Andrei Linde is Harold Trap Friis Professor of Physics at Stanford University and one of the most influential cosmologists of our time. Linde is one of the authors of the inflationary universe scenario, which is gradually becoming the standard paradigm of modern cosmology, replacing the previous versions of the big bang theory. In 1974, he pointed out that the energy density of a scalar field plays the role of the vacuum energy density (cosmological constant) in the Einstein equations. In 1976 to 1978, he demonstrated that the energy released during the cosmological phase transitions may be sufficient to heat up the universe. These observations became the basic ingredients of the inflationary scenario proposed by Alan Guth in 1981. In 1982, Andrei suggested the new inflationary universe scenario, which resolved the problems of the original model proposed by Guth, while preserving most of its important features. At present, he continues his work on inflation, creation of matter in the universe, the theory of the inflationary multiverse, and the cosmological consequences of string theory.
For his work, Linde has received multiple awards including the Dirac Medal (2002) along with Alan Guth (MIT) and Paul Steinhardt (Princeton University). In 2004 he received, along with Alan Guth, the Gruber Prize in Cosmology for the development of inflationary cosmology and in 2012 the Fundamental Physics Prize. Linde has also received the Kavli Prize in Astrophysics together with Guth and Starobinsky for "their pioneering work in the theory of cosmic inflation" and in 2018 the Gamow Prize.
In this interview we discuss about the developments that led to his revolutionary theory of cosmic inflation, as well as the motivation for the theories of eternal inflation and more recently of inflationary multiverse. We explore with Linde the various steps that led to the formation of inflationary cosmology, the legacy of his work as well as about the interplay between theory and experiment in our efforts to answer some of the most fundamental questions about our Universe.
What motivated you to study physics?
Both of my parents were physicists. My mother worked until the age of 86 as a Physics Professor at the Moscow State University. My father was a Professor of Radiophysics. Thus, physics seemed like a straightforward option for me, though this was not always the case. Until the eighth grade I wanted to be a geologist. I was dreaming of travelling around the world and discovering precious minerals.
It was during a road trip with my parents to the Black Sea, when I was 15, that I decided that I would like to become a physicist. I was sitting in the back seat of the car reading two books that my parents had given to me. The first was about astrophysics and the other about the special theory of relativity. By the time that we arrived at our destination I was already a physicist (laughs)!
I studied physics at the Moscow State University. I had asked many people whether I should become a theorist or an experimentalist. Theorists told me that I should be a theorist, because bad experimentalists do not know what they are doing, but bad theorists at least learn something. Experimentalists said that I should become an experimentalist, because bad theorists do not understand much, but bad experimentalists at least can participate in the discoveries made by others. This was rather discouraging, but then I stopped asking because gradually it became clear that I am a theorist.
Perhaps it is interesting to mention that a couple of months before our graduation, our Professor of Quantum Field Theory told us that we should not pursue theoretical physics as it was a dead field! He argued that the accelerator at Dubna didn’t offer any fascinating results, while he believed that theory was also a dry field as most of it was axiomatic field theory that could not give us new insights about nature. It was rather shocking to hear these thoughts from our own professor. His words puzzled me, but I had already made my decision.
How did you enter into cosmology?
Following my graduation from Moscow’s State University, I enrolled as a postdoc at the Lebedev Physical Institute, where I pursued my PhD under the supervision of David Kirzhnits at the Lebedev Physics Institute.
As an undergraduate I studied the physics of neutrinos. In January 1972, my first day in the Lebedev Physics Institute as a postdoc, I asked Kirzhnits whether I should publish my work. His reply shocked me: “Forget about it, the world has changed, we have a unified theory of weak and electromagnetic interactions based on the Higgs effect, it is beautiful, it is renormalizable, so just forget everything that you were doing before.”
Kirzhnits was an outstanding scientist. He possessed a deep intuitive understanding of many branches of theoretical physics. He had noticed that the Higgs effect is based on principles very similar to those of superconductivity. Superconductivity disappears at high temperature because of the evaporation of the Bose-condensate of Cooper pairs. What is an analogue of this effect in the theory of electroweak interactions? The difference between weak and electromagnetic interactions appears because of a special type of a scalar field, the Higgs field. Kirzhnits conjectured that at high temperatures the scalar field also evaporates, and when it happens, the difference between weak and electromagnetic interactions disappears.
