Inflationary cosmology and exponential growth

11 min readSep 28, 2020

Ciao, folks. Welcome to another post in the chronology of the universe series. In the previous post fundamental forces of nature, we discussed all the forces and fundamental particles and their interactions with each other. We also had a post about the early stages of the universe in after the bang of the big bang. In this post of Inflationary cosmology and exponential growth, we will talk about the inflation theory. Inflation theory simply suggests a rapid expansion of the early universe. This theory was proposed by Allan Guth of MIT. Guth had suggested that the universe increased by million million million million( 1 with 30 zeroes) times in just a tiny fraction of second. Let’s hop into the ride to understand the wild science of inflation.

Modern thinking is that time did not start with the big bang, and that there was a multiverse even before the big bang. In the inflation theory, and string theory there were universes before our big bang, and that big bangs are happening all the time. Universes are formed when bubbles collide or fission into smaller bubbles.
Michio Kaku

Back history

To understand why we needed inflation, let us go back to the probably first theory about the growth of the universe.

The predecessor of inflation

The hot big bang model describes the expansion and growth of the universe in great detail. It simply goes by as the universe expands all the matter and radiation also expends with it. With the expansion, its temperature gets cooler. There were no elements in the universe at the start, only energy. With drooping temperature, photons could smash together to produce fundamental particles. With every collision, a particle-antiparticle pair emerged. They came in contact with and annihilates each other in the puff of energy and protons.

The activation of fundamental forces

Those particles who were managed to escape from annihilation would have started feeling a strong force that will bind nuclear together. Quarks that ran away from antiquarks would have started combining to form protons and neutrons. Within a few fractions of seconds, the universe had photons, neutrinos electrons, and few protons and neutrons. About one hundred seconds after the big bang the neutrons and protons came together to form a nucleus that in return had attracted electrons. However, it took millions of years for the electromagnetic force to kick in. Once electrons started combining with nucleus atoms started appearing. Our universe keeps on expending and on slightly denser regions, gravity showed its magic. These regions came together to form galactic clouds of hydrogen and helium.

Galaxies, stars, and supernovae

As their gravitational pull increased they started attracting nearby matter. The matter started contracting around a central region. This had given rise to galaxies. As time went by large clouds separated into smaller ones and increasing gravity temperature also increased. Atoms started participating in nuclear reactions and not before long we had the first generation of stars. The heavier elements were produced inside the hot cores of these stars. When their energy extinguished and they died in supernova explosions, the heavy elements were spread out in the open space. Countless trillions of stars died out in Supernova explosions and trillions of amount of heavy elements were spread out in the space which then became part of rocky planets like earth.

After CMBR (cosmic microwave background radiation) there was no incident of light in the universe. The formation of first-generation stars had put gave the first true lightning in the universe. 5 billion years ago solar system formed with its star and other planets.

This picture seems quite right and understandable. We accepted the hot big bang model for quite some time. The need for inflations arises when we found some deeper problems in the hot big bang model.

Why we need inflation?

The horizon problem

There are several reasons to think that inflation might have happened. Firstly our universe (observable) is very large and flat. Secondly, CMBR is very smooth almost identical so it tells us that in the past our comparably very tiny universe was close enough that every part was in contact with another one. However, the size of the observable universe is so big that it would have not possible for parts to come in contact with each other. The speed of light would be the same so how did the universe manage to come in contact and be so similar. For different far away parts to get mixed up will take time. For instance, if we put 2 drops of two food colors into a plate separately it will take time for them to get in contact and mix. This similarity of CMBR is also called the horizon problem.

The flatness problem

Inflation explains that when the universe was very small( yes we are not talking about the singularity, nobody talks about singularity these days), inflation kicked off and it had blown up the universe into a very large size. It was large and different parts were unapproachable now but this smoothness was retained. According to the inflation theory, our observable universe is part of a larger wider universe. You can very well say it multiverse. Our universe is flat because it may be a tiny portion of the larger universe/multiverse. And this multiverse might be curved. Now the question arises that what force can expend the universe so fast. There are many terms for this force like dark energy or say a stronger version of dark energy that caused the inflation in the first place and still working in the weaker form for the normal expansion of the universe.

The math of inflation

The simple maths behind the expansion of the universe starts as after 10–37 seconds universe started to grew. With every passing 10–37 it grew double in size. Alan Guth had proposed at least 100 doubling periods for everything in the universe to get uniform. I used to think because of expansion, the universe must have gotten bigger. Which is correct but the bigger in my thinking was very large more than the size of a galaxy. But with research, I came to realize that inflation was one of the earliest activities in the universe. The most important aspect of it explains that it grew very large within a few fractions of second i.e. A very small amount of time.

When inflation stopped universe grew from a billionth of the size of a proton to about the size of the marble. After that Hubble expansion started. The universe grew up the size of a marble so let’s take it size 0.001 cm. The expansion lasted about 10–35 seconds so Speed= 0.001/10–35 =1033 m/s, which is more than the speed of light(3* 108 m/s). This conclusion doesn’t interfere with general relativity at all. This growth is property of space itself. Space was growing at this speed and photons inside it were moving at their natural speed.

