Eternal chaotic inflation and string theory landscape

The process of the division of the Universe into different parts becomes even easier if one takes into account the process of self-reproduction of inflationary domains. The basic mechanism can be understood as follows. If quantum fluctuations are sufficiently large, they may locally increase the value of the potential energy of the scalar field in some parts of the Universe. The probability of quantum jumps leading to a local increase of the energy density can be very small, but the regions where it happens start expanding much faster than their parent domains, and quantum fluctuations inside them lead to the production of new inflationary domains which expand even faster.

Self-reproduction of inflationary domains was first established in the context of the new inflation scenario, which is based on inflation near a local maximum of the potential [4,22,23]. The existence of this regime was used for justification of the anthropic principle in ref. [4]. However, nobody paid any attention to this possibility until the discovery of self-reproduction of the Universe in the chaotic inflation scenario [7].

In order to understand this effect, let us consider an inflationary domain of initial radius H-1 containing a sufficiently homogeneous field with initial value 0 » Mp. Equations (8.3) tell us that, during a typical time interval At = H-1, the field inside this domain will be reduced by A0 = Mp/(4n0). Comparing this expression with the amplitude of quantum fluctuations,

2n V3nMp one can easily see that for 0 » 0* — MpsjMp/m, one has \50\ » |A0|, i.e. the motion of the field 0 due to its quantum fluctuations is much more rapid than its classical motion.

During the typical time H-1, the size of the domain of initial size H-1 containing the field 0 » 0* grows e times, its volume increases e3 — 20 times, and in almost half of this new volume the field 0 jumps up instead of down. Thus the total volume of inflationary domains with 0 ^ 0* grows approximately ten times. During the next time interval H-1, this process continues, so the Universe enters an eternal process of self-reproduction. I call this process 'eternal inflation'.

In this scenario, the scalar field may wander for an indefinitely long time as the density approaches the Planck density. This induces quantum fluctuations of all other scalar fields, which may jump from one minimum of the potential to another for an unlimited time. The amplitude of these quantum fluctuations can be extremely large, 5<p — 5$ — 10-1Mp. As a result, quantum fluctuations generated during eternal chaotic inflation can penetrate through any barriers, even if they have Planckian height, and the Universe after inflation becomes divided into an indefinitely large number of exponentially large domains. These contain matter in all possible states, corresponding to all possible mechanisms of spontaneous symmetry-breaking, i.e. to all possible laws of low-energy physics [7,24].

A rich spectrum of possibilities may appear during inflation in Kaluza-Klein and superstring theories, where an exponentially large variety of vacuum states and ways of compactification is available for the original 10- or 11-dimensional space. The type of compactification determines the coupling constants, the vacuum energy, the symmetry-breaking scale and, finally, the effective dimensionality of the space in which we live. As shown in ref. [25], chaotic inflation near the Planck density may lead to a local change in the number of compactified dimensions. This means that the Universe becomes divided into exponentially large parts with different dimensionality.

In some theories one may have a continuous spectrum of possibilities. For example, in the context of the Brans-Dicke theory, the effective gravitational constant is a function of the Brans-Dicke field, which also experienced fluctuations during inflation. As a result, the Universe after inflation becomes divided into exponentially large parts with all possible values of the gravitational constant G and the amplitude of density perturbations 5p/p [26,27]. Inflation may divide the Universe into exponentially large domains with continuously varying baryon-to-photon ratio nB/nY [28] and with galaxies having vastly different properties [29]. Inflation may also continuously change the effective value of the vacuum energy (the cosmological constant A), which is a prerequisite for many attempts to find an anthropic solution of the cosmological constant problem [6,30-39]. Under these circumstances, the most diverse sets of parameters of particle physics (masses, coupling constants, vacuum energy, etc.) can appear after inflation. One can say that, in a certain sense, the Universe becomes a multiverse.

Recently, the multiverse scenario has attracted special attention because of the discovery that string theory admits many metastable de Sitter vacua with different properties, and different domains of the Universe may unceasingly jump between these vacua [40-42]. The lifetime of each of these states is typically much greater than the age of our part of the Universe. The total number of metastable vacuum states in string theory may be as large as 101000 [43,44].

Once this 'string landscape' became part of the string theory description of the world, it became very difficult to forget about it and return to the old idea that the theory must have only one vacuum state, with the goal of physics being to find it. One can either like this new picture or hate it, but it cannot be discarded purely on the basis of ideological considerations. If this scenario is correct, then physics alone cannot provide a complete explanation for all properties of our part of the Universe. The same physical theory may yield large parts of the Universe that have diverse properties. According to this scenario, we find ourselves inside a 4-dimensional domain with our kind of physical laws, not because domains with different dimensionality and with alternate properties are impossible or improbable, but simply because our kind of life cannot exist in other domains.

This scenario provides a simple justification of the anthropic principle and removes the standard objections against it. One does not need anymore to assume that some supernatural cause created the Universe with the properties specifically fine-tuned to make our existence possible. Inflation itself, without any external intervention, may produce exponentially large domains with all possible laws of low-energy physics. And we should not be surprised that the conditions necessary for our existence appear on a very large scale rather than only in a small vicinity of the solar system. If the proper conditions are established near the solar system, inflation ensures that similar conditions appear everywhere within the observable part of the Universe.

The new possibilities that appear due to the self-reproduction of the Universe may provide a basis for what I call the 'Darwinian' approach to cosmology [33,45,46]. Mutations of the laws of physics may lead to the formation of domains with the laws of physics that allow a greater speed of expansion of the Universe; these domains will acquire greater volume and may host a greater number of observers. On the other hand, the total volume of domains of each type grows indefinitely large. This process looks like a peaceful coexistence and competition, and sometimes even like a fruitful collaboration, with the fastest growing domains producing many slower growing brothers. In the simplest models of this type, a stationary regime is reached, and the speed of growth of the total volume of domains of each type becomes equally large for all of the domains [24].

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