Abstract
The theory of the inflationary universe was proposed not as an alternative to the big bang theory but to solve some problems in it. it was suggested by Alan Guth in 1980 that at some early time from the universe age and after the big band the size of the universe suddenly expanded by a factor of 10^50. This period is called the inflationary epoch. Based on this assumption the universe should be flat and this compatible to observations. Before the inflation, the universe was incredibly small, and it was homogeneous and in thermal equilibrium and this solve the horizon problem. The inflation rise the volume of the universe rapidly so it make the universe almost flat with some points have a density slightly more than other, this slightly difference in the density enough to explain the galaxies and other structure formation. Finally, perhaps in the beginning there was a certain number of monopoles, but because of this inflation these monopoles were scattered all over the universe and the side we are in (the visible universe) may be empty or have very few of these particles
Introduction
After the discovery of the expansion of the universe in 1929 by Edwin Hubble, it became recognized that there was a beginning of the universe. After that, scientists began to think about the mechanism by which the universe originated.
Many theories have been developed to explain the creation of the universe. The big bang theory was the most important and the most prominent theory of all proposed models. The big bang theory is usually studied in relation to elementary particle physics. [2]
Elementary particle physics witnessed a great and interesting development in the second half of the twentieth century, especially in regard to theories of unification. The end of the 1960s witnessed the introduction of the Glashow-Weinberg-Salam unification of the weak and electromagnetic interactions. The great unified theories of the strong, weak, and electromagnetic interactions came in 1974. Two years later, supergravity emerged, giving the first hope of unifying all fundamental interactions, including gravitation. Nowadays, superstring theory is the leading candidate for the role of "theory of everything." [1]
As any physical theory, the unified theory needs an experimental proof to verify that we are going in the right direction. Unfortunately, this appeared to be an extremely difficult task, due to the involved energy scale at which the unified nature of all four fundamental interactions is expected manifest itself at very large energies of about 1019 GeV.
The largest accelerator ring ever built on Earth, with a circumference of 40,000 km, could not accelerate particles beyond 108 GeV. This result is 12 orders of magnitude short of the energy necessary for a direct test of the unified theories. There are some indirect tests though, such as the search for proton decay and the search for supersymmetric partners of ordinary particles, but these experiments are still very hard to conduct. The only accelerator that could ever produce particles energetic enough for a direct testing of the unified theories of all fundamental interactions is the universe itself. The standard Big Band theory tell us how it would be.
At an earlier time, all the matter and energy content of the universe was confined to a very small space in a state of infinitely high temperature Τ and infinitely large density ρ
As the universe expanded rapidly, the average energy of particles, given as temperature, decreased and the universe also became colder. The temperature falls as the reciprocal of R, where R is the "radius" of the universe. Meanwhile, as the temperature decreased, the nuclei and atoms began to form, then stars and galaxies until they reached at what they are now as seen in (Figure 1 [3]).
The standard big bang theory succeeded in explaining many things such as the proportions of the existence of the elements in the cosmos, the cosmic microwave background and so on, but at the same time it opened the way to other questions, and it was unable to answer them. What follows is a brief discussion of the most important problems that appeared in the standard Big Bang theory.
1. The Problems Of The Stander Big Bang Theory
1- The first problem is the Flatness Problem: Why the universe appears so flat? It was found from the astronomical observations that the universe is flat. Einstein found, in his theory of general relativity, that the geometry of the universe, the curvature of the space time, shapes, angles and all the relations in the universe are related to the amount of the matter and energy in the universe. Since the energy and matter are what cause the spacetime to bend. Depending on the amount of matter per unit volume, see (Figure 2[3]), in the universe (its mass density), space curves in on itself such that parallel lines converge to a certain density called the critical density. For a mass density less than the critical density, parallel lines diverge, and the universe expands forever. This is called an open universe problem. For a mass density greater than the critical density, the expansion of the universe will eventually be halted and then the universe collapses on itself. This is called a closed universe problem. In the 1980s it appeared that the universe may be just at that critical density where we have a flat universe, or very nearly so. Such an occurrence would be quite an extraordinary circumstance.[3][4]
2- The second problem is the Horizon problem: By looking at large distances in all directions in the universe, it can be seen that there are regions that entered our horizon due to the expansion of the universe. When studying the properties of the microwave radiation and the other information that comes from these regions it is found that they have the same information and properties although they were not communicating yet. How can these regions have microwave radiation that is so similar? The temperature of the universe reflects the 3 K microwave background no matter in what direction we look. How can two regions of the universe have temperatures so similar and be 10^19 m apart and not able to communicate?
3- The third problem is the problem of Magnetic Monopole Problem: Monopoles are hypothetical particles. The Big Bang theory, which is based on elementary particle physics, says that at the beginning of the universe, in its first moments, the temperature was very high (billions of degrees). This high temperature is supposed to allow these particles to exist. These heavy particles have among them a monopole magnet, and it is assumed that these particles that arose at the beginning of universe existed, but we could not find them ? The occurrence of magnetic monopoles brings symmetry to Maxwell’s equations of electromagnetism and also satisfies other physics theories. Why have we not yet detected magnetic monopoles?
