To what extent does space stop expanding?

Cosmic inflation and the search for space-time fossils

Cosmic inflation is the era in which the universe doubled its diameter about a hundred times in a fraction of a second. Alternatives have been discussed in recent years

Today cosmologists have a very good theoretical understanding of the development of the universe from one second after the Big Bang. Even after just one microsecond (Quark era), the standard model of particle physics fits very well with the calculated temperatures and energies of the early universe.

From the quark era, when a so-called quark-gluon plasma filled the universe, three of the four elementary particle interactions have started to separate from one another (i.e. weak interaction, strong interaction and electromagnetism) and physicists can further develop the Follow the universe with the Standard Model and Einstein's theory of gravity. Much more speculative, however, are various phases before the Quark era, especially the period of the so-called inflation of the universe.

Was there anything before the big bang? There are several possible answers to this question. The first would be Stephen Hawking's very pragmatic reply. The Cambridge physicist said that events before the Big Bang can no longer be observed by us today and that we can therefore confidently start our clocks from there. In other words: There are no radiation or particle residues from the "pre-big bang" that we could investigate or measure. From a cognitive point of view, this time before the Big Bang cannot be recorded and is therefore irrelevant to us.

Theorists like Paul Steinhardt have proposed an alternative theory called bouncing cosmology, which postulates an oscillating universe that evolves from one big bang to the next. According to Steinhardt, the universe dilutes itself through expansion (over billions of years), only to start over with a fresh big bang every time. Steinhardt believes that by measuring the residues of the gravitational waves at the Big Bang, it may be possible in the future to decide who is right, i.e. the inflation or rebound theorists.

The famous Sir Roger Penrose proposed an analog oscillating universe that continues to expand and ultimately succumbs to cold death. Black holes eat their way through the cosmos and make it terribly empty and uniform. Then the entire universe collapses again to a small volume and a new big bang is the result. In contrast to Penrose, Steinhardt does not propose a previous collapse of the universe, but simply a periodic Big Bang that fills the dead and cold universe again with energy and gravity

Penrose even believes he can make the signature of the last rebound visible in the cosmic background radiation (Fig. 1). Together with the Armenian Vahe Gurzadyan, he discovered that patterns of concentric rings can be found in the cosmic background radiation. To do this, they took measurements from the WMAP satellite and other experiments over several years and calculated the variability (the variance) of the temperature of the background radiation. You will find concentric rings with low variance in the radiation. Both physicists interpret these as remnants of the gravitational waves of the collisions of black holes in the process of the collapse of the pre-universe

Such a groundbreaking announcement was of course immediately put to the test by other physicists, and it appeared that the special mixture of frequencies in the background radiation can generate such patterns spontaneously and randomly, so that the patterns themselves are not messengers from an earlier universe . They represent structures that can arise purely arithmetically. 3

Nevertheless, Penrose's idea is to look for effects in today's background radiation that might give us insight into the first microseconds after the Big Bang and even before it, an example of how physical theories can be put to the test. In cosmology one talks about periods of time that are beyond human experience. Although we can observe the history of the universe from the recombination with telescopes in the sky (i.e. from 380,000 years after the Big Bang), the background radiation itself hides everything that happened before the recombination like a curtain.

The neutrino background, generated one second after the Big Bang, would be very informative for this. But since neutrinos hardly interact with other particles, it is incredibly difficult to detect them. The physicists are happy when they can get hold of a handful of high-energy neutrinos from the sun in huge detectors under a mountain. The question, however, is whether there aren't other physical fossils that allow us to see behind the veil of recombination. The best candidates are currently the gravitational waves that were created during the Big Bang (or even before it like Penrose).

We don't normally think so, but actually the proportion between hydrogen and helium in the universe is one such fossil in space-time history. George Gamow was the first to model the early universe as a chemical retort and, together with Alpher, was able to explain the proportions of the light elements in the universe for the first time using the Big Bang theory. Another possible fossil is the polarization of the photons in the background radiation. Physicists will certainly be on the lookout for further detection methods in order to be able to put the proposed theories on a reliable experimental basis. Seen in this way, cosmologists today are something like Paleo astronomers, fossil hunters.

The inflationary universe

The inflation theory of the universe was proposed by Alan Guth in the early 1980s. The summary of these is simple, the explanation a little more complex, and the presentation of today's paradoxes much more complex.

