by Jaan Einasto
This time the Meeting was in Budapest; just recently Hungary’s membership in A&A had been accepted. When I entered the room where the Board had its Meeting, there was a burst of applause. I knew most of the members of the Board, and now I was congratulated because Estonia has regained its role in the European community. But a question immediately followed: “Will you publish papers on cosmology in our journal?” In mainland Europe cosmology was not as well developed as in the USA and Great Britain, and the Journal was interested in our publications. I answered that certainly we shall publish our future cosmology papers also in A&A; so far we published our papers mostly in “Monthly Notices of the Royal Astronomical Society”. Now we really use for publications mostly A&A. I participated a few times in Meetings of the Board over next few years, but soon I proposed that the Director of Tartu Observatory, Laurits Leedjärv, should take over the role of the Estonian representative in the Board. My suggestion was accepted. Now Estonia is already for many years a full member of the Journal. Once the Meeting of the Board was held in Tartu; members of the Board made a visit to our Observatory in Tõravere.
Soon Estonian membership in the International Astronomical Union was restored. The first IAU General Assembly after the restoration of our independence was in The Hague in August 1994. We participated with a fairly large delegation. Initially we planned to drive there in two personal cars, but one car broke down, so a group of four astronomers used my car, while the rest came in buses and trains — there were no flights still in those years. I felt proud to drive in the city with an Estonian number plate. At the opening ceremony I discovered that the Estonian flag was upside down. I hurried to the organisers, and during the break the flag was placed correctly. At the Assembly banquet around our table there were astronomers congratulating us. I had a longer talk with Harry van der Laan, the former Director General of ESO. During my visits to ESO we had discussions on our freedom movement. Now he had a small blue-black-white badge on his breast, which I had presented him in our discussions some years ago.
The next IAU General Assembly was held in Kyoto, the old capital of Japan. I was the representative of Estonia, so I participated. This was my only trip to Japan. Japan has old traditions and culture, a bit similar to the culture of China. We had a chance to visit the old Emperor’s palace and many other places of interest. In the opening ceremony of the Assembly Japan’s Emperor, Akihito, participated. It was very interesting to see all these old traditions still alive.
During the Assembly the American delegation organised a reception, and I had the honour to be invited. I came a bit earlier, and found only the head of the US delegation, Vera Rubin, awaiting guests. So we had plenty of time for a very friendly discussion. I thanked her for her popular paper in Scientific American on dark matter, where she gave a detailed overview of our work on the subject, always calling us Estonian or Tartu astronomers. She smiled and answered that our enthusiasm for Tartu and Estonia was so evident that everybody knew which observatory and country we are from.
Chapter 8
Cosmic inflation, dark energy and the evolution of the Universe
In this chapter I shall discuss some aspects of the evolution of the Universe. In the 1980’s our cosmology group welcomed 4 young cosmologists: Lev Kofman, Dmitri Pogosyan, Maret Einasto and Mirt Gramann. Lev was a postdoc in Moscow in the early 1980’s; his supervisor was Alexei Starobinsky. He studied the theory of inflation with Alexei Starobinsky and Andrei Linde, and models dominated by the cosmological term with Alexei Starobinsky. Kofman initiated the Tartu Cosmology Seminars; the first Seminar was held in May 1982, the Second in June 1985 (Kofman et al., 1986). In both seminars the main topics were the nature of dark matter, the evolution of the Universe, and inflation theory.
These theoretical studies started in the early 1980’s. Later theoretical studies were complemented with numerical simulations of cosmic evolution to understand some particular aspects of the evolution — the quasi-regularity of the structure, the understanding of the void problem, and the early evolution of the cosmic web. Our team is rather small and our computational possibilities modest, thus we were not able to study all aspects of the cosmic evolution. We concentrated on problems which for us seemed interesting, and where we had ideas on how to solve the problems.
8.1 The birth of the Universe and inflation
8.1.1 The classical inflation theory
Astronomers have direct data on the past by observing galaxies, clusters, quasars and other objects. The most distant objects found so far have a redshift about 6–8. The Universe was at this time rather young, about 1 billion years old. However, direct observational evidence is available for earlier epochs: CMB radiation was emitted when the Universe was about 350 thousand years old, and data on the nucleosynthesis of light chemical elements tell us what properties our Universe had when it was only a few minutes old. What happened in earlier moments we do not know so well.
According to the presently accepted Big Bang model the Universe started from a singularity. But “singularity” is a mathematical term. Big Bang theory says nothing about the physics of the primordial explosion. The theory of inflation is a physical description of the bang itself. It tries to answers a number of questions which could not be explained in the framework of the classical Big Bang model.
The first problem is the flatness problem. During the evolution the Universe expands so much that any deviation from exact critical density would increase during the expansion. In order to have an approximately critical density today, it must have critical density in the early epoch, at the time of nucleosynthesis, with an accuracy of at least 15 decimal places, i.e. it must be very accurately tuned.
