Download BAS_Paper2_TheEarliestEpochs

Schwennesen 1
The Earliest Epochs, or the Beginning of Everything
Ben Schwennesen
Duke University
Professor Hubert Bray
Schwennesen 2
The Earliest Epochs, or the Beginning of Everything
Why is the Big Bang theory so accepted?
If one was to approach any given person on the streets and ask them to start listing off all
the scientific theories they know of, chances are the Big Bang theory (BBT) would fall early in
the list. Indeed, today the vast majority of astronomers and astrophysicists believe that the Big
Bang model must reflect how the earliest knowable moments of the universe occurred [0, p.
219], which has led to an assimilation of some of its core concepts into popular culture. Though
“in the beginning there was nothing, then it exploded” is a description of BBT that would make
plenty of astrophysicists cringe (since, in order for something to explode, there must be space
into which it can do so), at least oversimplifications of this sort allow the complexities of the
theory to be expressed in a way that lay-folk can recall. Still, though most people will have some
conception of what the Big Bang describes, those who know why the theory is so successful and
popular are few and far between.
There is a wealth of observational evidence that has led the Big Bang model (or more
realistically models) of the universe to become so commonplace. Three key aspects of the
universe that become much less difficult to explain with BBT are the relative abundances of the
light elements in the universe, the Hubble expansion, and the startling uniformity observed in the
cosmic microwave background (CMB) radiation that pervades the universe [0, pg. 239]. Though
one does not need BBT to explain these phenomena, no alternative explanation with comparable
simplicity, generalizability, and elegance has yet emerged [0, pg. 219].
Hubble’s Law, Red Shift, and Accelerating Expansion
Edwin P. Hubble (1889 – 1953) is considered one of the great cosmologists of history for
his discovery made in 1929 at Mount Wilson (near Los Angeles) using its 100 in. diameter
Schwennesen 3
reflecting telescope: not only did Hubble find that light from distant galaxies was systematically
shifted towards red wavelengths (as compared to light from closer galaxies), the relationship
between magnitude of red shift and the galaxy’s distance was directly proportional [0, pg. 220]:
𝑟𝑒𝑑 𝑠ℎ𝑖𝑓𝑡,
𝑧 = 𝐻𝑑
𝑤ℎ𝑒𝑟𝑒 𝑑 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑜 𝑔𝑎𝑙𝑎𝑥𝑦
& 𝐻 = 𝐻𝑢𝑏𝑏𝑙𝑒 ′ 𝑠 "𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡" = (67 ± 1.2) 𝑘𝑚 𝑠 −1 𝑀𝑝𝑐 −1
(see http://arxiv.org/pdf/1303.5062v2.pdf, pg. 38, for most recent derivation of Hubble
constant’s value). (Note: the value of H is not actually constant, but varies with the scale of the
universe.) The relationship that Hubble (and perhaps more accurately others) inferred provided
an explanation for an issue in general relativity that Einstein struggled to reconcile; when applied
to the universe as a whole general relativity seems to imply that the universe cannot be static—
there must be either expansion or contraction [0, pg. 225]. Thoroughly-instilled dogma of the
time, however, held that the universe was in an overall steady state, and so Einstein added a
“cosmological constant” (Λ) to his field equations to accommodate a static universe. With the
acceptance of Hubble expansion by the scientific community, Einstein eliminated the term from
his equations; much later, the discovery that the universe’s expansion was accelerating due to
some “dark energy” led to a reintroduction of the cosmological constant. Thus, even when
Einstein was wrong, he was right. That said, credit for proving that general relativity must result
in a dynamic universe is owed to Alexander Friedmann, not Einstein himself [0, pg. 225].
Hubble’s law is often explained as a form of the Doppler effect, in which the sound from
an object moving away from an observer is shifted downwards in frequency (and vice versa; an
example is to imagine the sound of an ambulance as it passes). Such an explanation is
confusing, however, for though one certainly may observe genuine Doppler effects in light from
distant bodies, the Hubble shift is not among them [0, pg. 228]. This is because the Doppler
Schwennesen 4
effect applies to objects moving through space, which galaxies are not doing; instead, space itself
stretches between the galaxies, in-turn stretching (red shifting) the wavelength of travelling light
along with it. Still, it can be fruitful to calculate the apparent velocity of receding galaxies, as
such calculations help to approximate the rate of expansion of the universe, as well as its age [0,
pg. 229].
