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Evidence for Inflation

The standard big bang theory provides a successful account of the broad features of the Universe we observe. Built on the equations of general relativity, and nuclear and particle physics, which have been independently checked in many ways, it has three main successes. The first is a relation between the density and expansion rate of the Universe and the large scale spatial geometry. Based on the assumption of a hot, smooth, expanding early universe, it successfully predicted the existence and thermal spectrum of the relic cosmic microwave background. The most compelling success is the successful fit to the relative abundances of the five lightest elements with a single free parameter, the primordial baryon-to-photon ratio.

In spite of these successes, the theory is clearly incomplete. It does not explain many things about Universe, but merely attributes these to appropriate initial conditions. A striking example is the fact that the temperature of the cosmic microwave background radiation is very nearly identical at antipodal points on the sky. How could this be, when these points can have never communicated with each other - the light emitted from each is after all just reaching us, and we are in between them. So the initial conditions seem to be paradoxical and acausal. Similarly, despite the name, big bang theory does not explain cosmic expansion, it just assumes the initial conditions were rapidly expanding. A more accurate name would be the ‘big after-bang theory’. The density and the expansion rate had to be incredibly uniform, and the geometry very flat to be consistent with the large smooth Universe we see today. Nevertheless the density could not have been exactly uniform. There must have been variations from place to place of the right magnitude (about a part in a hundred thousand) to seed the process of gravitational collapse which formed galaxies, stars and planets.

Inflation offers a solution to some of these puzzles.A. Guth, Phys. Rev D23, 347 (1981). An unusual form of matter, ‘scalar field potential energy’, is assumed to have predominated over other forms of matter early on. Scalar field potential energy behaves like a cosmological constant, known since the 30’s to have a powerful repulsive gravitational field.P.J.E. Peebles, Principles of Physical Cosmology, Princeton 1993.This causes the Universe to expand exponentially, so that a region undergoing a relatively short period of inflation could nevertheless have expanded to a region much larger than the visible Universe today. This would resolve the paradox of the temperature being the same in opposite directions, because those two regions were originally causally connected in the inflationary, pre-big bang epoch. Guth realized that the exponential expansion would also have a flattening effect akin to what happens when a lumpy deflated balloon is blown up.

Unlike a cosmological constant, scalar field potential energy can ‘switch itself off’ after a period of exponential expansion, converting its energy into radiation and setting off the standard hot big bang. Thus inflation plays the role of setting up the initial conditions for the hot big bang, in a manner which preserves all the successes of the big bang theory.

Scalar fields were originally invoked for very different reasons in elementary particle physics, for the purpose of breaking symmetries and giving particles their mass. But unfortunately these scalar fields do not give interesting amounts of inflation, and special scalar fields have to be invoked, with potential energy functions which are picked in an ad hoc manner. Because of this inflationary models can at present only be viewed as a provisional.

The case for inflation nevertheless became much more convincing when it was realized that it automatically had a very beautiful (and originally unanticipated) side-effect, of producing density inhomogeneitiesS.W. Hawking, Phys. Lett. 115B, 295 (1982); A.H. Guth and S.-Y. Pi, Phys. Rev. Lett. 49, 1110 (1982); A.A. Starobinsky, Phys. Lett. 117B, 175 (1982); J. Bardeen, P. Steinhardt, and M. Turner, Phys. Rev....similar to those needed to account for the formation of galaxies and other structures in the Universe.Harrison, E. R., 1970, Phys. Rev., D1, 2726; Zeldovich, Ya. B., 1972, M.N.R.A.S., 160, 1

The primordial inhomogeneities are now being accurately probed by measurements of the cosmic microwave sky, providing us with detailed tests of inflationary models.A. D. Miller et al., Astrophys.J. 524 (1999) L1; P. de Bernardis et al., Nature, 404, 955, (2000); Hanany, S. et al., astro-ph/0005123 (2000). So inflationary models are certainly observationally testable. The last year has seen dramatic progress with the detection of the first ‘acoustic peak’ in the angular power spectrum of fluctuations in the cosmic microwave sky. The existence of such a peak had been anticipated long before inflation was invented, but its location at the position expected for a flat Universe, with the density inhomogeneities expected in simple inflationary models was rightly hailed as a success for inflationary theory. As someone who put a lot of effort into developing alternate theories of the origin of the inhomogeneities, I can testify that these observations have decisively disproved many alternate theories, thereby considerably strengthening the case for some simple inflationary model.

In spite of these major successes, inflation remains somewhat in a state of limbo because no convincing candidate for the needed scalar field has emerged. In fact, the most mathematically complete theories we have, string theory and supergravity, do not seem to yield fields with potential energy functions of the form needed without substantial special pleading.

Contributed by: Dr. Neil Turok

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Eternal Inflation Isn't


Neil Turok

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