The Big Bang

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Cosmology is the study of the origin and evolution of the cosmos, where by cosmos we mean everything – no less. This is a subject which has always fascinated mankind and has given rise to many fanciful and often farcical stories. It is one of the principle reasons for the invention of religion. We looked at one such story in the introduction, the cyclic creation, maintenance and destruction of the cosmos by Brahma, Vishnu and Shiva. Now let’s get serious.

What we know about the Big Bang

We know from astronomical observation that the universe – space – is expanding. The stars, galaxies and other distant celestial bodies are moving away from us (and we, from them). Observation of type 1a supernovae (explained later) has shown that for the last 7 Gy the expansion has been accelerating slowly.

If we do a backwards extrapolation of the measured expansion including theoretical considerations, we find that about 14 Gya all spatial objects were in the same place. This figure has recently been refined to 13.8 Gya.1)According to the WMAP project, the age of the universe is 13.77 ± 0.059 billion years. http://map.gsfc.nasa.gov/universe/uni_age.html. The ESA Planck probe finds 13.799 ± 0,021 billion years. We will settle for 13.8 Gya. The entire visible universe – “our universe “– once occupied a very small region, probably smaller than the size of an atom.

It is important to understand that we can see only part of the cosmos, the visible universe, or “our Universe”. It is limited in size because of the time light takes to get from a distant point to us and because of the age of the universe. Light travels with a finite speed, so the more distant an object or event, the more time light takes to reach us and the farther back in the past the event we are seeing. The most distant objects we can see are therefore the oldest, those which emitted their light at the time of the Big Bang, about 14 Gya. However, because space has been expanding in the meantime, such objects are now about 41 Giga light-years away, which is thus the current radius of the visible universe.

Current best hypothesis – inflation

Astronomers, cosmologists and physicists – the folks who worry about this sort of thing — generally accept the Inflationary Big Bang as the explanation of the origin of our universe. Although it is still somewhat speculative, it is capable of accounting for many facts left unexplained by the original, non-inflationary Big Bang hypothesis.

The inflationary Big Bang framework says that the universe has evolved in a two-step process:

  • a brief and extremely rapid expansion, called inflation, followed by
  • subsequent, slower expansion powered by the negative pressure of gravity (the cosmological constant).

In a nutshell, our universe started out smaller than the current size of an atom. It was roughly uniform but with tiny quantum-mechanical fluctuations (sometimes referred to as “jitters”). Almost instantly, on a human time scale, it inflated (expanded) enormously to about the size of a grapefruit.2)Tegmark (2014), 117. The rapid expansion isolated the quantum jitters before they could resolve. When inflation stopped, a mainly uniform space had been filled with matter formed from the spread-out quantum fluctuations. Since then it has expanded well beyond what we can see of it.

It must be stressed that when we speak of the expansion of space, we mean the “fabric” of space itself. The expansion is a property of space only: As it expands, the push to expand remains the same at each (new) point and does not dilute away. Only space expands and only on very large scales. On smaller scales, the other physical forces, such as gravity, keep particles together. Although the space around our galaxy, the Milky Way, is expanding, the galaxy is not. Nor are the stars, nor the planets, nor you nor I.3)If you are expanding, you cannot blame it on universal inflation.

One of the strong points of the inflationary Big Bang is that it explains how the expansion started. It was due to the properties of the inflaton field. Read on.

The origin of inflation is thought to be due to a field called the inflaton field (or false vacuum). This field was originally in a metastable state of high energy in which it exerted a huge outwardly-directed force which caused space to expand enormously, in fact exponentially, doubling its size every 10-37 seconds.

Such an increase in size rapidly becomes huge. At that scale, doubling its size every 10-37 seconds, one hundred doublings would have taken about 10‑35 seconds. But 100 doublings means a total increase by a factor of 2100 = 1.3×1030.4)Greene (2004), 308, Guth (1997), 173.  Max Tegmark says the doubling may have occurred every 10‑38  seconds.

The inflaton field was in a state of unstable equilibrium. Anyone who has ever been delicately balanced, say on a taut rope, so that if she leans one way or the other she starts to fall, understands what it means to be in unstable equilibrium. At about 10-35 seconds of age5)Greene (2004), 285., the field “lost its balance” and started to “fall” (metaphorically) off its high value. After about 10-32 seconds, space had “fallen” as far as it could in the inflaton field, effectively hitting “bottom”. More precisely, it reached its point of minimum energy in the inflaton field. The inflation stopped but the universe went on expanding, but more slowly, under the outwardly-directed pressure of gravity (the cosmological constant). The energy released by the “falling” inflaton field provided the energy and matter that constitute the universe today. As each bit of matter exerted a gravitational attraction on every other bit, the rate of expansion slowed down. When the universe attained the age of about 7 billion years, the expansion rate began accelerating. More on that later.