This concept gave birth to the idea that one could go back in time and study what happens in the early Universe as its temperature and energy density goes down. The main idea was that when the universe was very hot, there was not much difference between weak and electromagnetic interactions. The difference between the two appears only later, when the universe cools down, and a homogeneous Higgs field emerges everywhere. The theory of such cosmological phase transitions became a part of my PhD thesis.
How were these ideas accepted by your peers and how easy was to publish them?
The theory that we suggested seemed rather exotic, but we didn’t face any difficulties in publishing. Our first paper was published in Physics Letters B in 1972 . At first, it was quite difficult to convince our peers and get broader consensus on the interpretation of our results. One of the frequent questions was: “Where is the temperature in the Hamiltonian?” Our explanation that spontaneous symmetry breaking is similar to Bose condensation was often met with disbelief.
The turning point was when Yakov Zeldovich, the head of the Soviet cosmological school, together with Igor Kobzarev and Lev Okun, published their paper “Cosmological consequences of a spontaneous breakdown of a discrete symmetry”  merging the idea of cosmological phase transitions with a model of spontaneous CP violation proposed by T.D. Lee 
In 1974 we submitted to JETP, a Russian journal of theoretical physics, our second paper on the cosmological phase transitions . Similar results were obtained by Steven Weinberg  and by L. Dolan and R. Jackiw , confirming our main conclusions and elaborating in more detail the mechanism that we proposed. The support that we received from them lead to a wide acceptance of the theory of cosmological phase transitions.
How would you summarize the main point from this work and how this work shaped modern cosmology?
The main point stemming from our work is that the early universe is far more interesting than what was generally expected, because of new ideas in particle physics. The symmetry between the weak and electromagnetic interactions was restored in the early Universe, making the unification of different forces was more evident. In 1976 we found out that symmetry breaking between different interactions may occur discontinuously, as in the first order phase transitions. When the universe cools down, it may enter a supercooled state. The scalar field at first appears only due to tunneling from this state, inside separate expanding bubbles, resembling bubbles of vapor in boiling water. Eventually these bubbles collide, merge, and the scalar field penetrates everywhere. Few years later this concept became the foundation for the first models of inflationary cosmology.
To appreciate all of these developments, one may look at one of the best popular books on cosmology at that time and still today, Steven Weinberg's “The first three minutes” first published in 1977. At that time, it would be difficult to write a popular book about the first three milliseconds in the life of the universe, because at that epoch the density of the universe was greater than the nuclear density, so how could one say anything reliable about it? And our cosmological phase transitions happened much earlier, at densities much greater than the nuclear density.
The discovery of the Standard Model, the proof of its renormalizability, and the discovery of asymptotic freedom changed everything. As a result of these developments, it became possible to make calculations at high energies, and at high temperatures. Paradoxically, the higher the temperature and density, the more reliable the results, due to asymptotic freedom. This suggested that one could investigate properties of matter in the early universe all the way to the Big Bang, or at least up to the Planck time ~10-43 seconds, when effects of quantum gravity become important.
Following the understanding of the physics of phase transitions in the Early Universe, what was the next step that led to the theory of inflation?
After a few years of work on the cosmological phase transitions, Kirzhnits moved to other fields such as the theory of high-temperature superconductivity and the physics of black holes. But I was too excited by cosmology and switching to a different field was simply unimaginable.
The next big step took place in the beginning of the 80s with the introduction of inflationary cosmology. In the beginning, the idea of inflation was based on the theory of the cosmological phase transitions with supercooling. It took me some time to realize that the two were not necessarily linked.
Looking back, I would say that the basic principles of inflationary cosmology were very simple, and yet it required a big psychological change in our attitude to approaching some of the big questions about the early universe. Most of the theoretical tools and observations were around. The main difficulty here was psychological. At each step, it was necessary to give up some of the well-established principles of the previously accepted cosmological paradigm and propose something else instead. That was really hard, but also extremely exciting.