Production of the Light Elements
Elements heavier than helium are mere trace constituents of the universe as we observe it
today; together, hydrogen, deuterium (hydrogen’s heavy isotope), and helium make up nearly
100% of the universe, with approximate relative quantities of 75% hydrogen and deuterium and
25% helium [1, pg. 99]. In 1957, it was demonstrated that atoms heavier than helium were
almost certainly built up exclusively by nuclear fusion in stars’ cores and violent supernova
explosions [0, pg. 222]. The abundance of helium, however, cannot be explained in this manner
since (i) the amount of helium observed in stars does not correlate with their ages and (ii) the
conversion of hydrogen into helium releases so much energy (consider the H-bomb) that buildup
of 25% helium in the universe would cause stars to shine far brighter than they do in reality [0,
pg. 222]. The nucleosynthesis phase of the Big Bang explains helium’s abundance, providing
one of the most crucial experimental verifications of BBT to date [0, pg. 237].
The Planck Epoch (𝟎 𝒔 < 𝒕 ≤ 𝟏𝟎−𝟒𝟑 𝒔, 𝑻 ≥ 𝟏𝟎𝟒𝟎 𝑲)
Though physicists often describe “extrapolating backwards” to a point of infinite
temperature and density when explaining the Big Bang (and this is the reality of the mathematics
at work), for the purpose of comprehension working forwards from t → 0 seconds is preferable.
The time interval 0 𝑠 < 𝑡 ≤ 10−43 𝑠 is commonly referred to as the Planck epoch, though some
(not inaccurately) deem it the “epoch of ignorance” [10; 0, pg. 234]. Using classical general
Schwennesen 5
relativity, as t → 0 s, the size of the universe approaches zero, while its temperature and density
both approach infinity [1, pg. 99]. That is, backwards extrapolation through time using GR
results in an apparent singularity 13.8 billion years ago; though this may seem almost elegant, to
physicists it represents a huge flaw: the story of our universe beginning in a singularity causes
the laws of physics to break down entirely [10]. There is a good reason that physicists today will
not make strong claims about what specifically occurred during the Planck epoch (at least not if
they wish to be taken seriously); the two indispensable theories of modern physics, general
relativity (GR) and quantum mechanics, could be said to have a deep mutual animosity. In the
everyday experience of humanity, such an “animosity” is not important, since GR and quantum
physics tend to apply individually to their respective domains; during the Planck epoch,
however, one needs both theories, since the universe was simultaneously expanding (requiring
GR) and extremely hot and dense (requiring QM) [1, pg. 98]. The union of the two theories is
usually called quantum gravity, and one may describe physicists as being not even somewhat
close to unraveling its mysteries (though not for lack of effort). Barring the existence of higherdimensional branes (present in string theory and its offshoots) that would circumvent quantum
gravity, its effects would dominate particle interactions over a time-scale known as the Planck
time (tp). The calculation of tp using dimensional analysis is not exceptionally difficult [10]:
Let c be the speed of light (relativistic effects), h be Planck’s constant (quantum effects),
and G be the universal gravitation constant, i.e.,
c = 3 x 1010 cm/s, h = 6.63 x 10-27 gcm2/s,
& G = 6.67 x 10-8 cm3/(gs2)
Then, to find tp, we must combine the constants to obtain seconds units, i.e.,
𝐵
𝐷
𝑐𝑚 𝐴 𝑔 ∙ 𝑐𝑚2
𝑐𝑚3
𝑐 ℎ 𝐺 =𝑠⟹( ) (
) (
) = 𝑠.
𝑠
𝑠
𝑔 ∙ 𝑠2
𝐴 𝐵
𝐷
Schwennesen 6
The result is a system of linear equations that may be solved using Gaussian elimination
to find that
5 1 1
5
1
1
ℎ𝐺
𝐴 = − ,𝐵 = ,𝐷 =
⟹ 𝑡𝑝 = 𝑐 −2 ℎ2 𝐺 2 = √ 5 ≈ 10−43 𝑠𝑒𝑐𝑜𝑛𝑑𝑠.