2- The Inflationary Universe :
In 1980 Alan Guth proposed some modifications to the standard Big Bang theory and presented his theory of the inflationary universe that provides solutions to the problems described above. Guth proposed that at some time between roughly 10-35 s and 10-31 s after the Big Bang, the size of the universe suddenly expanded by a factor of 1050. This period is called the inflationary epoch which happens due to the separation of the nuclear and electroweak forces as can be seen in Figure 3. We have to remember that the size of the universe was incredibly small at that time, so the magnitude of such an expansion is remarkable. It is as if the electron of a hydrogen atom, which is normally only 10-10 m from a proton, suddenly found itself 1024 lightyears away![3] After the inflationary period, the universe resumed its evolution according to the standard Big Bang model.[3]
Thus ad hoc assumption of the inflation theory does mostly solve the problems mentioned above. The inflationary theory requires the mass density to be very close to the critical density. This solves the flatness problem.
This theory says that the universe was so tiny that it had already reached equilibrium before inflation occurred; this explains the homogeneous universe. But if the universe was so homogenous, how the stars, galaxies, cluster of galaxies and etc. were Formed? Therefore, scientists reconsidered this theory and found that there are always fluctuations (Changes) from point-to-point present in the density, making some points slightly denser than others, and this inflation raised them such that the contrast became greater, so galaxies and other objects began to form. This solves the galaxies formation. Subsequent to Guth’s work, cosmologists have contributed many suggestions to his inflationary idea. Magnetic monopoles would have to occur along the boundaries or walls of different domains. These domains might be thought of as different universes. This is why it is impossible to observe the magnetic monopoles if they exist and if they are at the edge of the universe. Inflationary theory is crucially connected to elementary particle theories. Nevertheless, there are problems with the inflationary theory, and there are other alternatives that will be briefly mentioned later.
3- The Inflationary Prardigm
The idea of the inflationary universe was not found suddenly, but it developed gradually in time. The idea was first presented by Erast Gliner. Then in 1970s Andrei D. Linde realization that homogeneous classical scalar fields φ, which are present in all unified theories of elementary particles, can play the role of an unstable vacuum state, and that their decay can heat up the universe. In 1979 Alexey Starobinsky (Landau Institute, Moscow) proposed an interesting model for the relation between the exponential expansion and the quantum corrections of the theory of the gravity.
The most important step in developing the inflationary paradigm was taken by Alan Guth in 1980 when he suggested to exploit the stage of exponential expansion in some supercooled vacuum-like state to solve the first three problems described above simultaneously.
Nowadays, there are several versions of the inflationary universe scenarios and the main feature of all these versions that are called the inflationary epoch at which the universe expands exponentially while it is in a vacuum-like state containing some almost homogeneous classical fields, but no or almost no particles. After the inflation epoch, the initial vacuum-like state decays into particles. These particles interacted with one another, and after the thermodynamic equilibrium was reached, the universe became hot. From then on it can be described by the usual hot-universe theory as seen in Figure 4.
Figure 4: The expansion of the universe for three possible inflationary scenarios - open (a), flat (b) and closed (c). The scale factor a(t) which, at least in the case of a closed universe, can be thought of as the radius of the universe, is plotted as a function of time. The inflationary universe starts either from a singular Big Bang or from a large quantum fluctuation of a pre-existing space-time metric. The inflationary epoch is followed, at 10-35 seconds, by a brief interlude of heating, after which the further evolution of the universe is adequately described by the standard noninflationary model (d) the noninflationary hot Big Bang model.[1]
In October 1981 Linde suggested the new inflationary scenario which resolved some difficulties of the original paper of Alan Guth. Few months later, the same idea was proposed also by Andreas Albrecht and Paul Steinhardt at the University of Pennsylvania. But this model was very difficult to realize in the context of realistic theories of elementary particles.
In 1983 another inflationary scenario was proposed, which was called the chaotic inflation scenario. This scenario is much simpler and more natural than other versions of inflation and it be the next point to be addressed here.
4- Chaotic Inflation
In the Grand unified theories, there are spinor fields that describe electrons, neutrinos, and quarks, and the vector field that mediates between their interactions. It also contains scalar fields. These scalar fields have a fundamental and a complicated role in the new inflation theory. In fact, inflation is based on the physics of scalar fields and gravity.
The scalar field theory has the ability to change the masses of particles, where such a scalar-fields are called Higgs fields. These fields, and by giving different masses to vector particles mediating different interactions, are responsible for the symmetry breaking between the weak, strong, and electromagnetic interactions in grand unified theories.
