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Inflation ALAN H Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4871-4877, June 1993 Colloquium Paper This paper was presented at a coUoquium entitled "Physical Cosmology," organized by a committee chaired by David N. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA. Inflation ALAN H. GUTH Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 ABSTRACT A short review of inflation is given, starting a box, letting the size of the box approach infinity at the end with a description of the underlying mechanism and the of the calculation. One can then think of the electromagnetic scenario of events. Four variations-old inflation, new infla- fields inside the box as a mechanical system. The field can be tion, chaotic inflation, and extended inflation-are discussed. expanded as a sum of normal modes, and the coefficients of It is claimed that the inflationary model provides a plausible the normal mode functions can be taken as the dynamical explanation for (i) the large number ofparticles in the universe, degrees of freedom of the system. It turns out that each of (ii) the Hubble expansion, (iii) the large-scale uniformity ofthe these coefficients obeys the equations of a harmonic oscil- universe, (iv) the nearness of the universe to a critical density, lator, and there is no interaction between the coefficients. (v) the absence of magnetic monopoles, and (vi) the scale- The system is quantized by the same rules that one uses to invariant spectrum of microwave background fluctuations quantize the harmonic oscillator, and the result is that each observed by COBE (Cosmic Background Explorer). Finally, it normal mode has evenly spaced energy levels. In this case, is argued that the plausibility ofinflation is enhanced by the fact we interpret the nth excited state as the state that contains n that inflation is eternal. photons in the specified mode. Thus, the photon is inter- preted as the quantized excitation of a field. The inflationary model is a modification of the standard big In contemporary particle theory, all elementary particles are bang model that provides answers to a number of questions described in this way. There is an electron field to correspond that the standard model fails to address. The inflationary to an electron, a quark field to correspond to a quark, a period lasts for only a small fraction ofa second, and then the neutrino field to correspond to a neutrino, etc. Among the inflationary model joins smoothly onto the standard model. different types offields, the simplest is the scalar field-a field The role of inflation is to set up the initial conditions for the that has the same value to any Lorentz observer. The quan- standard model, conditions which otherwise would have to tized excitation ofa scalar field is a spinless particle. Although be assumed without explanation. Before inflation the total spinless particles that are regarded as elementary have yet to mass contained in the universe could have been as small as be observed, they are nonetheless akey ingredienttoa number 10 kg. If inflation is right, then the inflationary mechanism is of important theories. In particular, the Glashow-Weinberg- responsible for producing essentially all of the matter, en- Salam model of the electroweak interactions makes use of a ergy, and entropy that exists in the universe today. scalar field, the Higgs field, to cause a symmetry in the theory In this lecture I will give a brief review of inflation, to be spontaneously broken. (If this symmetry were not describing the mechanism of inflation, the outline of the broken, then electrons and neutrinos would both be massless scenario, the different types of inflationary models, and the and would be indistinguishable.) This Higgs field corresponds evidence for inflation. Finally I will briefly discuss the eternal to a neutral spinless Higgs particle, which will hopefully be nature of inflation: once inflation begins, calculations indi- observed at the SSC (Superconducting Supercoilider), if not cate that it ends locally but not globally. Although this before. Grand unified theories make use of similar Higgs property does not appear to lead to any observable predic- fields, but at a much higher mass scale, to spontaneously break tions, it certainly affects the way we think about the universe the grand unified symmetry that relates electrons, neutrinos, as a whole. and quarks. There is much current interest in superstring theories, I. The Mechanism of Inflation which actually go beyond the pattern ofthe field theories that were described above. In these theories the fundamental Before explaining the arguments for inflation, I will first object is not a field but is really a string-like object, which has explain how the inflationary model works. length but no width. These theories are believed to behave as The mechanism of inflation depends on scalar fields, so I field theories, however, at energy scales well below the will begin by briefly summarizing the role of scalar fields in Planck scale (Mp 1/'G' = 1.02 x 1019 GeV, where G is particle physics. To begin with, the reader should recognize Newton's constant, and I use units for which A c 1; 1 that in the context of modern particle physics, all fundamen- GeV = 1.602 x 10-10 J). In fact, these field theories contain tal particles are described by fields. The best known example a large number of scalar fields. Thus, the particle physics is the photon. The classical equations describing the electro- motivation for believing that scalar fields exist is quite strong. magnetic field were written down in the 1860s, but then in the The electromagnetic field has a potential energy density early 20th century physicists learned that the underlying laws given by V = (2 + A2)/81r, but the potential energy density of nature are quantum and not classical. The quantization of of the scalar field has a wider range of possibilities. It is the electromagnetic field can be carried out in a very straight- restricted by the criterion that the field theory be renormal- forward way. For simplicity one can consider the fields inside izable (i.e., the requirement that the field theory leads ultimately to finite answers), but there are still several free The publication costs of this article were defrayed in part by page charge parameters involved in specifying the potential. The form of payment. This article must therefore be hereby marked "advertisement" the scalar field potential appropriate for the new inflationary in accordance with 18 U.S.C. §1734 solely to indicate this fact. universe model is shown in Fig. 1. The potential has a 4871 Downloaded by guest on October 1, 2021 4872 Colloquium Paper: Guth Proc. Natl. Acad. Sci. USA 90 (1993) Before: False Vacuum &,- FaLse Vacuum P=Pf , p=? (metastable) {True Vacuum lP=o, p=O \True After: Vacuum _ -- ~dV 0 -OF 0 101 dW -pdV =pf dV FIG. 1. The potential energy function for the scalar field 4, appropriate for the new inflationary universe model. FIG. 2. A thought experiment to calculate the pressure of the false vacuum. As the piston chamber filled with false vacuum is minimum at a value of the scalar field that is nonzero, a enlarged, the energy density remains constant and the energy in- property that is generic for Higgs fields. The potential also creases. The extra energy is supplied by the agent puffing on the has a plateau centered at = 0, a feature that Higgs fields do piston, which must pull against the negative pressure of the false not necessarily have. This property is necessary, however, in vacuum. order for the new inflationary scenario to be possible. T.. -pf :.3, , [2] A particle physicist defines the word "vacuum" to mean the state of lowest possible energy density, so it is the state where gAl = diag[--1, 1, 1, 1] is the Lorentz metric. Thus, the in which lies at the minimum of the potential, labeled 4t on tensor of the false vacuum is Lorentz- the diagram. For emphasis, I will call this state the "true energy-momentum invariant, as one would expect, since the state is Lorentz- vacuum." Notice that the energy density of the true vacuum invariant. That is, if a region of space has a scalar field with is shown as zero, which is equivalent to the statement that the a constant value = 0, to another Lorentz observer it will constant is either zero or small. cosmological immeasurably also look like a region of space with a scalar field of value Even if the constant has a value that is cosmo- cosmological = 0. One could in fact have used this Lorentz-invariance as logically significant, the effect on this diagram would be an alternative derivation of Eq. 1. energy completely imperceptible, since the scales of particle Finally, we are ready to discuss the gravitational effects of physics are so much higher. The explanation for the small- this very peculiar energy-momentum tensor. Starting with ness of the cosmological constant has been a long-standing the Einstein field equations mystery to particle physicists, although we now have at least a possible solution (1) in the context of a crude understanding 1 of quantum gravity. RILV g"vR = 87rGT1"' A~' [3] 2 The state in which the scalar field, in some region of space, is perched at the top of the plateau of the potential energy one sees that the effect of the energy-momentum tensor of diagram is called the "false vacuum." Note that the energy Eq. 2 is precisely the same as having a temporarily nonzero density of this state is pf and therefore is fixed by the laws of value of the cosmological constant A, related by physics.
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