[The following is an excerpt from Chapter 1 of my book, Block by Block – The Historical and Theoretical Foundations of Thermodynamics.]

The inflation theory of how the universe began and the atoms arrived

Ten or twenty billion years ago, something happened – the Big Bang, the event that began our universe. Why it happened is the greatest mystery we know. That it happened is reasonably clear – Carl Sagan [1]

So after a few of the most productive hours I had ever spent at my desk, I had learned something remarkable…[and began] to call it inflation – Alan Guth [2]

About 13.75 billion years ago our entire universe occurred as an infinitesimally small region, more than a billion times smaller than a proton, with a near-infinite temperature and density of 10²⁹ K and 10⁸⁰ gm/cc, respectively [3]. Staggering, unfathomable numbers.

Stop here and think about this. This region, very much smaller than the period at the end of this sentence, was all that there was. There was nothing else, at least nothing that influenced our universe.

Within the first second of what became the start of time arose a tremendous repulsive force, the “bang” in the Big Bang, that drove space itself, per Alan Guth’s inflation theory [4], to expand at tremendous rates. The cause of the repulsion? Nobody knows but presumably some form of “dark energy” repulsion having a different underlying physical process than the first form. Both forms of repulsion contribute to the repulsive force contained within Einstein’s cosmological constant and provide a counter-force to gravity in Einstein’s Theory of General Relativity.

This was not an explosion as we commonly know it. There was no center to this event, no edge, no boundary. It occurred simultaneously everywhere. Everything rushed apart from everything else. Space itself rapidly swelled.

During this brief flicker, which ended within the first 10-30 seconds of time, the “dark energy” repulsion caused the universe to expand exponentially, doubling in size once every 10-37 seconds, more than 100 such doublings in all, a huge factor, before extinguishing. The rapid decay in the repulsive force slowed the expansion and transferred energy into the rapid formation of particles. Photons, protons, electrons, neutrons and all sorts of anti-matter. Their creation occurred everywhere, almost perfectly uniformly filling the expanding universe, which at the end of inflation was only about one meter radius. The entire mass of the universe existed inside this small, inflated sphere.

Particles collided with each other so quickly that uniformity prevailed throughout the expansion. The collisions sometimes resulted in energy transfer, other times in the annihilation of the colliding particles and the creation of others. Photons collided with protons, neutrons with electrons, matter with anti-matter.

As the universe expanded, space itself stretched and, in turn, stretched the wavelength of the photons, causing their energy to decrease and the universe to cool. The cooling of the universe is sometimes confusingly attributed to the universe’s expansion from the standpoint that as a gas expands, it cools. But this cause-effect logic doesn’t work. While adiabatic expansion in a piston does lead to cooling, this is caused by the fact that the piston is doing work, thereby meaning that the gas molecules rebound from the retracting piston at a slower rate than when they struck the piston. But there is no such piston at work in the universe. There is no boundary that the universe is expanding against. So why then did the universe cool? The increasing wavelength of photons with increasing expansion of the universe follows from application of Einstein’s General Theory of Relativity. And this naturally begs another question: how does the resulting energy balance work? Where does the energy lost by the photons end up going? It appears that Einstein’s equations are not consistent with the conservation of energy. The actual mechanism by which the stretching of space causes the stretching of photon wavelength is unknown and not currently consistent with the conservation of energy.⁵

The stretching of space caused photon wavelength to increase and energy to decrease. Prior to recombination (when electrons combined with the nuclei), photons and matter existed in thermal equilibrium on account of the high collision frequency between all particles. Matter cooled as photons cooled. However, after recombination, radiation decoupled from matter and the former continued to cool with the expanding universe while the latter continued to cool by other pathways. After 1/10th of a second, the universe stood at 300 billion^oC. After a second, 10 billion^oC. After three minutes, one billion^oC.

After the first three minutes – one billion ^oC and the formation of heavier nuclei

The decreasing temperatures shifted the relative reaction rates between the particles such that at the end of three minutes, mostly photons remained, 1 billion per each nuclear particle. The cooling universe also opened the door for the formation of heavier nuclear particles, starting with the reaction of protons (protium) and neutrons to form deuterium nuclei; the electrons remained unattached in these high temperature conditions (Figure 1.1). The delay of this reaction, which became known as the “deuterium bottleneck,” was caused by the fact that deuterium is not stable at high temperature. After about three minutes, the cooled universe broke open the bottleneck, leading to the production of deuterium and then the subsequent rapid reactions involving deuterium to form the even heavier nuclei of tritium, helium-3 and ordinary helium, helium-4 (He-4). It was these primordial reactions that led to the large abundance of helium in the galaxy.⁶

He-4 was where Big Bang nucleosynthesis hit a roadblock. Everything piled up on a dead-end street with nowhere else to go. Further addition of single protons to He-4 and the reaction of He-4 with itself were both blocked since lithium-5 and beryllium-8 are both unstable. These bottlenecks became known as the “5-particle gap” and the “8-particle gap,” respectively.