The second problem is the homogeneity of the Universe. Data from the COBE satellite indicate that the gas in opposite directions of the sky have the same temperature with an accuracy of one part in 100,000 at the recombination epoch. Such high accuracy is possible only if these different regions have communicated. However, this was impossible at the time of recombination, since such communication would be possible only with a speed roughly 100 times the speed of light. In other words, the identical temperature must be achieved much earlier when the Universe was more compact.
These and some other difficulties of the classical Big Bang theory can be avoided if in the very early phase of the evolution of the Universe there was a period of very rapid expansion by a factor of at least 1026. This rapid expansion is called inflation. The inflation scenario was suggested by Aleksei Starobinsky (1980, 1982, 1985) and independently by Alan Guth (1981).
This classical inflation model solves the flatness problem. During the inflationary period the Universe is driven very accurately towards the critical mass density. The model also solves the problem of homogeneity. The presently visible Universe has a radius of about 15 billion light years. Since the expansion factor is at least 1025 times, the present Universe was before the inflation so small that there was plenty of time for it to come to a uniform temperature. So in the inflationary model, the uniform temperature was established before the inflation took place, in an extremely small region.
8.1.2 The new inflation theory and the birth of the Universe
The above classical version of the inflation model is called “old”. It provides a simple solution to several crucial problems, but does not answer some other fundamental questions: Why does the Universe have elementary particle parameters as they are? What happened before inflation started? To answer these questions Andrei Linde suggested a scenario of chaotic inflation (Linde, 1982, 1983).
Andrei Linde describes his first contacts with cosmologists from Western countries in discussing his new inflationary model (Linde, 2002b). In 1981 there was a conference on Quantum Gravity in Moscow. This was the first conference where Andrei gave a talk on the new inflation scenario. After the conference one of the participants, Stephen Hawking, was invited to give a talk at the Sternberg Astronomy Institute. Zeldovich asked Andrei to translate. At that time Stephen did not have hi
s computer, so his talks usually were given by his students. Stephen said one word, his student repeated the word, andAndrei translated it. BecauseAndrei knew the subject, he started adding lengthy explanations in Russian. In the second part of the lecture Stephen said that recently Andrei Linde had suggested an interesting way to solve the problems of the old inflationary theory. But then Stephen said that the new inflationary scenario cannot work. When the talk was over Andrei said that he translated but cannot agree, and explained why. Thereafter Andrei and Stephen discussed the issue privately. In Summer 1982 Stephen organised a workshop in Cambridge dedicated to the new inflation theory. As Andrei writes, this was the best and most productive workshop he ever attended.
A small remark. About the same time another Cambridge astronomer, Donald Lynden-Bell, visited Moscow and gave a talk at the Sternberg Institute. Zeldovich asked me to be the translator. Similarly to Andrei, I knew the paper, and added detailed explanations. It happened several times that I was ahead with my explanations, so when Donald finished a step in his talk, I had to say that I had already talked about this, accompanied with a laugh from the audience.
Linde (2002a) explains the problems which led him to his new inflation scenario as follows.
“Most of the parameters of elementary particles look more like a collection of random numbers than a unique manifestation of some hidden harmony of Nature. For example, the mass of the electron is 3 orders of magnitude smaller than the mass of the proton, which is 2 orders of magnitude smaller than the mass of the W-boson, which is 17 orders of magnitude smaller than the Planck mass Mp. Meanwhile, it was pointed out long ago that a minor change (by a factor of two or three) in the mass of the electron, thefine-structure constant, the strong-interaction constant, or the gravitational constant would lead to a universe in which life as we know it could never have arisen. These facts, as well as a number of other observations, lie at the foundation of the so-called anthropic principle. According to this principle, we observe the universe to be as it is because only in such a universe could observers like ourselves exist.”
Andrei continues:
“One can consider different universes with different laws of physics in each of them. This does not necessarily require introduction of quantum cosmology. It is sufficient to consider an extended action represented by a sum of all possible actions of all possible theories in all possible universes. One may call this structure a ‘multiverse.’”
Similar arguments were discussed by Martin Rees (2000) on the meaning of six numbers which determine the essential properties of our Universe. Martin considers as fundamental numbers the following: ≈ 1036 — the ratio of the strength of electrical forces that hold atoms together to the force of gravity; ε = 0.007 — the effectivity of the nuclear burning of hydrogen to helium; Ω = 0.28 — the amount of matter in the Universe, in units of the critical density; Λ = 0.72 — the amount of dark energy in the Universe, also in units of the critical density; ≈ 10−5 — the ratio of the energy needed to disperse large structures (superclusters) to their internal rest mass energy (mc2). The final important number is the number of spatial dimensions in our world, = 3. Martin shows that if these numbers were a bit different from their actual values, our Universe in such form as we know it would be impossible. The question is: Why do these number have exactly the values needed for the existence of our Universe and the life in it, including ourselves?
Martin discussed the possible explanations for the presence of just these values of fundamental numbers. One simple solution is favoured by theologists — this was the will of a Creator. The other possibility is that during the formation of the universe all possible values of these numbers were possible. It is clear that we can live only in an universe where all these numbers take ‘proper’ values. This leads us again to the concept of the multiverse.