In the beginning, people thought that inflation could only be explained by introducing complex concepts like super-cooling in a false vacuum, and quantum tunneling. But then I found that we don’t need all of these complications, and we can have inflation in a very broad class of models, including even in the simplest model of a scalar field with a quadratic potential, as in the theory of a harmonic oscillator. The scenario works even if initial conditions in the very universe were far from equilibrium, and even if the universe was very inhomogeneous and anisotropic. For me this was the turning point.
It was amazing to see that using a theoretical framework similar to the theory of a harmonic oscillator could effectively explain the large-scale structure of the universe, that one can start with a tiny universe with a chaotically distributed scalar field, and explain why the universe now looks uniform, isotropic and homogeneous. Previously people thought that quantum mechanics is important only for the description of the small-scale effects, and at large scales, while describing large objects like planets, quantum mechanics was considered not to be relevant. But we learned from the works by Mukhanov, Chibisov and others that the largest objects in the universe – galaxies – were produced by quantum fluctuations. It looked too good to be true!
What was the main difference with Alan Guth’s proposal?
Back in 1974-1976 I found that the homogeneous classical scalar field, which may appear during the cosmological phase transitions with supercooling, looks just like a vacuum state, but with a very large energy density. Some people call it “false vacuum”. We found that the universe in the false vacuum state may experience a stage of exponentially fast expansion. In 1977-1978 Chibisov and I studied this stage. We found that it leads to a violent end, with the creation of many bubbles of the true vacuum colliding with each other and making the universe very inhomogeneous. This seemed problematic, so we did not continue this investigation.
In the period 1979-1980 Alan Guth  studied the same process, came to very similar conclusions, but he made an incredibly important observation. He found that the stage of exponential expansion of the universe prior to the false vacuum decay could help to address many conceptual cosmological problems, developing a scenario that inspired many of our colleagues.
Everybody knows that the universe is large and uniform. Everybody knows that parallel lines do not intersect, and the geometry of the world around us is similar to the Euclidean geometry of a flat table. But why? This was called “flatness problem”. Most people simply consider uniformity and flatness of the universe as a set of facts that do not require an explanation. But suddenly a possible explanation was found, based on a very simple idea. Exponential expansion, which is what Guth called “inflation,”  could almost instantly make the universe extremely large and uniform. Think about a rapidly inflating helium balloon, which grows large, and its surface becomes very smooth and very flat.
But Guth also realized that the decay of the false vacuum after inflation makes the universe grossly inhomogeneous, just as Chibisov and I found. At the end of his paper he acknowledged this difficulty, but since the main idea of inflation was beautiful, he was brave enough to go ahead and publish the paper. In his words: “I am publishing this paper in the hope that it will highlight the existence of these problems and encourage others to find some way to avoid the undesirable features of the inflationary scenario”.
How did you hear about the paper by Guth? What was your first reaction?
I should say that several other people in Russia were also studying related issues at that time. For example, Alexei Starobinsky in the beginning of 1980 published a paper in Physics Letters describing exponential expansion of the universe in a modified theory of gravity. His model was quite popular in Russia, but he did not attempt to solve the cosmological problems discussed by Guth. Whereas the model of Guth had a problem with the end of inflation, the original version of the Starobinsky required very special initial conditions (absolutely uniform and empty universe), which made it difficult to explain the beginning of inflation.
I was very much influenced by the seminar given in early 1980 by Valery Rubakov and his collaborators, who tried to explain why the universe is so large. They attempted to relate it to exponential expansion in the early universe, but they also encountered problems. Shortly after the Rubakov’s seminar, I received a call from Lev Okun. He asked me whether I have seen the paper by Guth where he was trying to solve the flatness problem. I answered that I did not know anything about it, and went on telling him what I expected to be in the paper and why this wouldn’t work. For many months I was trying to think whether it was possible to improve the scenario proposed by Guth. This was very challenging, in fact so challenging that I think that is why I got an ulcer. The idea was beautiful, and thus it was painful to miss such a simple opportunity to solve many cosmological problems. For about a year, many scientists, including Alan Guth and Stephen Hawking, were trying to find a solution to this problem, but it seemed impossible to do it.
Murray Gell-Mann and Andrei Linde in the Shelter Island following Linde's first talk on chaotic inflation in 1983.