So after the first three minutes, the nuclear mass in the universe consisted of about 75% unattached protons (protium), 25% He-4, and a vast sea of photons. Free neutrons no longer existed. With a half-life of only 10 minutes, they could only exist in the early minutes of the universe. Their capture by protons effectively saved these Big Bang neutrons from extinction; additional neutrons would form later from proton-proton reactions inside the stars. Unattached electrons also existed, one for each proton; the universe was still too hot for them to establish orbits around the nuclei.

For the next 300,000 years, the universe continued to expand and cool, little happening in the way of further nuclear reactions as the density of matter was too low. Photons continued to collide with the electrically charged electrons, preventing the formation of atoms (electrons in orbit around nucleus) while also creating an opaque universe due to their resulting scattered lines of travel.

After the first 300,000 years – 3,000^oC and recombination

At 300,000 years a transition occurred. By then the universe had finally cooled enough (3,000^oC) for electrons to stabilize in orbits around the nuclei and thus form hydrogen (protium) and helium (He-4) atoms while also making the universe transparent to light. Since bound electrons do not scatter light like free electrons do, recombination⁸ also made the universe transparent to light. No longer influenced by the presence of the electrically charge electrons, the photons commenced an unimpeded journey through the universe.

At this point in time, the universe was uniform, with photons and the newly formed atoms spread evenly throughout. Well, almost evenly. Small variations in density, on the order of 1 part in 100,000, created the smallest of imperfections, the slightest of wrinkles. And from such small imbalances, atoms started to be pulled more in one direction than the other by the force of gravity.

Slowly, during the ensuing millions of years as the universe continued to expand, atoms found other atoms and clouds formed. Gravity increasingly pulled more and more atoms into the clouds and increasingly pulled the clouds in on themselves, so causing the transformation of potential energy into kinetic energy and the corresponding increase in temperature and pressure. Electrons were stripped off atoms, leaving bare nuclei (packed at much higher density) to start fusing together inside the early stars. Free protons fused together to form deuterium, one of the reactant protons having converted to a neutron in the process, and the resulting deuterium nuclei fused together to form He-4 (Figure 1.1). This “hydrogen burning” process generated tremendous radiant energy and served to push matter outwards, against the inward pull of gravity.⁸ A kind of push-pull, contract-expand balance existed for many more years, with the pull of gravity slowly overtaking the decreasing push of radiation as the hydrogen fuel was consumed, leading to smaller, denser and even hotter stars.

The formation of the elements

The stars are the seat of origin of the elements – Burbidge et al. [9]

The increasing temperature and density inside these early stars (10⁸ degrees and 10⁵ gm/cc) eventually enabled a leap over the 8-particle barrier mentioned earlier. This barrier couldn’t be breached in the early universe since by the time He-4 was created, the density was too low, around that of water, to promote this breakthrough. While He-4 can react to form beryllium-8, consisting of 4 protons and 4 neutrons, this product is very unstable, having a half-life of less than a millionth of a billionth of a second. In the early universe, the fleeting formation of such nuclei led to nothing. However, in the aged universe when dense new stars came into existence, the high-density center ensured that He-4 nuclei were physically close enough to beryllium-8 nuclei to react with them before they had a chance to break apart. The result? Carbon-12. While slow, such “helium burning”¹⁰ when viewed over billions of years was significant.