2
2
2
𝑐
Aside on Useful Quantities
There are a number of physical quantities which change monotonically (i.e. increase OR
decrease; no points of inflection) throughout the history of the universe, making such quantities
useful in tracking its state throughout the various epochs. These quantities are: the age of the
universe t, scale factor (dimensionless function of time representing the state of the universe’s
expansion) a, redshift (as measured today) z, and the temperature of the CMB radiation Tγ (today
approximately 2.7 Kelvin) [10]. These quantities are strongly inter-related by the formulas [10]
𝑎(𝑧) =
1
1
⟺ 𝑧(𝑎) = − 1,
1+𝑧
𝑎
𝑇𝛾 (𝑎) = 2.7𝑎−1 ⟺ 𝑇𝛾 (𝑧) = 2.7(𝑧 + 1).
The general relationships of the quantities to the age of the universe t involves far more rigorous
calculations, but it is generally sufficient to understand that in a radiation-dominated universe,
𝑎 ∝ 𝑡1/2 (i.e., age scales as the square of scale factor a), while in a matter-dominated universe
𝑎 ∝ 𝑡 2/3 [0, pg. 233].
For our purposes, the most important factors are t and Tγ (which we will now simply
denote by T); the universe’s age is relevant for obvious reasons, and temperature is a highly
useful quantity for various reasons. Here, we will primarily use the temperature of the universe
to know when the threshold temperature of various particle species are exceeded, i.e., the
temperature at which a given particle may exist independently without rapidly decaying out of
existence. Such measures are only meaningful because the particles within the universe remain
in thermodynamic equilibrium, otherwise their average kinetic energy would not be constant
Schwennesen 7
(meaning T would be indeterminate) [0, pg. 231]. Temperatures in the Planck epoch were (at
least) a staggering 1040 K [10].
The Grand Unification Epoch (𝟏𝟎−𝟒𝟑 𝒔 ≤ 𝒕 ≤ 𝟏𝟎−𝟑𝟔 𝒔, 𝟏𝟎𝟑𝟔 𝑲 ≤ 𝑻 ≤ 𝟏𝟎𝟒𝟎 𝑲)
If supersymmetry turned out to be correct, during the Planck epoch all four fundamental
forces were unified under the regime of quantum gravity [10]. At the end of this era, however,
the universe had cooled and expanded enough for gravity to decouple from the other three
fundamental forces, the strong and weak nuclear forces and electromagnetism [0, pg. 234].
According to Grand Unification Theories (GUTs, of which there exist many in competition),
these three forces remained unified as a single force, sometimes referred to as the electronuclear
force (or the GUT force) [10; 0, pg. 234]. Temperatures at the time exceeded the threshold for
the hypothetical X & Y bosons (and their antiparticles, 𝑋 & 𝑌), which are the would-be forcecarriers for the electronuclear force. As a result, the universe contains quarks, leptons, and all
force-carrying particles. Throughout
the epoch, the GUT interaction is
suspected to maintain equal amounts
of quarks, antiquarks, leptons, and
antileptons; once T drops below the X
& Y particles’ threshold, however,
annihilations and decays quickly
cause these particles to vanish from the
Retrieved from: http://www.hep.ucl.ac.uk/theory//unification.png
universe. A crucial prediction of GUTs is that their decay results in a small excess of quarks
over antiquarks, to the tune of 109+1 quarks for every 109 antiquarks [0, pg. 234]. Though this
Schwennesen 8
excess may seem negligible, were it (or a similar excess) not there, matter and antimatter would
have annihilated completely and the universe would have been an expanding void of radiation.
During this era, physical characteristics like mass and charge were effectively meaningless.
Towards the end of the epoch, the strong interaction “freezes out” of the electronuclear force,
leaving what is known as the electroweak force [10].
Inflationary Epoch (𝟏𝟎−𝟑𝟔 𝒔 ≤ 𝒕 ≤ 𝟏𝟎−𝟑𝟐 𝒔, 𝟏𝟎𝟑𝟑 𝑲 ≤ 𝑻 ≤ 𝟏𝟎𝟑𝟔 𝑲)
As successful as the Big Bang theory has been, a number of very serious issues have been
raised which it alone could not explain. These issues include, interestingly enough, one of the
three essential pieces of evidence for why BBT has become so accepted: the overall uniformity
and isotropy (uniformity in all direction) observed in the cosmic background radiation. To solve
the issue (sometimes called the horizon problem), one requires an extension of BBT known as
inflation. The horizon problem was so vexing to physicists because the intensity of the CMB
(when corrected for the motion of the Earth) is the same in all directions to the startling precision
of “one part in 100,000” [5, pg. 2]. The CMB was released about 380,000 years after the Big
Bang, and its uniformity suggests that the universe’s temperature had become uniform, too, at
that time. In order for such a uniformity in temperature to occur in that time span, in preinflationary Big Bang models, information would need to propagate at 100 times the speed of
light, a clear contradiction of the established laws of nature. In the context of inflation, however,
there needs not be faster-than-light diffusion of particles: the uniformity is established at
microscopic scales by standard thermal equilibrium processes, then being scaled to a much larger
region of near-perfect uniformity by the rapid acceleration of expansion [5, pg. 3].