Let's start with the summary: Almost immediately after the Big Bang, the universe went through a period of ultrafast expansion. Before inflation, the universe was much smaller than a proton. Then the universe experienced about 100 doubles in size in a surprisingly short time. At the end of the inflationary period, the universe was about the size of an apple. From then on, things continued "normally" with the slower (but nevertheless fast) expansion of the universe predicted by the so-called Friedmann equation (Fig. 2).

Alan Guth's original motivation was to investigate the conditions for grand unified theories of the forces of nature. Such a standardization only happens at ultra-high temperatures and energy concentrations. So you have to go back to the time of the birth of the universe to be able to find such conditions. Guth found more than he was looking for when he postulated a type of vacuum energy that behaves as a "scalar field". This is a type of energy whose density remains constant even as the universe grows. If, on the other hand, a gas is distributed over ten cubic meters in a cubic meter, the density of matter is thinned by a factor of 10.

But vacuum remains vacuum, and when the vacuum increases by a factor of 10, the vacuum energy also increases by a factor of 10. At the same time, however, a gravitational field is generated. The gravitational potential is negative, i.e. the rapid increase in the size of the universe is the ultimate "free lunch" (as Guth says). The positive energy, which becomes larger in the scalar field in the vacuum, balances out with the negative energy of the gravitational field created. If the balance is perfect, firstly, the law of conservation of energy is not violated, and secondly, the universe becomes "flat".

Guth didn't know, but he had found a solution similar to Willem de Sitter in 1917 when he investigated a universe without matter using the Einstein equation. He implicitly put a positive cosmological constant in the equations of what we would call "dark energy" today. De Sitter concluded that such a universe should expand exponentially. But since de Sitter's universe contained no matter, it seemed to be a kind of pure arithmetic exercise. In a de Sitter universe with a positive cosmological constant, the derivative of the scaling parameter of the size of the universe is equal to that constant times the scaling parameter (i.e. a = Λa), i.e. an equation that gives the solution a = eΛt owns. And that's exponential growth. If Λ is very large and dominates all other parameters, the result is ultrafast expansion.

Fig. 3 shows Guth's proposal. In a very short time, the universe (billions of times smaller than a proton) has grown to the order of centimeters in diameter. Fig. 3 uses a logarithmic scale so that the growth lines in the figure correspond to exponential growth. During inflation, the observable universe expanded more than by a factor of two than in the 13.7 billion years afterwards.

Guth's physical explanation for the inflation phenomenon was that the early universe started in what is known as a false vacuum, i.e. the vacuum did not have the absolute minimum of energy possible. As long as the false vacuum exists, the scalar field pushes outwards (negative pressure) and in this way enlarges the space, as de Sitter's solution envisages. But this state cannot be sustained forever. The scalar field eventually "rolls" into the energy minimum and the expansion of space from this source stops. The energy stored in the field then breaks down into normal matter and energy and the "bang" in the Big Bang is thus over. From then on, the universe will evolve according to the same pattern as it does today.

As counterintuitive and bizarre as this representation sounds, Guth's suggestion met with a great response from cosmologists because the inflation theory could solve three problems with a single mechanism. These problems were:

  • The horizon problem
  • The flatness of the universe
  • The absence of magnetic monopoles

The last problem is the easiest to explain. After the grand unified theories one could establish full symmetry in the equations of electromagnetism if not only the electrical charges but also the magnetic poles could also be found individually. Then electrical and magnetic charges would be dual and symmetrical properties of elementary particles. The experimental problem, however, is that despite all their efforts, the physicists still cannot find the postulated monopoles. Since a period of inflation scatters any pre-existing particles incredibly widely, it would be no wonder they can no longer be found. There should be less than such a primordial monopoly in the entire solar system.

The horizon problem means the following: The cosmic background radiation shows that the universe was in thermal equilibrium 380,000 years after the Big Bang. That is, the temperature is the same in every direction that can be measured. But since light, because of its finite speed, could not propagate from one side of the universe to the other in the previously existing time (see Fig. 4), the early universe was divided into many islands of "causality" (these are the small circles in the picture). Thermal equilibrium could arise on each island, but not between islands that were very far apart. But if the universe were much smaller, thermal equilibrium could have been established, i.e. in an ultra-small universe there is a causal connection everywhere. The subsequent inflation starts the subsequently enlarged universe in thermal equilibrium.

The problem of the flatness of the universe has to do with the critical energy density. Today astronomers believe that the sum of the energy of matter, dark matter and dark energy gives exactly the so-called critical energy density. The critical energy density is that which makes the universe Euclidean. In a Euclidean universe, two photons that were shot on parallel orbits fly in parallel forever. They neither come closer nor diverge any further. The relationship between measured and critical energy density is represented by Ω. In a Euclidean universe, Ω = 1.

