Inflation, Gravitational Waves and the Cosmic Background Radiation: Theory and Experimental Verification

The new observations open a door to understanding the early universe.

The greatest discovery in twentieth-century cosmology was the expansion of the universe: very distant galaxies are moving away from each other. The question was asked, why do they do this? Let's assume that we are in the "center of the universe" and imagine that once upon a time in the past there was a kind of "explosion" at this exact point and this "explosion" was called the Big Bang. Since we are in the center of the universe where the explosion happened, the galaxies that received the greatest speed are now the greatest distance from us.

Let's say a big bang did occur. When did it occur? Let's take two bodies that are a distance D from each other today and assume that when the universe was born in the big bang they were close together. From the moment of the big bang they began to move away from each other at a constant speed. If they always moved away from each other at the same speed, the distance they are today is equal to their speed times time, the age of the universe: D = VT. According to Hubble's law we know that the velocity V is equal to V = HD, where H is the Hubble constant. Let's assume that the speed of the bodies is the same speed as today. From these two equations we find that the age of the universe is: 1/H = T. We find that the age of the universe is approximately equal to 14 billion years.

There are cosmologists who will tell you that they study the entire universe, which is apparently infinite in size, from the beginning of time until today - 2014. They will tell you that the entire universe is like this and like that... don't believe them, because there are parts of the universe that are too far away for us to see and all that we can To do is to imagine and guess what is happening there. What can be explored in the universe? In cosmology we can only study that part of the universe that we can see from the remote corner where we are. If we agree that the universe began at some time in the past, there is a limit to how far things can be seen. The most distant parts of the universe that we can hope to see are the regions that emitted photons or gravitational waves at the time of the Big Bang, and these reach us today after traveling at the speed of light since the Big Bang.

More of the topic in Hayadan:

• First direct evidence of the existence of gravitational waves that caused the universe to swell immediately after the big bang
• How does the telescope at the South Pole that discovered the gravitational waves created by the Big Bang work?
• What are gravitational waves?
• An attentive ear to the echoes of the Big Bang

In Minkowski space-time we will describe the light cone of these photons. The light cone of their past stretches like a triangle backwards in time, with its apex at our point in time and its base at the Big Bang. The sides of the triangle are the limits or horizon of the universe that we can see. Any area outside this horizon has not yet had time to send us signals and therefore we cannot yet say anything scientific about it. Tomorrow when we make new observations this horizon will expand and events will be added that we can see and thus every day the size of the visible universe increases.

From Hubble's law it is possible to calculate the horizon of the visible universe, its edges, what is the maximum distance D up to which we can look. Place the speed of light c instead of the speed V. We are moving away from the galaxies and they are moving away from us at the speed of light. and therefore Dmax = C/H. And that's a billion light years. Can't see beyond that. At this limit you get infinite redshift and the electromagnetic radiation has no more frequency and the photons have no more energy. This is the edge of the visible universe. Can't see past this edge.

Let's say that astronomers on Earth look at the most distant galaxies from all sides of the Earth and from all the ends of their light has already moved 80% of the time since the Big Bang (from the age of the universe). When astronomers look at the most distant galaxies in any direction they are looking back in time as far back as possible to the Big Bang. Suppose they are looking at two groups of such very distant galaxies that are in two opposite directions from us. The light from a galaxy from one group traveled 80% of the age of the universe by the time it reached us, so it obviously didn't have enough time to reach the galaxies in the other group, which we see in the other direction. This means that the galaxies in the first group have not yet entered the visible universe of the second group. Let's say there are intelligent beings living on the first group of galaxies and they see our Earth as it was at 20% of its age. They cannot see the galaxies in the other group. But we can see both sets of galaxies at the same time.
When we proposed the big bang theory we assumed that we are at the center of the universe and imagined that once upon a time in the past there was an explosion at this exact point and we called this explosion the big bang. Is it even reasonable to assume that we are at the center of the universe? Let's imagine that we are a small dot on a balloon, which is full of such small dots. Now we inflate the balloon. All points see the other points moving away from each other and all see the same Hubble law. Each point sees the universe expanding away from its point. The further the points move away from each other, the faster we find that their speed is greater. The interesting thing is that every other point on the balloon thinks exactly like we do about the other points on the inflatable balloon; She thinks she is very special and she is the one in the center of the balloon precisely because all the points are moving away from her in the same way. And so every point will invent the law of mourning and think that it is special. It will conclude that the speed of the other points is linearly proportional to the distance.