Martin writes that “the multiverse concept lies within the province of science as a tentative hypothesis. This hypothesis allows to map what questions must be addressed in order to put the concept on a more credible footing”.
Trimble (2008) describes the status of the multiverse concept as follows: “The core multiverse concept is that our universe (the 4-dimensional spacetime with which we are or could be connected and all its contents) is one of many, perhaps infinitely many, probably with different values of the constants of nature and other physical differences, which cannot communicate with ours even in principle. Such ensembles are predicted by some versions of inflation, string and M-theory. The anthropic principle is the idea that our universe has (or even must have) the structure, physics, chemistry and all required for me to be writing this and you to be reading it (editors are optional).
On previous occasions, Martin Rees has said that he has enough confidence in the multiverse to bet his dogs life on it, while Andrei Linde said he would bet his own life. Weinberg concludes his contribution by saying that he has just enough confidence in the multiverse to bet the lives of both Andrei Linde and Martin Rees’s dog.
The problem with the multiverse concept is that it cannot be proved nor disproved, because there is no possibility in principle to contact other universes. On the other hand, it reflects the nature of science to try find answers to ultimate questions like: Why we are here?
Now back to our activities. Together with Kofman and Linde we discussed cosmic voids (bubbles) as remnants from inflation (Kofman et al., 1987). Kofman & Shandarin (1988) developed the adhesion model to find the skeleton of the present cosmic web from density peaks in the early universe just after the inflation stage. Calculations show that the seeds of the present cosmic web were created already in the very early Universe. Since the expansion of the Universe was in the early phase very rapid, all perturbations exceeding some scale (about 140 Mpc) were outside the horizon and could not grow or have mutual contact after inflation and before recombination (CMB radiation epoch).
8.2 Structure formation in hot, cold and lambda models
8.2.1 Initial conditions
In numerical simulation of the evolution of structure two issues are of crucial importance: (1) the method to evolve the ensemble of particles, and (2) initial conditions for calculations.
In the first numerical simulations of the evolution the authors applied the direct integration of equations of motion under the influence of mutual gravitational interaction of particles. As particles usually galaxies were considered. Pioneering numerical simulations of the evolution of the structure of the Universe using direct integration method were made in the 1970’s by Peebles (1970, 1971b, 1974b), Aarseth (1971b,a); Aarseth et al. (1979), Miller (1978) and others. The number of particles was in the interval from ∼300 to ∼1000. As to initial conditions, mostly particles were put at random locations with either zero or random initial velocities. Several values of the density parameter of the Universe were used: Ω = 1, and Ω 0.1 for the present epoch. To compare results of simulations with observations usually the correlation function was used. Also plots of the distribution of particles were compared with similar plots found for actual galaxies. According to the dominant ideas of the early 1970’s the first objects to form are globular cluster sized systems (Peebles & Yu, 1970), which by clustering form larger objects, such as galaxies and clusters of galaxies. This hierarchical clustering model is sometimes called the bottom-up scenario.
Yakov Zeldovich and his team in Moscow used a completely different approach to study the evolution of the structure of the Universe. First of all, Zeldovich started from the fact that the primordial matter is a continuous medium — the primordial gas. For this reason the evolution of the medium must be treated as a hydrodynamical problem. Since the early Universe was almost uniform, it is convenient to use the perturbations of coordinates (displacements from the uniform state) and the perturbations of velocities (departures from the Hubble velocities) with respect to the uniform (unperturbed) state. Initial perturbations were small and the evolution was in the linear regime.
Zeldovich found one crucial aspect of the early c
osmic evolution. In the linear regime the gravitational instability amplifies a particular combination of coordinate and velocity perturbations. This combination is called the growing mode. In the growing mode the initial displacements in the medium and its initial velocities are proportional to each other. Therefore, it requires only one function to describe both displacements. The other combination of the displacements and velocities comprises the decreasing mode that decays in the course of the evolution and can be neglected.
To evolve the ensemble of particles Zeldovich’s team applied the “cloud-incell” (CIC) method which makes it possible to study the collective effects of a large number of particles, while suppressing two-body effects (Hockney & Eastwood, 1981). In this case the medium is considered as a continuous one, i.e. a fluid, and particles are used only as markers or test objects to show the evolution of the medium. Particle masses are distributed over a finite volume (cloud), their movement is followed in a mesh. On this mesh Poisson equations are solved using the fast Fourier transform (FFT) with periodic boundary conditions. Since the FFT works very fast, it is possible to use much more particles than in the direct integration method to simulate the evolution of the Universe.
Further Zeldovich (1970) investigated how far the linear theory can be applied. He found that the linear theory can be used also for further stages of the evolution, this approach is called the “Zeldovich approximation”. Using this approximation the density and velocity are calculated for a continuous medium, not for a finite number of discrete point masses, as in the CIC method. For practical purposes it is convenient to place test particles in a regular grid, and calculate perturbations for each particle. Perturbations correspond to density waves of different scale and phase, and have a certain power spectrum. Zeldovich assumed that perturbations consist of common motion of photons and baryons. These perturbations conserve entropy and therefore are called “adiabatic”.