In the chaotic inflation scenario, we do not need to assume that the Universe starts at the top of the potential, in a false vacuum state. There can be parts of the universe where inflation does not occur. These parts remain small. Meanwhile other parts of the universe, where inflation takes place, become exponentially large and dominate the total volume of the universe. We can start with a chaotic universe, and then some of its parts inflate, and become exponentially large and uniform. This shows how the order and uniformity of our world may emerge from a chaotic initial state. And we do not need a large universe to start with. If inflation begins in a smallest possible domain of the Planck length 10-33 cm, it is enough, because inflation can make this tiny domain much greater than the part of the universe that we see today.
Was this only a theoretically driven approach? Which were the experimental results driving forward theory development at that time?
Inflation was developed as an effort to explain some well-known observational data, and help us answer questions like: Why is the Universe so large? Why is it uniform? Planets rotate about the Sun, the Sun rotates about the center of our galaxy, so why our Universe does not rotate? Inflation provided a simple explanation to all of these observations, and I am unaware of any other well-established theory that would do it. Thus, inflation was driven by observations from the very beginning.
As I already mentioned, inflationary theory predicts the existence of tiny quantum fluctuations of the scalar field driving inflation. These fluctuations are produced during inflation, exponentially stretched, and become seeds for galaxy formation. In addition, these fluctuations lead to temperature and density fluctuations, making the temperature of the cosmic microwave background radiation (CMB) slightly different in various places in the sky.
In the early 80’s we expected that the amplitude of perturbations of temperature should be of the order 10-3, to match the theory of galaxy formation. I remember how one distinguished cosmologist gave a talk proving that inflation is ruled out because no perturbations at that level are found in CMB. Ten years later, these perturbations have been discovered by the Cosmic Background Explorer satellite (COBE), for which the leaders of COBE received the Nobel prize. The amplitude of these perturbations is much smaller than 10-3, and it is just fine, but only if one takes into account the role of dark matter in galaxy formation.
Then in the early 90’s astronomers told us that the universe is open, rather than flat, as predicted by inflation. The measure of flatness is described by the parameter Ω. Inflation predicts that Ω=1. Meanwhile astronomers claimed that Ω ~ 0.3, which would rule out most inflationary models. However, the discovery of dark energy in 1998 increased Ω by 0.7, bringing everything in agreement with the inflationary predictions. The latest Planck results confirm that Ω=1 with accuracy better than 1%.
Inflationary perturbations are predicted to have some specific properties: They must be adiabatic. Their spectrum must be flat, but not exactly flat (the spectral index ns should be close to 1, but it should be slightly different from 1, which is a separate very important prediction), and they should be almost exactly Gaussian. All of these predictions are confirmed by observations. Back in 2012-2013 there were persistent rumors that the Planck results should reveal a very small non-Gaussianity, which, however, would be large enough to rule out 99% of all existing inflationary models. For a year we were waiting, preparing for a disaster. But the Planck 2013 data release confirmed that the perturbations are Gaussian. They concluded that “With these results, the paradigm of standard single-field slow-roll inflation has survived its most stringent tests today.” The subsequent Planck data releases further strengthened this conclusion.
But different inflationary models make different predictions. Can we really prove inflation?
In answering your question, one should distinguish between the general predictions of inflationary cosmology and specific predictions depending on the choice of a particular inflationary model.
The basic principles of all inflationary models are very similar, and their main predictions are very similar to each other. A discovery that Ω ~ 0.3 would kill 99% of inflationary models. A discovery that inflationary perturbations are strongly non-Gaussian would kill 99% of all inflationary models. Cosmological perturbations can be classified as scalar, vector and tensor perturbations. Inflation produces scalar and tensor perturbations, but not vector ones. A discovery that the cosmological perturbations are of the vector type would kill most inflationary models. A discovery that the universe slowly rotates as a whole would kill most inflationary models. Thus, there are many general inflationary predictions. During the last 40 years most of them have been confirmed by observations.