There is gravity which attracts and therefore the different parts of the universe attract each other. Hence the spread is slowed down. The rate of expansion in the past was faster than today and at some time in the past, at the beginning of time, in the singularity, the galaxies and gas in the universe were all packed together at an infinitely high density. In fact it is believed that very early in the beginning of the universe there was initially an acceleration followed by a deceleration, and then there may have been an acceleration again.

Astronomical observations that have detected and measured very distant Type Ia supernovae have provided evidence that the expansion of the universe is actually accelerating today. That is, the mourning constant was smaller in the past than it is today. Hence it is possible and possible to watch the first moments of the hot big bang, watch "everything" except for the second fraction of the singularity at the beginning, make measurements and propose a physical theory that will decide whether there was indeed a big bang.

In 2002 two groups of researchers used such supernovae to determine the value of the cosmological constant in the field equations of general relativity. They measured the redshifts from the galaxies that contain the supernova and the result they got was that the universe is accelerating.

From the cosmological constant you get a physical field with negative pressure, repulsive gravity, which exerts a gravitational effect that is greater than the gravitational attraction of all the normal matter in the universe. The explanations for the accelerated universe raise this hypothesis that there is such a physical field, Einstein's cosmological constant. Astrophysicists have called this field dark energy and hypothesize that it behaves like the cosmological constant. It is invisible except through its gravitational effects and creates anti-gravitational effects.

The early universe was hot and dense, so matter existed in the form of plasma. The atoms of the gas were moving so fast at this temperature that when they collided they ionized each other and stripped the electrons from the nuclei. Because of Planck's blackbody law, radiation in a dense plasma has a spectrum of blackbody radiation. And this was the case when the universe was very young and hot. As it began to expand, the plasma cooled and the electrons combined with the nuclei to form a neutral gas. At this point the radiation in the plasma is released, because the photons are scattered from charged particles and not from neutral atoms. So when the particles in the universe became neutral, the photons no longer scattered. When this combination took place between the electrons and the nuclei, the photons left the material. The photons had a blackbody radiation spectrum with a temperature that is insufficient to ionize hydrogen. The universe continued to expand and this photon gas also continued to expand and like any expanding gas it cooled. Since these photons have been moving freely in the universe since that recombination and they have not been scattered by anything, they have been cosmologically redshifted just as happened to light emitted from galaxies later. Each photon is redshifted so these photons still have a blackbody spectrum, but their temperature has been redshifted to a much smaller value.

These photons have been observed and are in the microwave part of the spectrum. Their temperature is about 2.7K. This radiation is called the cosmic background radiation (CMB). When looking at the CMB we are actually looking at the universe at its very young age. You look in all directions and see the same type of CMB radiation, with the same temperature and the same degree of uniformity. The CMB reaches us from directions that are separated from each other by such distances, that they have no ability to know about each other, at the time when the radiation was emitted; In addition, it also reaches us from distances close to each other.