Another important property of these fields is that they are related to the potential energy density V(φ) which, in some cases, may lead to the exponential or quasiexponential expansion of the universe.
Now, by considering the theory of a massive scalar field φ, whose quanta is a particle of nonzero mass m and with m much smaller than MP:
MP >> m (1)
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where MP is the Planck mass, assuming that the field is minimally coupled to gravity, its potential energy density V(φ) is:
Figure 5: Classical evolution of φ, the homogeneous scalar field in the chaotic inflation scenario, with a quanta of mass m, m ` MP. For |φ| larger than Mp/5 (but smaller than Μ ρ 2/ m) the field (represented by the ball) rolls very slowly down toward the potential energy minimum at φ = 0. This is the inflationary epoch, during which the universe expands quasiexponentially. When |φ| becomes smaller than Mp, it oscillates rapidly about φ = 0 and its energy is transformed into heat.[1]
Suppose the field φ is initially nearly homogeneous in some domain of space-time that looks locally like an expanding universe with a growing scale factor a(t) and a Hubble constant H(t), defined:
.png){kind=small}
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.png)
Its evolution can then be described by the usual Klein-Gordon[1] equation modified by cosmic expansion:
.png){kind=small}
and by the Einstein equation:
.png){kind=small}
where k is + 1 ,
—1 or 0, for a closed, open or flat universe, respectively. The term 3Ηφ(" phi dot" which is the first derivative of φ) in Eq.4 plays the role of a friction term in the
equation of motion of the field φ. Eq.5 tells us that if φ is
initially large enough, the friction term will also be large. It can be shown
that if the initial field φ0 is greater than MP/5,
friction makes the variation of the field φ very slow, such that
one can neglect
.png)
From these equations it follows that for times t earlier than φ /(m Mp) the universe is expanding quasiexponentially:
.png)
where the Hubble "constant" is given by:
.png)
The exponent Ht is much larger than unity if φ exceeds the Planck mass in these early moments. This is just the inflationary regime we wanted to obtain.
Evidence And Experiments To Prove The Theory:
An experiment that took place several years ago and it was called BICEP 2, which is a radio observation of the universe that took place from the south pole of the Earth. The scientists in charge of this experiment stated that the microwave background radiation found the effects of cosmic gravitational waves (from the beginning of the universe) and these effects are fully compatible with what the theory of cosmic inflation predicted. But it quickly became clear after months that these effects were rather the effects of galactic dust and not the effects of primordial cosmic gravitational waves.
Currently, a second experiment with much more accurate setup than the previous one, called BICEP3 or BICEP Array, is still in progress and scientists are waiting for its results . If the results are strong and identical to the theory of cosmic inflation, then it can be said that there is a stronger proof of this theory, even if it still needs some modifications.[4][8]
Criticisms Against The Inflation Theory:
Although the inflationary model is widely acceptable, there are some criticism that have been leveled against it. It has been claimed that this theory has untestable predictions and a lack of serious empirical support. In order for this theory to be accepted , and as pointed out by Roger Penrose since 1986, inflation requires extremely specific initial conditions of its own to be realized. A recurrent criticism of the inflation theory is that the invoked inflation field does not correspond to any known physical field, and that its potential energy curve seems to be an ad hoc contrivance to accommodate almost any obtainable data.
Conclusions:
The development of the inflationary universe scenario was useful in solving many different problems related to cosmology and particle physics such as the problem of magnetic monopoles and the problem of the origin of density perturbations necessary for the subsequent formation of the large-scale structure of the universe . Inflation may lead to a multiple production of exponentially large strings, walls, bubbles, and other large-scale inhomogeneities of a nonperturbative origin. Investigation of the evolution of such objects may lead to a considerable modification of the usual approach to the problem of formation of the large-scale structure of the universe. This theory is generally accepted in theory but still requires a stronger experimental background. In general, progress in cosmology is relatively slow, since it is difficult to prove any theory related to the universe, and the equations needed to describe these theories can easily become too complex to understand and solve.
References:
1- Inflation and Quantum Cosmology, A. D. Linde, Lebedev Physical Institute Moscow, USSR.
2-Introduction to Cosmology, Third Edition, Matts Roos.
3- Modern Physics for Scientists and Engineers, Fourth Edition, Stephen T. Thornton, University of Virginia, Andrew Rex, University of Puget Sound.
4- https://youtu.be/J2SRVokb3IA
5- Superstring Theory, Jala Alden Alhag.
6- https://www.thoughtco.com/what-is-inflation-theory-2698852#:~:text=%20Description%20%26%20Origins%20of%20Inflation%20Theory%20,two%20closely%20related%20variants%20of%20the...%20More%20
7- Lectures of Inflationary cosmology my Alan Guth.
8- Wikipedia.
9- https://www.researchgate.net/publication/1896715_What_is_Special_About_the_Planck_Mass
10- https://scienceblogs.com/files/startswithabang/files/2011/03/300px-Horizon_problem.png
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