Alan Guth’s model

We all know that gravity is attractive according to the Newton principle but it was proposed to be repulsive by Einstein’s theory of general theory of gravity. In 1929 the first time in history we came to know that our universe is expanding. Before that scientists used to the thought that the universe had to be static. When Einstein had seen his own equation of general relativity is showing an expanding universe he introduced cosmological constant. When people accepted the expanding universe the next thought was like how was the universe in past. It had to very close, every matter in one place with high density and temperature. Then came the very obvious response of singularity. Once everything was in one point, every matter and energy of the universe. The universe came into existence from somethingness or nothingness.

But now the idea that the universe emerged after the big bang is not supported well. The physics equation can not work in singularity and it was sounding too divine. After the discovery of CMBR, many researchers had like David Wilkinson, Robert Dicke, and Jim Peebles had proposed that perhaps all the matter and energy of the universe had come from the collapse of the previous universe. In this sense, we do not have to worry about whole matter and energy (that is in a huge amount just think about only the milky way) sprouting from nothingness. The universe was initially filled with energy and photons. We know from the experiments at the LHC that high energy photon smashes can produce particle pairs like electron and positron etc. So now the question is from where photons come from.

The intact symmetry and antigravitational push

To understand Guth’s model we have to go the same way as the hot big bang model. In the early universe, everything was very chaotic and because of extremely high energy, the universe was full of radiation. At that time all the four fundamental forces were combined in one single force. Their symmetry was still intact. With the ongoing expansion, symmetry had to break and all force would become separate. Guth suggested that in the inflationary universe the temperature dropped down to a critical point but symmetry remain intact and hadn’t broken. It was an unstable stage and this has produced more energy which otherwise would have not been there. This energy had created an antigravitational push. The universe was also expanding in the first place but this push had increased the speed of expansion very fast.

Inflation lasted for 10–35 seconds and there were 100 doubling episodes. With every episode, the universe grew double in size. This increment of space had uniformed the universe at large levels The inflation stooped after a certain time. If inflation would have gone on there would have no matter in space. Particles would have not to produce following other processes like star formation, galaxies, and other structures. The inflationary phase ended as symmetry started to broke off. Forces started to separate and the universe went to the normal stage of Hubble expansion.

Drawbacks of the old inflationary model

The model explained by Alan Guth has some minus points According to also Guth the phase transition(the symmetry breakage) happened very fast, almost immediately. The universe was already very large after inflation. Symmetry breakage happened in local small regions at different times and slowly these regions met with each other and the whole universe went into a normal expansion stage. There were some problems. Even if inflation stopped but the universe was still growing with the speed of light. The local regions of symmetry breakage couldn’t mix with others before they were drifted apart because of the growing size of the universe. In this situation, with passing time different regions would only be kept on moving away. Then, they would have developed into different patches of the universe with different characters. But we see whooping uniformity on large scale.

Revisions of inflationary theory and new models

The above drawback of Alan Guth’s model was explained by new models. The new inflationary model was put forth by Andrei Linde, Paul Steinhardt, and Andreas J. Albrecht. First explained by Andrei Linde it says that we can avoid the problem joining of local regions. Let’s take those regions as bubbles. These bubbles could not join because the universe is moving with the speed of light. There is one way for them to interact if those regions would be very big, almost as big as the size of the observable universe. The symmetry breakage would have happened very slowly inside those bubbles. Later it was said that symmetry must have broken in the whole universe at the same time instead of inside local regions.

Andrei Linde had presented another version of inflation called the chaotic inflationary model. It states that the early universe had a spin-zero field. Because of quantum fluctuation, this field had larger values in some regions. These larger values of energy had acted as cosmological constant/ dark energy and started the inflation. As these regions expanded the energy had decreased and inflation slowed down to Hubble expansion.

Inflation had suggested the existence of multiverse and parallel universes. We will discuss it in the next section. Read what is inflation theory by NASA.

The emergence of a multiverse

Although many theories are pointing towards multiverse our concern is eternal inflation. Now scientists think that maybe our universe had emerged from another universe. All matter and energy came from that universe and inflation is the property of the universe itself. Our observable universe is just a part of a big cosmic plan. Physicist Alexander Vilenkin had suggested that we are part of a big cosmos. In our observable universe inflation stooped and matter formed. On the other part, it is still going one. Now, these separate parts are behaving like separate universes thus making bubble universes. In these other universes law, the law of physics might be totally different than ours.

String theory, quantum mechanics are among reputable theories that point towards multiverse. You can read This is why multiverse must exist article on Forbes for more information.

The new insight on inflationary cosmology

To complement the chaotic inflationary theory, scientists believe that the quantum field was responsible for inflation. It is unlike any force we have seen before. Quantum field called inflaton in this case can create space and it has inert energy that acts as repulsive gravity/cosmological constant. So this energy of inflation had started the exponential expansion. When the inflation ended then started the particle pair production of matter. BICEP -1 and 2 was created for the study of the early universe and gravitational field. These two telescopes were used to detect the gravitational filed waves(traveling at light speed) produced at the time of inflation. These gravitational waves could remain forever and they could change the properties of CMBR. Scientists working on that claimed to have detected the gravitational waves from the inflation. It was one of the first trials for inflation detection.