A second issue resolved by inflation, considered by some to be even more impressive
than the first due to the numbers involved, is called the flatness problem. The problem concerns
Schwennesen 9
the ratio of the universe’s average total mass density to the critical mass density that would make
the universe spatially flat (exactly 3H2/8πG). If this ratio (which we’ll denote as Ω) was exactly
one, it would remain so forever
[5, pg. 3]. Though the current
value of Ω is one to within only
a few percent (Ω = 1.012+.018
−.022 ),
initial conditions for the
universe where Ω deviates from
one by any amount at all (positive or
Retrieved from: https://apatruno.files.wordpress.com/2014/03/f1-large1.jpg
negative) results in amplification of that deviation over time, so we can infer that the value of Ω
in our universe’s very early history must have been dramatically close to one (at tp = 10-43s, Ω
must have been equal to one to 59 decimal places) [5, pg. 4]. While such incredible flatness has
no explanation in pre-inflationary Big Bang models, inflation naturally predicts it. During the
epoch of inflation, Ω is actually driven closer to one with exponential swiftness: Ω − l ∝
𝑒 −2𝐻𝑖𝑛𝑓 𝑡 , where Hinf is the value(s) of the Hubble parameter (“constant”) during inflation. So,
inflation implies that the initial value of Ω is essentially irrelevant; exponential expansion will
always drive it to approach unity [5, pg. 4].
There are a number of other issues that inflation addresses, including the absence of
magnetic monopoles from the universe and the slight anisotropy of the CMB. The latter issue
refers to the fact that though the CMB is incredibly uniform on large-scales, there remains
enough variation in different directions (anisotropy) to seed the formation of structures like
galaxy clusters. Though the exponential expansion during inflation indeed smoothens the
universe to almost perfect uniformity, the necessary density fluctuations are produced towards
Schwennesen 10
the end of inflation by quantum fluctuations in the “inflaton field” [5, pg. 4]. The inflaton is a
scalar field that is theorized to be a product of a phase transition (of somewhat ambiguous
nature) that occurred at the end of the Grand Unification epoch [10]. As the inflaton progressed
into its lowest energy state, it created a massive repulsive force that streched the fabric of
spacetime with exponential rapidity. Eventually, the inflaton field could no longer remain stable,
at which point its huge potential energy was released as a hot, dense sea of quarks, antiquarks,
and gluons, known as the quark-gluon plasma (QGP). Since the expansion of the inflaton field
red shifted all previously-existing matter to extremely low densities, without this conversion of
the inflaton’s energy (a process known as reheating), the universe would be devoid of matter
entirely [10].
The exact cause of the exponential expansion described by inflation remains unknown;
some physicists believe, however, that it may be explained by eternal inflation, in which it is
hypothesized that speaking of a time “after inflation” may be unwarranted, since (in at least some
parts of the universe/multiverse) there is no necessary reason to assume inflation ever halts.
Their reasoning explains the process of
(Retrieved from: [6])
inflation as a result of a “false vacuum,” a
metastable state that appears to be a true
vacuum (of the lowest possible energy state),
but in reality has a lower energy state that may
be reached through quantum tunneling, likely
initiated by quantum fluctuations [5, pg. 6; Figure 3 retrieved from this page]. When the false
vacuum eventually decays into its lower energy state, a bubble of true vacuum rapidly expands to
Schwennesen 11
encompass the entire universe. Any
successful theory of inflation with the false
vacuum describes that its rate of expansion
is much faster than its rate of decay, and
therefore even though the false vacuum
continually decays, it may never shrink in
volume. The implication of this is that the
false vacuum continually births local universes, while still expanding itself ad infinitum [5, pg.
