Elsevier

Physics Reports

Volumes 333–334, August 2000, Pages 555-574
Physics Reports

Inflation and eternal inflation

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Abstract

The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Vilenkin's proposal for avoiding these problems is also discussed.

Introduction

There are many fascinating issues associated with eternal inflation, so I can think of no subject more appropriate to discuss in a volume commemorating David Schramm. The shock of Dave's untimely death showed that even the most vibrant of human lives is not eternal, but his continued influence on our entire field proves that in many ways David Schramm is truly eternal. Dave is largely responsible for creating the interface between particle physics and cosmology, and is very much responsible for cementing together the community in which this interface developed. His warmth, his enthusiasm, and the efforts that he made to welcome young scientists to the field have strengthened our community in a way that will not be forgotten.

I will begin by summarizing the basics of inflation, including a discussion of how inflation works, and why many of us believe that our universe almost certainly evolved through some form of inflation. This material is not new, but I think it should certainly be included in any volume that attempts to summarize the important advances that Dave helped to develop and promote. Then I will move on to discuss eternal inflation, attempting to emphasize that this topic has important implications, and raises important questions, which should not be dismissed as being metaphysical.

Section snippets

How does inflation work?

The key property of the laws of physics that makes inflation possible is the existence of states of matter that have a high-energy density which cannot be rapidly lowered. In the original version of the inflationary theory [1], the proposed state was a scalar field in a local minimum of its potential energy function. A similar proposal was advanced by Starobinsky [2], in which the high-energy density state was achieved by curved space corrections to the energy–momentum tensor of a scalar field.

Evidence for inflation

No matter which form of inflation we might envision, we would like to know what is the evidence that our universe underwent a period of inflation. The answer is pretty much the same no matter which form of inflation we are discussing. In my opinion, the evidence that our universe is the result of some form of inflation is very solid. Since the term inflation encompasses a wide range of detailed theories, it is hard to imagine any reasonable alternative. The basic arguments are as follows:

(1)

Eternal inflation: mechanisms

The remainder of this article will discuss eternal inflation – the questions that it can answer, and the questions that it raises. In this section I discuss the mechanisms that make eternal inflation possible, leaving the other issues for the following sections. I will discuss eternal inflation first in the context of new inflation, and then in the context of chaotic inflation, where it is more subtle.

Eternal inflation: implications

In spite of the fact that the other universes created by eternal inflation are too remote to imagine observing directly, I nonetheless claim that eternal inflation has real consequences in terms of the way we extract predictions from theoretical models. Specifically, there are three consequences of eternal inflation that I will discuss.

First, eternal inflation implies that all hypotheses about the ultimate initial conditions for the universe – such as the Hartle–Hawking [36] no boundary

Difficulties in calculating probabilities

In an eternally inflating universe, anything that can happen will happen; in fact, it will happen an infinite number of times. Thus, the question of what is possible becomes trivial – anything is possible, unless it violates some absolute conservation law. To extract predictions from the theory, we must therefore learn to distinguish the probable from the improbable.

However, as soon as one attempts to define probabilities in an eternally inflating spacetime, one discovers ambiguities. The

The youngness paradox

If one chooses a truncation in the most naive way, one is led to a set of very peculiar results which I call the youngness paradox.

Specifically, suppose that one constructs a Robertson–Walker coordinate system while the model universe is still in the false vacuum (de Sitter) phase, before any pocket universes have formed. One can then propagate this coordinate system forward with a synchronous gauge condition,2

An alternative probability prescription

Since the probability measure depends on the method used to truncate the infinite spacetime of eternal inflation, we are not forced to accept the consequences of the synchronous gauge probabilities. A very attractive alternative has been proposed by Vilenkin [45], and developed further by Vanchurin et al. [29].

The key idea of the Vilenkin proposal is to define probabilities within a single-pocket universe (which he describes more precisely as a connected, thermalized domain). Thus, unlike the

Conclusion

In this paper I have summarized the workings of inflation, and the arguments that strongly suggest that our universe is the product of inflation. I argued that inflation can explain the size, the Hubble expansion, the homogeneity, the isotropy, and the flatness of our universe, as well as the absence of magnetic monopoles, and even the characteristics of the nonuniformities. The detailed observations of the cosmic background radiation anisotropies continue to fall in line with inflationary

Acknowledgements

The author particularly thanks Andrei Linde, Alexander Vilenkin, Neil Turok, and other participants in the Isaac Newton Institute programme Structure Formation in the Universe for very helpful conversations. This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative research agreement #DF-FC02-94ER40818, and in part by funds provided by NM Rothschild & Sons Ltd and by the EPSRC.

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    This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative research agreement #DF-FC02-94ER40818, and in part by funds provided by NM Rothschild & Sons Ltd and by the EPSRC.

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