We have seen that the universe is homogeneous. We will go back in time. The universe cooled and its ionized matter became neutral, the electrons recombined with the protons and the photons no longer had enough energy to scatter from the electrons. The CMB (cosmic radiation) remains. The initial homogeneous gas began to expand. How can clumps of irregular matter like galaxies form in such a gas? The formation of planets, stars and galaxies means that there is an attractive gravitational force that leads to instabilities in the gas. There is an irregularity in a certain area where there is a greater density than usual and it is increasing. The region changes the direction of its expansion and collapses gravitationally. This scenario does not seem so likely, since such a random creation of clumps of matter in a gas of particle masses is rare. Statistically speaking, for every particle approaching another particle, there is likely to be another particle moving away from it. Even if we assume that nothing is perfectly homogeneous and it will lead to the formation of clumps, galaxies cannot form from these clumps and need some mechanism to create them. Random creation of clumps in gravitational collapse does not create galaxies, because the number of particles needed to form a star, let alone a galaxy, is enormous. Therefore, random fluctuations in the positions of the particles cannot create clusters of particles with the density necessary to form stars and galaxies. Something had to cause density irregularities on large orders of magnitude. So they proposed the dark matter that provides these irregularities. Dark matter is a sea of ​​electrically neutral heavy particles and they are called cold dark matter (CDM).

Physicists link the CDM idea to swelling, inflation: initially at a very early stage there was a very rapid expansion in the universe, which was driven by negative pressure dark energy, like a huge cosmological constant. Inflation increases density irregularities by a very large factor. Even a small fluctuation in density from a quantum uncertainty, before the period of inflation, is amplified after inflation to a significant irregularity in the distribution of dark matter particles.

Observations of the CBM helped establish the standard cosmological model called Lambda-CDM. The lambda is the cosmological constant. The universe is dominated by cold dark matter and has a cosmological constant that drives accelerated expansion at late times. According to this model our universe is spatially flat.

When we first dealt with the simplistic example of the inflatable balloon with dots on its envelope, we saw that our universe is a homogeneous universe of expanding galaxies. But from the balloon example we see that Hubble's law describes the expansion of the universe from a local point of view: how it inflates around our point. We want to know what the global properties of the entire universe are: is the balloon flat or curved. This is the geometry of the universe. Einstein described gravity in terms of geometry. Since at global scales the universe is homogeneous and isotropic (nothing changes from one direction to another), a sphere can be drawn around any point. Since all the distances are the same, we create a surface from all the points on the shell of the sphere. This distance to the points is the radius of the sphere. A large circle can be drawn on the ball. The length of the circle is the circumference of the sphere. The ratio of the circumference to the radius of the sphere in Euclidean geometry is two pi. Space is homogeneous and therefore all spheres drawn around all points will have a ratio between the circumference and the radius equal to two pi. If this ratio is less than two pi, it means that the space is curved: all spheres drawn around the points of the space will have a ratio between the circumference of the circle and the radius of the sphere that is less than two pi.

The geometry of the universe can be determined by measuring the total mass density of the universe around us and the Hubble constant. When you do this for the visible universe you find that the curvature is close to zero and it seems that we live in a flat universe.

The inflationary model corrects the standard big bang model and offers an explanation for the homogeneity of the universe.

Inflation suggests that there was a very early period dominated by dark energy and it acted as a sort of cosmological constant. It drove rapid expansion exponentially (exponentially): according to inflation theory at the beginning of the universe about 10-36 seconds after the big bang the universe underwent such a violent exponential expansion that its volume increased by a factor of about 1078. If inflation lasted long enough and the acceleration was strong enough , everything we see today was once within a tiny area. The homogeneity and smoothness in the universe on global orders of magnitude that we see today was obtained before inflation: large regions expanded from small regions just before inflationary expansion occurred, even if the universe was very random. Locally the uniformity was broken because the galaxies and stars were formed when inflation provided an explanation for this: the expansion due to inflation created irregularities by amplifying the quantum fluctuations that existed before the inflationary phase. These effects led to the creation of the galaxies, and this explanation of the inflation theory that creates the right amount of inhomogeneity at the local level, is the heart of the theory: inflation promises to solve both the problem of homogeneity at the global level and the problem of breaking the homogeneity in exactly the right dose at the local level.

