Andrei Linde

Professor of Physics

Contact Information

Department of Physics
Varian blg. 386
Stanford University
Stanford, CA 94305

Research Interests

I am one of the authors of the inflationary cosmology and of the theory of the cosmological phase transitions. These two topics remain the main subject of my work. Current research also involves the theory of dark energy, investigation of the global structure and the fate of the universe, cosmological constraints on the properties of elementary particles, and quantum cosmology.

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1. A.D. Linde, INFLATION AND QUANTUM COSMOLOGY (Academic Press, Boston 1990)

2. A.D. Linde, PARTICLE PHYSICS AND INFLATIONARY COSMOLOGY (Harwood Academic Publishers, Chur, Switzerland 1990)

Career History

Curriculum Vitae

Inflationary Multiverse

Inflationary theory describes the very early stages of the evolution of the Universe, and its structure at extremely large distances from us. For many years, cosmologists believed that the Universe from the very beginning looked like an expanding ball of fire. This explosive beginning of the Universe was called the big bang. In the end of the 70's a different scenario of the evolution of the Universe was proposed. According to this scenario, the early universe came through the stage of inflation, exponentially rapid expansion in a kind of unstable vacuum-like state (a state with large energy density, but without elementary particles). Vacuum-like state in inflationary theory usually is associated with a scalar field, which is often called ``the inflaton field.'' The stage of inflation can be very short, but the universe within this time becomes exponentially large. Initially, inflation was considered as an intermediate stage of the evolution of the hot universe, which was necessary to solve many cosmological problems. At the end of inflation the scalar field decayed, the universe became hot, and its subsequent evolution could be described by the standard big bang theory. Thus, inflation was a part of the big bang theory. Gradually, however, the big bang theory became a part of inflationary cosmology. Recent versions of inflationary theory assert that instead of being a single, expanding ball of fire described by the big bang theory, the universe looks like a huge growing fractal. It consists of many inflating balls that produce new balls, which in turn produce more new balls, ad infinitum. Therefore the evolution of the universe has no end and may have no beginning. After inflation the universe becomes divided into different exponentially large domains inside which properties of elementary particles and even dimension of space-time may be different. Thus the universe looks like a multiverse consisting of many universes with different laws of low-energy physics operating in each of them. Thus, the new cosmological theory leads to a considerable modification of the standard point of view on the structure and evolution of the universe and on our own place in the world. A description of the new cosmological theory can be found, in particular, in my article The Self-Reproducing Inflationary Universe published in Scientific American, Vol. 271, No. 5, pages 48-55, November 1994. A nice introduction to inflation was written by the journalist and science writer John Gribbin Cosmology for Beginners . The new cosmological paradigm may have non-trivial philosophical implications. In particular, it provides a scientific justification of the cosmological anthropic principle, and allows one to discuss a possibility to create the universe in a laboratory.

A Brief History of the Multiverse

The idea of an inflationary multiverse (the universe consisting of many universes with different properties) was first proposed in 1982 in my Cambridge University preprint Nonsingular Regenerating Inflationary Universe . A more detailed discussion of this possibility was contained in my paper The New Inflationary Universe Scenario published in the book "The Very Early Universe," ed. G.W. Gibbons, S.W. Hawking and S.Siklos, Cambridge University Press, 1983, pp. 205-249. Implications of this picture for the "SUSY landscape" (the universe with different properties corresponding to different vacua of supersymmetric theories) was discussed in my paper Inflation Can Break Symmetry In SUSY, Phys. Lett. B131, 330 (1983). A major step in the development of the theory of the multiverse was related to the discovery of eternal inflation; for a discussion of its anthropic implications see the last page of my paper Eternally Existing Self-Reproducing Chaotic Inflationary Universe, Phys. Lett. B175, 395 (1986). The methods of calculation of the probability to live in the parts of the universe with different properties were developed in my paper with Dimitri Linde and Arthur Mezhlumian From the Big Bang Theory to the Theory of a Stationary Universe, in my paper with Juan Garcia-Bellido and Dimitri Linde Fluctuations of the Gravitational Constant in the Inflationary Brans-Dicke Cosmology, and in the paper by Alex Vilenkin Predictions from Quantum Cosmology, who called these methods "the mediocrity principle."

One of the most important implications of the anthropic principle in the context of inflationary multiverse is the possility to solve the cosmological constant problem. The first anthropic solution of the cosmological constant problem was proposed at the last page of my review article The Inflationary Universe , Rept. Prog. Phys. 47, 925 (1984). My second proposal was made in my paper Inflation and Quantum Cosmology. It was written in June 1986, and published in the book "300 years of gravitation," (Eds.: S.W. Hawking and W. Israel, Cambridge Univ. Press, 1987), 604-630. The main goal of these two papers was to propose a physical mechanism which would allow the existence of different exponentially large parts of the universe with different values of the cosmological constant. Until the invention of the inflationary theory, this was an unsolvable problem. In addition to this problem addressed in my papers mentioned above, one must also show that life can hardly exist in the parts of the universe where the cosmological constant is much greater than the present energy density in our part of the universe. Validity of this order-of-magnitude condition was pretty obvious even 20 years ago, and it was taken for granted in my works mentioned above. However, in order to have a reliable anthropic solution for the cosmological constant problem one should know a more precise anthropic bound on the cosmological constant. The progress in this direction began in 1987 with the famous paper by Steven Weinberg Anthropic Bound on the Cosmological Cosntant . His work and the subsequent developments confirmed the assumption that the probability of existence of life of our type becomes strongly suppressed if the cosmological constant is much greater than the present energy density in the universe. The experimental discovery of the cosmological constant satisfying the anthropic bound was greeted as an experimental evidence in favour of the multiverse scenario.