6]. That is, the process repeats literally forever, producing an infinite number of non-interacting
universes (a multiverse), typically hypothesized to form an elegant fractal structure of pocket
universes [5, pg. 7].
Should this theory of inflation prove correct, the implications for our universe could be
troubling. This is because the mass of the Higgs boson measured by CERN, about 125 GeV,
implies that the universe remains in a state of metastability, and so, “without warning, a bubble
of true vacuum could nucleate somewhere in the universe and move outwards at the speed of
light,” the end result of which would be the end of the universe as we know it [2]. Though
researchers have calculated that the time before such a decay would occur in our observable
universe would be far longer than its current age, it turns out that intense gravitational fields, like
those found around black holes, could serve as seeds for nucleation of the true vacuum [6].
Luckily, tunneling into a true vacuum bubble is only likely around black holes with very large
curvature at the horizon, i.e., around very small black holes. Since the black holes discovered
thus far tend to be massive and growing via accretion of mass, it is unlikely that such a small
Schwennesen 12
black hole will cause the erasure of the universe anytime soon (barring the existence of
primordial black holes) [6].
Though eternal inflation could prophesize the end of our universe, it would be at least
tens of billions of years before humans need to worry about the approaching bubble of true
vacuum [2]. Furthermore, other researches have cast doubts on the mathematical validity of
eternal inflation [7], and alternative theories to explain the accelerated era of expansion are
proposed frequently [see 8, for example]. Regardless, today most physicists believe that the
evidence for inflation is so overwhelming that something like it must have happened. Overall,
calculations indicate that the linear dimensions of the universe must have increased by at least a
factor of 1026 (potentially much larger), and in-turn must have increased in volume by at least a
factor of 1078; this is very difficult to explain without some form of inflation [10].
Electroweak Epoch (𝟏𝟎−𝟑𝟐 𝒔 ≤ 𝒕 ≤ 𝟏𝟎−𝟏𝟐 𝒔, 𝟏𝟎𝟐𝟎 𝑲 ≤ 𝑻 ≤ 𝟏𝟎𝟑𝟑 𝑲)
By the end of inflation, the strong nuclear force had separated completely from the
electroweak force (the merger of electromagnetism and the weak force). This electroweak force
is far less speculative than the electronuclear force of GUTs, since the temperatures at which it
exists (≈ 100 𝐺𝑒𝑉 ≈ 1015 𝐾) may be reproduced in particle accelerators [10]. The exact
temperature reflects the threshold of the W and Z bosons that mediate the weak interaction [0,
pg. 234]. During this era, quarks and antiquarks existed at such close proximities that the strong
force (which, we recall, is stronger over longer ranges) was unable to bind them into hadrons, at
least not without being instantly blasted apart by high energy photon collisions.
Quark Epoch (𝟏𝟎−𝟏𝟐 𝒔 ≤ 𝒕 ≤ 𝟏𝟎−𝟔 𝒔, 𝟏𝟎𝟏𝟔 𝑲 ≤ 𝑻 ≤ 𝟏𝟎𝟐𝟎 𝑲)
At the end of the electroweak era, the fundamental interactions had finally all taken on
their present forms, but the temperature of the universe remained too high to allow quarks to
Schwennesen 13
bind into mesons or baryons; the universe remained filled with a quark-gluon plasma, now
containing quarks, gluons, and leptons. Approaching the end of this era (about 10-6 seconds after
t = 0), the average energy of interactions between particles fell below the the binding energy of
hadrons, and so quarks became permanently confined within protons, neutrons, and other
hadrons, in a process known as baryogenesis [10; 1, pg. 99]. The small excess of quarks over
antiquarks left behind by Grand Unification is now manifest in a small excess of protons and
neutrons over their antimatter foils [0, pg. 234].
Hadron Epoch (𝟏𝟎−𝟔 𝒔 ≤ 𝒕 ≤ 𝟏 𝒔, 𝟏𝟎𝟏𝟐 𝑲 ≤ 𝑻 ≤ 𝟏𝟎𝟏𝟔 𝑲)
In the era known as the Hadron epoch, the mass of universe was dominated by hadrons;
initially, the temperature in this interval was high enough to allow the formation of hadron/
antihadron pairs [10], which kept matter and antimatter in thermal equilibrium via the following
reactions (where p = proton, n = neutron,  = photon, and bars ind. antiparticles) [0, pg. 235]:
𝑝 + 𝑝 ⇋ 𝛾 + 𝛾, 𝑛 + 𝑛 ⇋ 𝛾 + 𝛾.