At its pre-inflation size, the universe was so small that it must be explained using quantum mechanics, according to which states of energy normally forbidden by the Law of Conservation of Energy can exist for very short periods of time, as explained in the theory chapter. So there were a great number of relatively very tiny places where the energy was higher or lower than the average. The rapid inflationary expansion caught these energy fluctuations unawares, so to speak, and scattered them out over macroscopic scales before they could merge and even out the energy. They gave rise to particles and antiparticles. This tiny non-uniformity has been observed in the cosmic microwave background radiation (explained shortly).

The inflationary Big Bang solves the so-called horizon problem: How the universe managed to reach large-scale uniformity without there having been enough time for light to traverse it. Before the inflaton field started “falling”, the universe was so tiny that light could travel from any part to any other, so it managed to reach a state of internal equilibrium in which it was all at practically the same temperature everywhere. As the universe inflated, this region of almost constant temperature did too, so the universe we see today is approximately homogeneous, at least on a large scale, a fact which is confirmed by satellite observation.6)NASA WMAP project, http://map.gsfc.nasa.gov/universe/bb_cosmo_fluct.html. These results have been refined by the more recent Planck probe.

Inflation also resolves the so-called flatness problem, since it was so fast that the resulting universe looks flat. (Think of the surface of a balloon which is rapidly inflated to a very large size.7)Better yet, glue some 2-centime pieces to the balloon, before you inflate it more. You will see how the coins move apart without getting any larger.) In cosmology, flatness is very important, as it means the expansion will continue; otherwise, the universe would begin to collapse back together, terminating in a “Big Crunch”.8)The flatness problem is more complex than this says, but it gives the idea. (More on flatness later.)

There are several reasons to think inflationary exponential expansion took place. It explains why expansion took place (the inflaton field), as well as why space has a uniform temperature everywhere on the average. And it shows how perfectly “normal” quantum-mechanical phenomena (briefly-existing spots of non-conserved energy) gave rise to packets of energy and eventually particles.

This much is agreed on by almost all versions of the inflationary Big Bang theory. Since there are several versions, it should be understood that the Big Bang is currently a framework, rather than a theory.

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Time line of the inflationary Big Bang, from WMAP via NASA

Time line of the inflationary Big Bang, from WMAP via NASA

Infinite expansion and the inflationary multiverse

No one knows if the universe infinite, but it seems hard to imagine that it is not and most cosmologists today accept that it is.

Indeed, in most versions of inflation, expansion goes on forever in time, too. If the inflaton field decays with a well-defined lifetime, like radioactive elements, then regions of the universe regularly fall off their metastable energy peak to give up energy to form … universes! Each one looks like ours to the extent that it has been born out of an inflationary burst. This process has been compared to cell division9)Guth (1997), 251., but does this suggest that the inflationary multiverse should be regarded as an evolutionarily revolving population of universes? Perhaps not.

Such universes within the inflationary multiverse have been called “pocket” or “bubbleuniverses. Each one is infinite. Although the pocket may seem finite from the outside, time is transformed into space inside due to the effects of relativity, making the interior infinite!

Since inflation continues forever in this scenario, the Big Bang at the origin of our universe was really the moment when inflation in our part of the multiverse stopped.

This multiverse hypothesis is a suggestion on the extreme edge of cosmology, but it is taken seriously by many cosmologists. In fact, there are other multiverses proposed. For more info, see the multiverse page.

L’après Big Bang — nucleosynthesis and background radiation

Once the inflaton field’s energy was spent, inflationary expansion ended. The universe went on growing under the pressure of the cosmological constant, but the gravitational attraction of all that mass limited the expansion. As the universe expanded, it cooled.10)Think of how a bicycle tire gets hot as you pump air into it; this is just the opposite phenomenon. All temperatures from Guth (1997), 86-94.

Time after Big Bang Temperature of universe
 10‑39 secs  1020K
 1 sec  1010K
 7 days  17×106K
 1 year  2×106K
 100 Kyrs  5.8×103K

 

Big-Bang nucleosynthesis, the creation of the light chemical elements, hydrogen, helium and lithium, took place in the period from about 1 sec to 3-4 minutes after the Big Bang.