It is, however, the case that the equations for the evolution of Ω over time punish any deviation from one very quickly. If Ω had been about 1.02 at the beginning of the universe, we would have had Ω = 2 after less time. Today's universe then had to show a high curvature of space, one that we do not observe. Since today's measurements give a value for Ω very close to 1.0, the universe started perfectly or almost perfectly with Ω = 1, precisely to fifteen decimal numbers. Guth's theory of inflation gives the desired Ω = 1, because the gravitational field perfectly balances the generated energy and both components dominate any other residues of pre-energy. The pre-energy of the universe corresponds to only 25 grams of matter - after inflation, however, billions and billions of solar masses.

We cannot cover the necessary equations for all of these estimates here, but over time inflation theorists have put them up and recalculated the number of doublings in the diameter of the universe during inflation. The more precise result depends on the initial conditions, however, and here there has been a split, so that today we do not have an inflation theory, but rather a family of theories (more than a hundred, depending on how they are grouped).

Paradox of Eternal Inflation: Steinhardt's Critique

Paul Steinhardt today no longer agrees with the inflation theory, although at the beginning he made significant contributions to its implementation (and even received the Dirac Prize for it). Today he has his own theory (bouncing cosmology) and is constant criticism of the inflation theory.

Steinhardt's main problem is the so-called "graceful exit" from inflation. Fig. 5 shows a model for the slow rolling of the scalar field along a potential down to the minimum. When "re-heating" the energy of the scalar field breaks down into matter and normal energy and the universe, which has been emptied by inflation, fills up again. Now the exact development of the inflation period depends on the shape of this potential (which nobody knows) and so various potential profiles have been proposed. Each of these changes the details of the inflation period. That is why there are so many theories of inflation, many of which only differ in terms of their potential.

But something more important bothers Steinhardt: The end of inflation is a quantum mechanical phenomenon and is therefore stochastic. Inflation can stop at one point in the universe, but if neighboring points continue to expand, the further expanding parts will dominate the entire universe very quickly. This is called "eternal expansion" and is a real problem in theory (although Guth makes it more of a feature of theory).

One way out of the paradox of eternal inflation is to declare our own space-time bubble, where expansion stopped, as our universe. Other bubbles develop into parallel universes, in which natural constants may even have different values. This is the idea of ​​the fractal "multiverse" popularized by Andrei Linde. We then live in a universe in which life and cognition can develop (the anthropic principle), but there would be many other universes in which galaxies and planets may not be able to form, for example because there is too little or too much dark matter there gives.

In quantum theory, too, there is the many-worlds theory, which postulates parallel universes whenever a quantum effect can produce two different results. Stephen Hawking called such theories very economical in terms of the necessary initial conditions but very expensive in terms of universes. Steinhardt shows a similar attitude: It cannot be that we are already able to forego calculating and understanding the natural constants, if their values ​​are only a coincidental result in our universe and we cannot observe the other universes anyway .

Steinhardt's proposal is no less resourceful, however. He models the universe with the help of "membranes" derived from string theory. In string theory there are additional dimensions of the universe that are not directly perceptible to us. Our universe is such a "brane" (made of membrane) that periodically collides with another universe (another brane). Every collision is like a big bang, but not locally in the case of a singularity, but a global big bang, so that the horizon problem cannot arise. The monopoles would not be formed in such a scenario either and the flatness of the universe would be guaranteed by the mechanism of collision

Steinhardt received a lot of criticism with his suggestion from the corner of the inflation theorist, but one has to admit that he only needs two and not many universes. After all, Sabine Hossenfelder read the riot act among inflation theorists. She says maybe there are simply no magnetic monopoles, the initial conditions of the universe were simply Ω = 1, and thermal equilibrium at the beginning of time is also conceivable.

What she ignores, however, is that the existence of magnetic monopoles theoretically explains the quantization of charges and that Ω = 1 presupposes a very fine tuning of the entire mass of the universe with its expansion. In any case, the debate is not over and the inflation theorists and the critics will have to work hard until a satisfactory theory can be concluded.

But why do we even care what a microsecond after the Big Bang was when we can more or less explain the remaining 13.7 billion years and even see a large part of it? You could say "because it's there", like Mount Everest. But a better explanation would be Hilbert's dictum, which, in relation to mathematics, is: "We have to know, we will know".

The fact that scientists sometimes get lost along the way and incorporate epicycles and other epicycles into incorrect theories is nothing to complain about - it would be much worse not to try. (Raúl Rojas)

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