Only four years after his discovery that galaxies truly are extragalactic, Hubble made his second fundamental breakthrough: he showed that the recession velocities of galaxies are linearly related to their distances (Hubble, 1929; see also Hubble & Humason 1931), thus demonstrating that our Universe is expanding. This is undoubtedly the greatest single discovery in the history of cosmology. It revolutionized our picture of the Universe we live in.
The construction of mathematical models for the Universe actually started somewhat earlier. As soon as Albert Einstein completed his theory of general relativity in 1916, it was realized that this theory allowed, for the first time, the construction of self-consistent models for the Universe as a whole. Einstein himself was among the first to explore such solutions of his field equations. To his dismay, he found that all solutions require the Universe either to expand or to contract, in contrast with his belief at that time that the Universe should be static. In order to obtain a static solution, he introduced a cosmological constant into his field equations. This additional constant of gravity can oppose the standard gravitational attraction and so make possible a static (though unstable) solution. In 1922 Alexander Friedmann published two papers exploring both static and expanding solutions. These models are today known as Friedmann models, although this work drew little attention until Georges Lemaitre independently rediscovered the same solutions in 1927.
An expanding universe is a natural consequence of general relativity, so it is not surprising that Einstein considered his introduction of a cosmological constant as ‘the biggest blunder of my life’ once he learned of Hubble’s discovery. History has many ironies, however. As we will see later, the cosmological constant is now back with us. In 1998 two teams independently used the distance–redshift relation of Type Ia supernovae to show that the expansion of the Universe is accelerating at the present time. Within general relativity this requires an additional mass/energy component with properties very similar to those of Einstein’s cosmological constant. Rather than just counterbalancing the attractive effects of ‘normal’ gravity, the cosmological constant today overwhelms them to drive an ever more rapid expansion.
Since the Universe is expanding, it must have been denser and perhaps also hotter at earlier times. In the late 1940s this prompted George Gamow to suggest that the chemical elements may have been created by thermonuclear reactions in the early Universe, a process known as primordial nucleosynthesis. Gamow’s model was not considered a success, because it was unable to explain the existence of elements heavier than lithium due to the lack of stable elements with atomic mass numbers 5 and 8. We now know that this was not a failure at all; all heavier elements are a result of nucleosynthesis within stars, as first shown convincingly by Fred Hoyle and collaborators in the 1950s. For Gamow’s model to be correct, the Universe would have to be hot as well as dense at early times, and Gamow realized that the residual heat should still be visible in today’s Universe as a background of thermal radiation with a temperature of a few degrees kelvin, thus with a peak at microwave wavelengths. This was a remarkable prediction of the cosmic microwave background radiation (CMB), which was finally discovered in 1965. The thermal history suggested by Gamow, in which the Universe expands from a dense and hot initial state, was derisively referred to as the Hot Big Bang by Fred Hoyle, who preferred an unchanging steady state cosmology. Hoyle’s cosmological theory was wrong, but his name for the correct model has stuck.
The Hot Big Bang model developed gradually during the 1950s and 1960s. By 1964, it had been noticed that the abundance of helium by mass is everywhere about one third that of hydrogen, a result which is difficult to explain by nucleosynthesis in stars. In 1964, Hoyle and Tayler published calculations that demonstrated how the observed helium abundance could emerge from the Hot Big Bang. Three years later, Wagoner et al. (1967) made detailed calculations of a complete network of nuclear reactions, confirming the earlier result and suggesting that the abundances of other light isotopes, such as helium-3, deuterium and lithium, could also be explained by primordial nucleosynthesis. This success provided strong support for the Hot Big Bang. The 1965 discovery of the cosmic microwave background showed it to be isotropic and to have a temperature (2.7K) exactly in the range expected in the Hot Big Bang model (Penzias & Wilson, 1965; Dicke et al., 1965). This firmly established the Hot Big Bang as the standard model of cosmology, a status which it has kept up to the present day. Although there have been changes over the years, these have affected only the exact matter/energy content of the model and the exact values of its characteristic parameters.
Despite its success, during the 1960s and 1970s it was realized that the standard cosmology had several serious shortcomings. Its structure implies that the different parts of the Universe we see today were never in causal contact at early times (e.g. Misner, 1968). How then can these regions have contrived to be so similar, as required by the isotropy of the CMB? A second shortcoming is connected with the spatial flatness of the Universe (e.g. Dicke & Peebles, 1979). It was known by the 1960s that the matter density in the Universe is not very different from the critical density for closure, i.e. the density for which the spatial geometry of the Universe is flat. However, in the standard model any tiny deviation from flatness in the early Universe is amplified enormously by later evolution. Thus, extreme fine tuning of the initial curvature is required to explain why so little curvature is observed today. A closely related formulation is to ask how our Universe has managed to survive and to evolve for billions of years, when the time scales of all physical processes in its earliest phases were measured in tiny fractions of a nanosecond. The standard cosmology provides no explanations for these puzzles.
A conceptual breakthrough came in 1981 when Alan Guth proposed that the Universe may have gone through an early period of exponential expansion (inflation) driven by the vacuum energy of some quantum field. His original model had some problems and was revised in 1982 by Linde and by Albrecht & Steinhardt. In this scenario, the different parts of the Universe we see today were indeed in causal contact before inflation took place, thereby allowing physical processes to establish homogeneity and isotropy. Inflation also solves the flatness/time-scale problem, because the Universe expanded so much during inflation that its curvature radius grew to be much larger than the presently observable Universe. Thus, a generic prediction of the inflation scenario is that today’s Universe should appear flat.