However, once the universe dropped below about 1013 K (~ t = 7 x 10-7 s), temperatures were
below the threshold of protons and neutrons, and so these particles ceased to be a major
independent constituent of the universe. Generally, protons and neutrons annihilated with
antiprotons and antineutrons, leaving only a single proton for every 109 photons in the universe,
a number which agrees with current measurements and predictions from GUTs [0, pg. 235]. The
remaining protons and neutrons were kept in thermal equilibrium with the universe on the whole
by the neutrino reactions [0, pg. 235]:
𝑝 + 𝜐𝑒 ⇋ 𝑛 + 𝑒 + , 𝑛 + 𝜐𝑒 ⇋ 𝑝 + 𝑒 − .
These reactions occurred in such a way that (due to the slight mass difference between protons
and neutrons) neutrons were gradually converted into protons as the universe aged. At 10-5
Schwennesen 14
seconds, the temperature drops below the threshold of pions and muons, and so these more
exotic particles cease being a significant presence in the universe [0, pg. 235].
Lepton Epoch (𝟏 𝒔 ≤ 𝒕 ≤ 𝟑 𝒎𝒊𝒏, 𝟏𝟎𝟏𝟏 𝑲 ≤ 𝑻 ≤ 𝟏𝟎𝟏𝟐 𝑲)
This seems an appropriate time to contemplate the fact the only one second has passed
since the beginning of everything. At 1.09 seconds, the temperature and density of the universe
have dropped low enough that neutrinos no longer have enough energy to interact with matter
regularly; from this moment on they decouple from the universe (they DO NOT disappear, but
interact so infrequently as to be a hardly detectable background actor of the universe) [0, pg.
236]. Without neutrino interactions, there is no process to keep protons and neutrons in thermal
equilibrium; the ratio of protons and neutrons (p/n) at the moment of decoupling was about
82/18. This ratio would increase with time, due to the decay of free neutrons [0, pg. 236]. At
approximately 100 seconds (~ T = 1010 K), electrons and positrons annihilate [10], leaving a
small excess of e- due to the inequality established in the GUT epoch. The remaining electrons
maintain thermal equilibrium with photons since they are free charges (and hence readily partake
in interactions with electromagnetic radiation) [0, pg. 236].
Epoch of Nucleosynthesis (𝟑 𝒎𝒊𝒏 ≤ 𝒕 ≤ 𝟏𝟑 𝒎𝒊𝒏, 𝟏𝟎𝟗 𝑲 ≤ 𝑻 ≤ 𝟏𝟎𝟏𝟏 𝑲)
About 3.2 minutes after the Big Bang, the temperature is low enough for the first
deuterium to form without being blasted apart by photons. This marks the start of the process of
nucleosynthesis, wherein helium is formed from deuterium by nuclear reactions [0, pg. 236]:
𝑑 + 𝑑 → 3𝐻𝑒 + 𝑛 → 3𝐻 + 𝑝
&
3
𝐻 + 𝑑 → 4𝐻𝑒 + 𝑛.
Since 4He is the most stable of all nuclei, the process ceases here. The production of helium via
nucleosynthesis bounds all the free neutrons in the universe into nuclei, allowing the strong
interaction to cease further decay of neutrons. By this time, the p/n ratio has been shifted to
Schwennesen 15
about 87/13. Thus, since for every 200 particles, 26 neutrons and 26 protons will combine into
13 helium nuclei, we are left with 148 protons to form other elements, implying the mass ratio of
nuclei produced to be
4(13)⁄
200 = 26%, which accounts almost perfectly for the observed
proportion of helium in the universe [0, pg. 237]. As asserted earlier, this is among the key
experimental confirmations of Big Bang theory. Nucleosynthesis ceases at about t = 13 minutes,
when temperatures become too cool to sustain nuclear reactions.
