Modern Cosmology -
Part V: From Inflation to CMB
Jacobs University Bremen

Inflation

Caption: In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1025 in radius, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part of the electroweak epoch following the grand unification epoch. It lasted from 10-36 seconds after the Big Bang to sometime between 10-33 and 10-32 seconds. Following the inflationary period, the universe continues to expand. As a direct consequence of this expansion, all of the observable universe originated in a small causally connected region. Inflation answers the classic conundrum of the Big Bang cosmology: why does the universe appear flat, homogeneous and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the Big Bang, a highly curved, heterogeneous universe? Inflation also explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the universe.

Inflation and Perturbation
1. Primordial Nucleosynthesis

A series of nuclear reactions took place when the Universe was seconds old and made the lightest elements in the periodic table. The successful predictions of big-bang nucleosynthesis make it a cornerstone of the hot bigbang cosmology. It also leads to the most accurate determination of the baryon density of the Universe, provides the linchpin in the case for the existence of nonbaryonic dark matter, and permits the study of fundamental physics in regimes beyond the reach of terrestrial laboratories.

In 1942 George Gamow began talking about the big-bang origin of the elements. In the 1948 paper that marks the beginning of big-bang nucleosynthesis (BBN), Gamow, his student Ralph Alpher, and Hans Bethe proposed that the periodic table was built up by neutron capture minutes after the big bang. Critical physics corrections made by Chushiro Hayashi, Enrico Fermi and Anthony Turkevich led to the seminal 1953 paper of Alpher, Robert Herman and James Follin that described correctly the big-bang synthesis of large amounts of 4He and little else. As Fermi and Turkevich had pointed out, Coulomb barriers and the lack of stable nuclei with mass 5 and 8 preclude significant nucleosynthesis beyond 4He. BBN required a hot beginning, and in 1949 Alpher and Herman predicted a 5 K temperature for the relic radiation now known as the Cosmic Microwave Background (CMB).

As the above diagram shows, within all theoretical and observational errors, the Big Bang Nucleosynthesis are impressively accurate. Except in the leftmost part, the pale blue strip indicating the observed value for helium-4 can hardly be distinguished from the theoretical curve. The green deuterium curve meets the pale green strip indicating the observed value almost exactly at the value indicated by the WMAP observations (vertical golden strip), and similarly the WMAP observations, the magenta helium-3 curve and the observed upper limit for helium-3 coincide very well. Only for lithium-7 is there an appreciable gap between prediction and observation though, given the uncertainties of determining the initial abundance of this element from observations, this discrepancy is likely to teach us more about stellar physics than about Big Bang Nucleosynthesis. All in all, this match between theory and observation constitutes one of the big successes of the standard models of cosmology.

2. Inflation in the Early Universe

INFLATION has become a cosmological buzzword in the 1990s. No self-respecting theory of the Universe is complete without a reference to inflation - and at the same time there is now a bewildering variety of different versions of inflation to choose from. Clearly, what's needed is a beginner's guide to inflation, where newcomers to cosmology can find out just what this exciting development is all about.

The reason why something like inflation was needed in cosmology was highlighted by discussions of two key problems in the 1970s. The first of these is the horizon problem -- the puzzle that the Universe looks the same on opposite sides of the sky (opposite horizons) even though there has not been time since the Big Bang for light (or anything else) to travel across the Universe and back. So how do the opposite horizons "know" how to keep in step with each other? The second puzzle is called the flatness problem This is the puzzle that the spacetime of the Universe is very nearly flat, which means that the Universe sits just on the dividing line between eternal expansion and eventual recollapse.

The flatness problem can be understood in terms of the density of the Universe. The density parameter is a measure of the amount of gravitating material in the Universe, usually denoted by the Greek letter omega (O), and also known as the flatness parameter. It is defined in such a way that if spacetime is exactly flat then O = 1. Before the development of the idea of inflation, one of the great puzzles in cosmology was the fact that the actual density of the Universe today is very close to this critical value -- certainly within a factor of 10. This is curious because as the Universe expands away from the Big Bang the expansion will push the density parameter away from the critical value.

Inflation was proposed in January 1980 by Alan Guth as a mechanism for resolving these problems. At the same time, Alexei Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the universe with an exponentially expanding deSitter phase. In October 1980 Demosthenes Kazanas suggested that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem, and Sato suggesting that an exponential expansion could eliminate domain walls (another kind of exotic relic.) In 1981 Einhorn and Sato published a model similar to Guth's and showed that it would resolve the puzzle of the magnetic monopole abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would very likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions.

3. Perturbations and Growth of Structure

Caption: The composite image on the left is of the galaxy cluster Abell 85, located about 740 million light years from Earth. The illustration on the right shows snapshots from a simulation, representing the growth of cosmic structure when the Universe was 0.9 billion, 3.2 billion and 13.7 billion years old (now).

In a universe dominated by matter and radiation (as opposed to dark energy), the mutual gravitational pull of all the particles tends to slow down the expansion rate as the universe expands. When the universe was smaller and more dense, it therefore follows that the expansion rate was much larger than it is today. Indeed, as we extrapolate the universe further back in time, we reach a point where the density, temperature, and expansion rate were all infinitely large. This point is a singularity, which we refer to as the Big Bang (although that term is also used for the entire cosmological model that includes the later universe as well). At the Big Bang, our knowledge of what happens gives out; the fact that physical quantities become infinite is a sign that we don't know what is going on. Presumably, in the real world there is no singularity; instead, something happens that cannot be described by physics as we currently understand it.

Exercises VI
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Exercises VI - Solutions
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Lecture Notes: Part V
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