Once carbon-12 started to form inside the early stars, the floodgates opened and synthesis of the elements began (Figure 1.1). Successive addition of He-4 led to peaked production of oxygen-16, neon-20, magnesium-24, silicon-28 and so on, while successive addition of protons filled in the nuclei between these numbers. The relative rates and concentrations involved in these reactions shifted over time as the composition of the stars shifted over time. The first stars were naturally composed solely of hydrogen and He-4. As the hydrogen exhausted itself by burning to additional He-4, the outward radiation push dropped off, causing the stars to collapse further due to gravity; internal temperatures then rose, triggering the next reaction in line, He-4 to carbon-12. As He-4 then exhausted itself, the stars collapsed even further, reaction conditions became more severe and the next reactions in line were triggered, this time the He-4 addition reactions. The progression of these contractions and reactions were not always as smooth as written here. At times, the speed at which they occurred was such that sudden releases of energy resulted, leading to explosions and sometimes super explosions, especially during the rapid collapse of very massive stars. During such violent events, the contents of the stars spewed back out into the universe, only to be pulled back into other clouds and other stars, starting the whole cycle over again, with one critical exception. Each new generation of stars began with heavier elements contaminating the hydrogen, leading to a different set of element-building reactions. In this way, the temperature and density inside the stars grew over time as progressively heavier nuclei participated in the reactions, all the way up to iron, the most stable of nuclei.

Alongside these reactions was a separate set of reactions. Production of lithium, beryllium and boron was very low as these rare light elements were not primary products of either hydrogen or helium burning processes. Some lithium production occurred during primordial nucleosynthesis but was very limited due to the aforementioned 5-particle barrier. Additional lithium production together with beryllium and boron production resulted from “spallation” reactions in which cosmic rays (mostly protons) struck heavier nuclei such as carbon and oxygen nuclei with so much energy that the nuclei broke apart, generating the light elements. The rarity of these reactions accounts for the relative scarcity of these elements in the universe today. Nuclei heavier than iron (atomic number 26) originated when exploding stars shot neutrons into existing star nuclei, resulting in the formation of elements all the way up to uranium (atomic number 92), the heaviest naturally occurring element.¹¹

Observed elemental population distributions of the universe are consistent with these reactions.¹²

References

[1] Sagan, Carl. 1980. Cosmos. New York: Random House, p. 246.

[2] Guth, Alan H. 1997. The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Reading, Mass.: Perseus Books, p. 176.

[3] Guth, pp. 86, 109, 170, 185.

[4] Guth, p. 186.  If Guth’s theory is indeed correct, then the observed universe is only a “minute spec” in a universe that is many orders of magnitude (10²³ times) larger.

[5] Hawley, John Frederick, and Katherine A. Holcomb. 2005. Foundations of Modern Cosmology. 2nd ed. New York: Oxford University Press. For a good discussion of this topic see Hawley and Holcomb pp. 414-415.  Where does the energy lost by the photons go?  It seems to just disappear, but that is incompatible with energy conservation.  However, we do not currently understand whether the law of conservation of energy applies to the universe as a whole or what a consistent definition of the total energy of the universe might be. Perhaps further research into the nature of space and time will explain this mystery.

[6] Weinberg, Steven. 1993. The First Three Minutes: A Modern View of the Origin of the Universe. Updated ed. New York: Basic Books, p. 113.  “There is, of course, extremely little helium on earth, but that is just because helium atoms are so light and so chemically inert that most of them escaped the earth ages ago.”

[7] While this word is generally used to describe the historical event when electrons entered into orbits about nuclei to establish atoms, it’s a bit of a misnomer as the electrons were not previously in such orbits.

[8] Even though photons are massless, they still carry momentum in their electromagnetic field and can “collide” or otherwise interact with electrons with sufficient force to cause the electrons to recoil, thus resulting in pressure. 

[9] Burbidge, E. Margaret, G. R. Burbidge, William A. Fowler, and F. Hoyle. 1957. “Synthesis of the Elements in Stars.” Reviews of Modern Physics 29 (4), p. 550.

[10] Burbidge et al., p. 550-551.  “Except at catastrophic phases a star possesses a self-governing mechanism in which the temperature is adjusted so that the outflow of energy through the star is balanced by nuclear energy generation… [when] hydrogen becomes exhausted as stellar evolution proceeds, the temperature rises until helium becomes effective as a fuel.  When helium becomes exhausted the temperature rises still further until the next nuclear fuel comes into operation, and so on. The automatic temperature rise is brought about in each case by the conversion of gravitational energy into thermal energy.”

[11] Uranium atom = U-238 = 92 protons + 146 neutrons + 92 electrons.  This is the most common isotope of uranium.  Heavier elements do exist, up to atomic number of 118 (ununoctium) as of 2016, but do not occur naturally.  They are produced in man-made accelerators and are not stable.

[12] For a wonderfully detailed discussion of all the reactions that led to the formation and population of the periodic table, along with the supporting data, read (Burbidge et al., 1957)

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