Epoch of Recombination (𝒕 ≈ 𝟑𝟖𝟎, 𝟎𝟎𝟎 𝒚𝒆𝒂𝒓𝒔, 𝑻 ≈ 𝟑𝟎𝟎𝟎 𝑲)
Relatively little of interest happens between the era of nucleosynthesis and the next
crucial epoch of the early universe. That next (and final, for our purposes) epoch, that of
recombination, occurred simultaneously with the density of matter first exceeding the density of
radiation [0, pg. 237]. Prior to recombination, the energy of photons in the universe was high
enough to ionize any hydrogen atoms that managed to form, such that free electrons were
prolific. Recombination occurred when photons’ energies dropped low enough for electrons to
readily combine with protons into neutral hydrogen atoms. Since free electrical charges are now
rare, photons have nothing left to interact with and decouple from the matter of the universe. At
this point, the universe can be said to become transparent: prior to recombination, Thomson
scattering of photons by electrons occurred so frequently that the universe was practically
opaque [0, pg. 237]. The moment of recombination is fascinating for many reasons, most
prominently because photons are allowed to travel freely after it (albeit travel while being
drastically red shifted); therefore, the earliest light observed in the universe by humans, the
cosmic microwave background, was released precisely at the moment of recombination.
Schwennesen 16
Conclusion: Pragmatism and the Big Bang theory
The works of many great artists, perhaps most memorable those of Vincent van Gogh, are
often overlooked (or even downright mocked) during the artist’s life. This phenomenon can
serve as an analogy to the research physicists perform into very early phases of the universe: the
scientists at CERN may not know exactly what practical applications will emerge from their
work on high-energy particle collisions, but the proposition that nothing useful will come of it is
naïve. Throughout history, ideas in science and mathematics have tended to emerge prior to
humanity’s understanding of how to utilize them fully (for example, quantum mechanics may
have seemed too “spooky” to be useful when it was discovered, but nowadays quantum
computation could allow humans to solve optimization problems that would take classical
computers longer than the life of the universe to perform). Some may say particle physicists are
bogged down in a realm of abstraction that has no guarantee of aiding humanity in a tangible
way; perhaps such criticism is not unfounded, but even if no practical applications emerged,
knowledge of how the universe emerged would seem indispensable to eventually addressing why
our universe exists in the way it does, and how it might one day come to a close.
Schwennesen 17
References
[0] Allday, J. (1998). Quarks, Leptons, and the Big Bang. Bristol: Institute of Physics Pub.
[1] Bojowald, M. (2011). Quantum gravity in the very early universe. Nuclear Physics A, 862863, 98-103.
[2] Boyle, A. (n.d.). Will our universe end in a 'big slurp'? Higgs-like particle suggests it might.
Retrieved from http://cosmiclog.nbcnews.com/_news/2013/02/18/17006552-will-ouruniverse-end-in-a-big-slurp-higgs-like-particle-suggests-it-might
[3] Eisenstein, D. (n.d.). Baryon Acoustic Oscillations. Retrieved from
http://scholar.harvard.edu/deisenstein/book/baryon-acoustic-oscillations
[4] Ellis, J. (2006). From Little Bangs to the Big Bang. J. Phys.: Conf. Ser. Journal of Physics:
Conference Series, 50, 8-21.
[5] Guth, A. H. (2007). Eternal inflation and its implications. Journal of Physics A:
Mathematical and Theoretical J. Phys. A: Math. Theor.,40(25), 6811-6826.
[6] Hossenfelder, S. (2015, April 02). Could Black Holes Destroy the Universe? Retrieved from
https://medium.com/starts-with-a-bang/could-black-holes-destroy-the-universede8a3135856f#.d4vw3aqlt
[7] Kohli, I. S., & Haslam, M. C. (2015). Mathematical issues in eternal inflation. Class.
Quantum Grav. Classical and Quantum Gravity, 32(7).
Schwennesen 18
[8] Sivaram, C., & Kenath, A. (2011). Enigmatic aspects of the early universe: Possibility of a
‘pre-big bang phase’! Astrophys Space Sci Astrophysics and Space Science, 333(1), 9-10.
[9] Smoot, G. F., Gorenstein, M. V., & Muller, R. A. (1977). Detection of Anisotropy in the
Cosmic Blackbody Radiation. Phys. Rev. Lett. Physical Review Letters, 39(14), 898-901.
[10] Terzić, B. (Spring 2008). History of the Very Early Universe. Lecture. Retrieved from
http://www.nicadd.niu.edu/~bterzic/PHYS652/Lecture_13.pdf