-forming galaxies at z ~ 3. I will focus on specific paradigms that underly these successes and assess the need for refinement both in data and in theory that may be required before we can be confident that we have found the ultimate model of cosmology.

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