Perhaps an analogy with particle physics can be helpful here. In 1967-1972, the development of the Glashow-Weinberg-Salam model on electroweak interactions and the proof of its renormalizability by `t Hooft made everyone talk about the beauty and simplicity of this model. But in the early 1972, Georgi and Glashow introduced a simpler model with one coupling constant, and no anomalies, that was generally perceived as a better approach. However, the Georgi-Glashow model predicted that there are no neutral currents. Two years later, the neutral currents were discovered at CERN, and we were back to the Glashow-Weinberg-Salam model, which gradually became the Standard Model of particle physics.
The Standard Model has many free parameters, which do not follow from general principles and must be determined experimentally. For example, nobody expected the top quark and the Higgs boson to be so heavy. The number of free parameters in supersymmetric generalizations of this model is much greater. We are still very far from deriving the standard model from string theory. But all versions of the standard model share the same basic principles such as gauge interactions and spontaneous symmetry breaking.
2014 Kavli Prize winners in Astrophysics. From left: Alexei Starobinsky, Andrei Linde and Alan Guth. (Credit: Scanpix)
Similarly, all inflationary models share some general principles that help to explain many properties of our world and lead to general predictions, which were confirmed by observations. But we want to do more, to find out a detailed mechanism of inflation, and the most elegant way to implement it, for example, in string theory or supergravity. There is a multitude of different inflationary models, and whereas their main predictions are similar, some of their predictions are slightly different.
For example, 30 years ago we only knew that the spectral index ns of inflationary perturbations is close to 1, but now observations are good enough to distinguish between ns = 0.965 and 0.97. The new generation of experiments are expected to measure ns with accuracy better than 0.002. This may rule out many inflationary models and help us find better candidates.
Is there an absolute experiment to prove or disprove inflation?
We already have many observational results confirming basic predictions of inflation, but of course any additional evidence is welcome. In particular, there are many experiments going on trying to find gravitational waves produced during inflation.
Gravitational waves are universally produced during inflation, but their amplitude is strongly model-dependent. They can be large enough to be experimentally found, or too small to detect. This makes it a win-win game. Not finding inflationary gravitational waves would allow us to concentrate on the specific models predicting small level of gravitational waves. But if inflationary gravitational waves are discovered, this will be stunning, and not only because it will be an additional confirmation of inflation.
Several years ago, we witnessed the massive wave of enthusiasm after the discovery of the gravitational waves produced by black hole collisions. This offered a spectacular confirmation of predictions of the classical Einstein’s theory of gravity. If GW from inflation are discovered, it will be the next important step, a direct confirmation of quantum theory of gravity at the energies a billion times higher than the energies accessible at LHC. This is a mind-blowing possibility!
However, some experts in the theory of inflationary perturbations, such as Mukhanov, may argue that we already have ample evidence for quantum gravity, because it is hard to disentangle quantum fluctuations of the scalar field from quantum fluctuations of the gravitational field in the theory of perturbations responsible for the CMB anisotropy discovered by COBE, WMAP and Planck.
As for disproving inflation, it is not an easy task because its basic predictions are already confirmed with high accuracy, and small variations of these predictions, which may be required to fit new data, typically can be achieved by proper modifications or extensions of inflationary models.
Do you think that the Higgs field could play a role in inflation?
This is an extremely interesting idea linking elementary particle physics and inflationary cosmology. The Higgs field with a specific “non minimal” coupling to gravity, could, in principle, play a double role as a field driving inflation, and, later on, breaking symmetry between weak and electromagnetic interactions.
The first models of this type were introduced in the 80’s, but the real interest in such models emerged after the paper by Bezrukov and Shaposhnikov in 2008. These models are in good agreement with the presently available cosmological data. Rather mysteriously, cosmological predictions of Higgs inflation almost coincide with the predictions of the Starobinsky model invented back in 1980, even though these models are very different from each other.
The deep reasons for this coincidence have been revealed soon after the Planck 2013 data release, in a series of our papers with Renata Kallosh, Sergio Ferrara and Diederik Roest. This helped to develop a new class of inflationary models, which we called cosmological attractors, or α-attractors. These models generalize the Starobinsky model and the Higgs inflation. They have very similar predictions for the spectral index ns but allow lots of flexibility for the amplitude of inflationary gravitational waves. A different but closely related class of inflationary models was also developed by John Ellis, Dimitri Nanopoulos, and Keith Olive.