At .1 sec ABB, it was too hot for atomic nuclei to form,. The universe was filled with rapidly moving protons and neutrons, electrons and positrons, neutrinos and antineutrinos and lots of radiation (photons). Protons and neutrons underwent reactions in which one changed to the other.11)The ratio of protons to neutrons was 1.61, due to the equilibrium rate of the reactions.

Remember the four basic forces of physics? At such high temperatures, their impact was negligible, even zero. But as temperatures fell and particles moved more slowly, the strong force was able to exert its influence – by forming nuclei (but not yet atoms).

At around one second of age12)Guth (1997), 94., the temperature was “cool” enough that the frenetic activity of all those particles calmed down. Protons stopped changing into neutrons. Neutrons still decayed into protons and electrons13)Since neutrons are slightly heavier than protons., but those which did not decay combined to make an isotope of hydrogen called deuterium (2H, one proton + one neutron). Electrons and positrons annihilated to form huge amounts of photons, visible today as the Cosmic Microwave Background radiation. By 30 seconds of age, about half the electrons and positrons had annihilated.

At about 3 minutes of age, the universe was a nuclear furnace. Deuterium nuclei combined to form helium. In this way, the lighter elements, including small amounts of lithium, were formed. BB nucleosynthesis was the first of three steps in the formation of the elements of the universe.

The Cosmic Microwave Background Radiation (CMB)

As the universe continued expanding and cooling, more heat was given off in the form of radiation, i.e., photons. But it was still too hot for electrons to be bound to nuclei as atoms, so the matter remaining was in the form of a plasma, mostly rapidly-moving free protons, neutrons and electrons. The electrons scattered the photons, which were thus like light in a cloud or fog. In a word, the universe was opaque.

After about 380,000 years, the temperature descended to around 3000 Kelvin, and the electromagnetic force became effective, binding electrons with nuclei to form atoms, a process called recombination by cosmologists. Photons now were no longer deflected by electrons and the universe became transparent, although the number of photons was still far too low for space to be called luminous. That radiation, which was emitted in all directions, is still “visible” today.14)Since it is in the microwave frequency, we cannot really see it. This Cosmic Microwave Background Radiation (CMB) is light from 13.3 Gya.

When we look up into the sky, we are looking into the past, because of the time light from distant celestial objects takes to reach us. But because the universe was opaque until 380 Ky ABB, we can see no farther back than that. The most distant light we can detect is composed of the remnants of radiation emitted then, now reduced now reduced by the expansion of space to microwave frequencies.

Just as we cannot see past the surface of a cloud, we cannot see past the time when the universe became translucid. From NASA

Just as we cannot see past the surface of a cloud, we cannot see past the time when the universe became translucid. From NASA

The great uniformity in the distribution of this radiation supports well the cosmological principle, the idea that the universe is uniform or homogeneous on very large scales, on the order of 106 light-years.

After about 200My, something happened to dispel the darkness. To find out what, read about the life of stars.

Notes   [ + ]

1. According to the WMAP project, the age of the universe is 13.77 ± 0.059 billion years. http://map.gsfc.nasa.gov/universe/uni_age.html. The ESA Planck probe finds 13.799 ± 0,021 billion years. We will settle for 13.8 Gya.
2. Tegmark (2014), 117.
3. If you are expanding, you cannot blame it on universal inflation.
4. Greene (2004), 308, Guth (1997), 173.  Max Tegmark says the doubling may have occurred every 10‑38  seconds.
5. Greene (2004), 285.
6. NASA WMAP project, http://map.gsfc.nasa.gov/universe/bb_cosmo_fluct.html. These results have been refined by the more recent Planck probe.
7. Better yet, glue some 2-centime pieces to the balloon, before you inflate it more. You will see how the coins move apart without getting any larger.
8. The flatness problem is more complex than this says, but it gives the idea.
9. Guth (1997), 251.
10. Think of how a bicycle tire gets hot as you pump air into it; this is just the opposite phenomenon. All temperatures from Guth (1997), 86-94.
11. The ratio of protons to neutrons was 1.61, due to the equilibrium rate of the reactions.
12. Guth (1997), 94.
13. Since neutrons are slightly heavier than protons.
14. Since it is in the microwave frequency, we cannot really see it.

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