Initial conditions for the Universe.
Gregory Vereshchagin
Abstract
I’m going to describe here, how we understand initial conditions for the Universe nowadays, and how, historically, we came to this understanding. There are two aspects of this problem. Studying the dynamics, evolution of the Universe in time, one will address soon or later the question: is the Universe eternal or it perhaps has the beginning and maybe the end? Studying spatial dynamics of the Universe one has to set at some moment of time distribution of some physical quantity, for example mass, in space. These two aspects and their vision at different epoch of cosmology development will be discussed.
For the first time introduced within the famous Friedman’s solutions of General Relativity cosmological equations, the problem of initial state of the Universe has not been solved completely until now. According to these solutions and a Big Bang theory, which was built on them, there is a moment in the past, so called singularity, beyond which one can not move in past direction. It is clear, that singular state with infinite values of physical quantities, like temperature or energy density, should be excluded from cosmological model. We believe, that in quantum gravity such phenomenon is absent, but, unfortunately, quantum gravity is not still built up. From the other hand, the possibility to avoid initial singular state leads to conclusion, that the Universe as a whole exists eternally. These two different pictures of the Universe evolution, as well as some problems of modern cosmology, will be discussed.
First, let’s turn to these problems taking as a basis well known Newton’s gravity. In classical mechanics equations of motion are symmetric in time. This means, that if there are no dissipation processes, or if we deals in other words with loosing of energy, the evolution of isolated system (which do not interact with other systems) can be predicted if one set at some moment of time initial conditions. In the case of self-gravitating system, the only things we should know about it is particle masses and its’ coordinates and velocities at some moment in time. At any different moment these coordinates and velocities can be calculated according to Newton’s laws. The most important thing here is, that we can move in both directions – to the future as well as to the past.
If further on we consider infinite volume filled by massive particles (we can call different objects as particles, if their size is small comparing to the distance between them), they will attract each other, but our volume will still be infinite, since it was infinite initially. In Newton’s time the only cosmic objects known were stars. And infinite Universe, filled by stars, was considered as static one.
In the alternative case, when we consider initially finite volume, filled by stars, this volume will decrease in time, and at a certain moment all stars turn out to be at the center of this volume (in the previous case there is no center!). This model of the Universe was called nonstatic.
When Albert Einstein discovered his General Relativity, he attempted to apply the new theory to cosmology, i.e. to the whole Universe. In this theory space and time can no longer be considered as separate things. Moreover, the spacetime appears to be not flat, as we used to imagine it, but curved. He quickly understood, that it’s impossible to obtain static solution. The only way to get it was to modify equation, and in this modification one of the most puzzling was the problem of Lambda term, from here it takes the origin.
However, Alexander Friedmann soon obtained his famous cosmological solutions. These solutions were nonstatic (the Universe appeared expanding), and they were soon confirmed by experimental observations of expansion by Edwin Hubble. This story is well described in popular books on cosmology.
Figure 1. Friedmann Universe. The scale factor (size of the Universe) depending on time. These three curves correspond to close, flat and open cosmological models.
The most striking feature, appeared in Friedmann solutions, was the beginning of time. Because the Universe is nonstatic and expanding, at some moment in the past its size should be very small. According to General Relativity, this means, that at this moment the density, temperature and curvature of the Universe should be very large. If we try to continue our motion, we’ll see, that physical quantities mentioned above tend to infinity, and we can no longer move to the past. This state of the Universe was called initial cosmological singularity.
Friedmann solutions have one more interesting feature (Figure 1). In the Universe there is so called critical density, which depends on the speed of expansion. If its density exceeds the critical one (so called close model), the expansion will stop in the future and the contraction will begin. Otherwise, the Universe will be expanding all the time (open model; exact equality of density to critical one corresponds to flat model).
The theory, that was based on Friedmann solutions, is called Big Bang. This theory was a great achievement of cosmology in the past century. A lot of things were understood, for instance, chemical evolution of the Universe (primordial nucleosynthesis, light elements). One of important predictions of this theory, cosmic microwave background radiation, was proved experimentally in 1965, and from that time the Big Bang becomes conventional theory. It remains conventional theory until now, when speaking about relatively late evolution of the Universe.
About 30 years ago Stephen Weinberg wrote his famous "First three minutes", where he popularly described the evolution of the Universe, starting from moments close to initial singularity. From that time it was clear, that particle physics and cosmology, studying two different worlds – micro- and macroscopic, must be both considered, if we want to understand the early Universe.
However, as in any theory, there are problems also in Big Bang. Among them that initial conditions. From the one hand, almost everybody now understand, that initial singularity is simply a state of the Universe, where one can not apply Einstein’s General Relativity. We expect, that solution of this problem could be found in quantum gravity. The alternative to initial singularity is eternal Universe, also nonstatic, perhaps oscillating, if its energy exceeds the critical one.
From the other hand, the structure of our Universe at very large scales is still a problem for cosmology. According to the Big Bang, that objects we can see today,galaxies, clusters and superclustes of galaxies, were not formed from the very beginning. The picture of the Universe, we can get from background radiation, shows, that it was highly homogeneous and isotropic after 106 years from that superdense state. There were very small inhomogeneties with amplitude 10-5, and from these inhomogeneties observable structures developed. But this value 10-5 can not be obtained from the Big Bang theory.
Moreover, there are additional problems, linked with initial state of the Universe. We know well, that the speed of light is the maximum velocity, existing in nature. We know also, that the speed of expansion grows with distance from galaxies. Thus, it could be possible, that at large distances the expansion rate is higher, than the speed of light. It does not go contrary to the theory, simply one can not know anything about processes beyond this distance, which is called cosmological horizon. At the early stage of the Universe the horizon size was very small. However, from background radiation we can see, that at scales much larger than the horizon size (at that time) the Universe demonstrates very similar properties. This was a great puzzle for the Big Bang before inflationary models were introduced.
The basic idea of these models is to prepare initial conditions for the Big Bang. According to inflation at the very early stage of the Universe some processes lead to domination of above mentioned Lambda-term. It is not a constant now, and its domination is temporary and takes about 10-35 s. However, since the Universe expands exponentially at this incredibly small period, it’s size becomes much larger, than scales we can observe today. This small modification allows us to solve numerous problems appearing in theBig Bang.
The main prediction of inflation is flatness of the Universe. In other words, its density today is very close to critical one. Moreover, quantum fluctuations of matter density, produced during inflation, allow one to obtain initial inhomogeneties, that are necessary to following structure formation, which we observe today. However, inflation is still hypothetical mechanism. Its nature is closely connected with particle physics at the very high scales of energy. Experimental physics, looks like never going to reach these scales. "The only great laboratory, which costs us nothing", as Ya.B. Zel’dovich, famous soviet cosmologist, once said, is the early Universe.
We are still on the way to understanding physics, space and time. Last century was very rich for different discoveries, from quantum mechanics to superstring theories. But the future is not less attractive. At the end of the XIX century most of the physicists believed that the physical science was already done, and it would be quite boring to deal with physics. At the end of the XX century we don’t think so – this century left us a lot of problems and puzzles in physics, for instance, high temperature superconductivity or the vacuum energy density. In cosmology one have to apply all physical knowledge, because the object of study is the whole Universe. And, who knows, perhaps, by studying the origin and the evolution of the Universe, we’ll solve the above mentioned existing problems and will better understand the complexity of Nature.