One of the most important recent steps in the development of the multiverse theory was a discovery of the KKLT mechanism of moduli stabilization in string theory, which allows to explain accelerated expansion of the universe and inflation in the context of string theory. The KKLT mechanism can lead to an incredibly large number of different vacua, perhaps 10100 or even 101000, corresponding to different local minima of energy in a vast string theory landscape. This means that our multiverse may consist of exponentially many exponentially large domains (universes), each of which may live in accordance to one of the exponentially large variety of laws of the low-energy physics.

Are there any Alternatives to Inflation?

There were many attempts to replace inflation by other theories. One attempt that attracted a lot of attention in the media is called the ekpyrotic/cyclic scenario. However, ekpyrotic/cyclic scenario scenario is plagued by numerous problems. The original version of the ekpyrotic theory, which was supposed to be a true alternative to inflation, did not work. It was replaced by the cyclic scenario, which also suffers from many problems, including the yet unsolved problem of the cosmological singularity. Independently of these issues, solving the homogeneity problem in the cyclic scenario requires an infinite sequence of periods of accelerated expansion of the universe in a vacuum-like state, i.e. an infinite number of inflationary stages. In this sense, instead of being a true alternative to inflation, the cyclic scenario is a rather unusual and problematic version of inflationary theory. Thus, at present, inflation remains the only robust mechanism that produces density perturbations with a flat spectrum and simultaneously solves all major cosmological problems.

Dark Energy and the Fate of the Universe

Observational data indicate that the universe accelerates. If this is caused by the positive vacuum energy (cosmological constant), acceleration of the universe will continue forever. However, recently we have found that in a broad class of theories describing the present stage of acceleration of the universe, this acceleration may end and the universe may eventually collapse. Rather unexpectedly, we found that this may happen not in an extremely distant future, as one could expect, but in about 10-20 billion years. This may happen in a broad class of realistic theories of elementary particles, including, in particular the popular theories based on M-theory and supergravity. This is not a doomsday prediction because other outcomes (such as eternal acceleration of the universe) are also theoretically possible and are equally compelling. The only way to find out which of these possibilities is more realistic is to make cosmological observations. These results may have important implications. One may argue: Why do I care about the most abstract theories of elementary particles, such as M-theory, string theory or supergravity? Why do I care about precise measurements of cosmological parameters? Why do we need to spend billions of dollars for the development of science? Now we can add something new to the existing arguments: Without the development of these theories and without cosmological observations we will be unable to know the fate of the universe and the fate of the mankind. Here one can find a popular discussion of our work (see also an article in SF Chronicle).

1. Self-Reproduction of the Universe

Inflationary cosmology is different in many respects from the standard big bang cosmology. Domains of the inflationary universe with sufficiently large energy density permanently produce new inflationary domains due to stochastic processes of generation of the long-wave perturbations of the scalar field. Therefore the evolution of the universe in the inflationary scenario has no end and may have no beginning. Here we present the results of computer simulations of generation of quantum fluctuations in the inflationary universe. These processes should occur in the very early universe, at the densities just below the Planck density. 1) Series of figures in gold show generation of fluctuations of the scalar field $\varphi$ during inflation. Classically, the value of this field should decrease, but quantum perturbations lead to formation of exponentially large domains containing the scalar field which is much bigger than its initial value. In particular, calculation of the volume of the parts of the universe corresponding to the peaks of the ``mountains'' shows that it is much bigger than the volume of the parts where the scalar field rolled to the minimum of its energy density.

2) Series of figures in red, blue and green show evolution of another scalar field, which has three different minima of its potential energy density. In the regions when the inflaton field is large (it is represented by the hight of the mountains), the second field strongly fluctuates. In the domains where the inflaton field is small, the second field relaxes near one of the three minima of its potential energy density, shown by red, blue and green correspondingly. Each such domain is exponentially large. If the second field is responsible for symmetry breaking in the theory, then the laws of low-energy physics inside domains of different colors are different. The universe globally looks not like an expanding ball, but like a huge fractal consisting of exponentially large domains permanently produced during inflation.

3) The third movie shows only the evolution of the second field, determining the choice of the symmetry breaking (shown by dirrerent colors), so the images are two-dimensional. This made it possible to perform simulations on a much greater scale and with a much better resolution. We called this series of images ``Kandinsky universe,'' after the famous Russian abstractionist.



PowerPoint Talks






Varna 2008