We will return to the cosmic radiation and the experimental evidence regarding the theory of inflation. The CMB cosmic background radiation is one of the main sources for the study of the universe as a whole. The CMB provides a window into the early universe and measuring the temperature of the CMB can provide information about gravitational waves. For that we will talk a little about gravitational lenses. In general relativity, the presence of matter, the density of matter, can distort space-time and therefore the path of light fluctuates as a result. This process is called gravitational lensing and is analogous in a sense to what happens in optics, the igniting of light by a glass lens. Gravitational lensing is therefore the distortion of the path of light caused by gravity. Gravity acts like a lens for a light source. If there is a star that is at some distance from us, the light rays coming from it are modulated and therefore we see it in a position slightly different from its real position. On cosmological scales we have such a source that passes through gravitational lensing and is the CMB cosmic background radiation. Between the CMB and us there is a range of material that interferes with the paths of the light rays coming from the CMB on their way to us. So this is a special case of gravitational lensing known as polarization of the CMB.

While the CMB opens a window into the universe as it was roughly 400,000 years after it was formed, the polarization of the CMB is caused by the matter between us and the CMB and allows us to gain information about the evolution of the universe. We get information about the temperature changes from place to place in the sky and we get information about the gravitational lens or the polarization. This information is related to the total mass along the line of sight.
Since inflation theory was conceived 30 years ago, all of its predictions have been verified except for one: the unobserved prediction that quantum fluctuations created a gravitational wave background (GWB) in the early universe. When it was discovered now it was the "smoking gun" for inflation theory, and it can also tell us how strong inflation was.

How is the GWB detected? As we said above the CBMs are polarized. They are polarized due to an effect called Thomson scattering. This effect is due to density fluctuations that occurred in the early universe. There is a smaller amount of polarization caused by gravitational waves. These two sources - Thomson scattering and gravitational waves - yield two different types of polarization. Just like in classical electromagnetic theory, you get a polarization map that consists of two orthogonal bases, or two orthogonal modes called: mode-E and mode-B. Mathematically, mode E looks like a gradient and mode B looks like a curl. Therefore, if we draw a map of the CBM polarization and break it down into E-cycles and B-cycles and find B-cycles that are not zero, then we have discovered GWB gravitational waves and thus verified the existence of inflation!

E-cycles were discovered already 10 years ago, but B-cycles were not discovered until yesterday and as mentioned can only be created by gravitational waves. Gravitational waves are ripples that propagate through space-time itself. As the waves traversed the early universe they set charged particles in motion. The periodic, regular motion of these particles left a characteristic imprint on the CBM's light by polarizing it into the B-mode. That is, as a result, the cosmic radiation oscillates in certain directions. It can be imagined as a sort of vortex of heat and cold of waves oscillating in different directions in the sky. These directions are B-polarized.

How do we know that the signal received by the BICEP2 telescope at the South Pole is gravitational waves? If the signal is uniform and the same, it means that it is random noise. This conclusion is reached by a process called "Jackknifing". It is also possible that sources such as dust in our galaxy could appear experimentally as if they were gravitational waves. In the latest experiment, the results of which were published yesterday, the researchers compared the data to the results obtained from a previous task called the "Plank task". They concluded that the signal could not be explained by dust in the galaxy. Another source why the signal may not be gravitational waves is: the radiation coming from the CBM to us undergoes a process of gravitational lensing by the galaxies between us and the telescope located at the South Pole. The galaxies can distort the path of light and create a signal that can appear as if it were gravitational waves obtained in an experiment. But such a signal is not strong enough and has a different shape than the inflationary gravitational waves, and it seems that the latter were discovered experimentally.

The new observations open a door to understanding the early universe. Inflation theory predicts that if you take into account the exponential (exponential) expansion along with the quantization of the gravitational field you get GWB gravitational waves that left their unique and characteristic stamp on the CMB in the form of B-mode polarization. This seal cannot be formed by fluctuations in the density of matter. The discovery of B-mode polarization of the CMB provides a single-valued verification of inflation theory.