In my view, cosmological attractors, in combination with a family of string theory motivated brane inflation models, can describe practically any value of the spectral index ns and any amplitude of inflationary gravitational waves compatible with the latest Planck data .
How big is the Universe according to the latest models of inflation?
Back in 1982, in my first talks on new inflation, I often apologized when I mentioned that according to that model, the universe after inflation has size about 10300 cm. I used to say that this is unusually large, so probably in realistic models it will be much smaller. But a year later I found that in the simplest version of chaotic inflation, the universe could easily acquire size 10100000000000 cm. For comparison, the size of the part of the universe that we see now is only about 1028 cm.
Later on, I found that quantum fluctuations in the chaotic inflation scenario can be so large, that instead of slowly rolling to the minimum of its potential, the scalar field driving inflation may occasionally jump uphill. The probability of such events is very small, but the parts of the universe where it happens become exponentially rewarded by an even faster growth of their volume. As a result of this process, inflation ends in some parts of the universe, in one of which we live now, but it may eternally continue in many other parts, making the universe infinitely large .
Moreover, quantum fluctuations generated in this process can be powerful enough to take scalar fields from any minimum of their potential and place it to another minimum. In the simplest version of the Standard Model, there is only one minimum, but in supersymmetric GUTs one may encounter dozens of different minima corresponding to stable or metastable vacua. Properties of elementary particles in these vacua are different from each other.
This is similar to what is well known in chemistry: Water can be liquid, solid, or vapor. It is the same water, but fish can live only in the liquid water. Similarly, the universe may consist of different exponentially large parts with different properties, different types of symmetry breaking, different laws of low-energy physics realized in each of these parts, and we can live only in those parts that are compatible with our existence.
The situation is especially interesting in string theory, where the number of different metastable vacua can be exponentially large. This is often called “string theory landscape.” In that case, eternal inflation may divide the universe into exponentially many parts of exponentially large size with exponentially large variety of different laws of low energy physics operating there. The universe becomes a multiverse .
Is there any experimental evidence for the multiverse if we cannot see its different parts?
Yes, I believe so, but this evidence is somewhat unusual and indirect. To explain it, let us do a warm-up exercise.
Here is the question asked long ago by Zeldovich at one of his talks: “Do we have any experimental evidence of baryon non-conservation?” The simple-minded answer would be “No”, because we did not see decaying baryons. However, the true answer is different, and somewhat paradoxical. The main experimental evidence of the baryon number non-conservation is that parallel lines do not intersect.
This may sound like a joke to you, but as we already discussed, the only available way to explain why the parallel lines do not intersect is provided by inflationary cosmology. But at the end of inflation the density of all previously existing elementary particles becomes exponentially small. The excess of matter over antimatter emerges after inflation, which requires baryon number non-conservation. In this sense, the fact that the parallel lines do not intersect is an observational evidence of the baryon number non-conservation.
Now let us return to the multiverse and consider a certain group of experimental facts. The electron mass is 2000 smaller than the proton mass. The proton mass almost coincides with the neutron mass. The electrostatic repulsion between two protons is 36 orders of magnitude stronger than their gravitational attraction. The cosmological constant (or dark energy) is 120 orders of magnitude smaller than the Planck density.
These and several other experimental facts of similar nature do not have any simple explanation, but they have something in common: If we significantly change any of these parameters, life as we know it would be impossible. For example, if the cosmological constant were much greater than its present value, it would lead to a rapid expansion of the universe, which would not allow galaxies to form. And if it were large but negative, the universe would rapidly collapse.
It is tempting to consider this as an anthropic explanation of these parameters, but it does not seem to make any sense, because the true constants are not supposed to change. However, in the string theory landscape some of the “constants” become environmental parameters, which take different values in different exponentially large parts of the multiverse. Then it is only natural that we can live and measure values of different parameters only in those parts of the multiverse where the laws of low-energy physics are compatible with our existence.
The theory of the multiverse is extremely complicated. There are many technical and conceptual problems to be addressed, and we should not pretend otherwise. But this theory provides the only presently available framework where a large series of well-established experimental facts may find an explanation.