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The Earliest Epochs, or the Beginning of Everything

Ben Schwennesen

Duke University

Professor Hubert Bray

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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

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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 whered=distance¿ galaxy¿ H=Hubbl e' sconstant=(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

effect applies to objects moving through space, which galaxies are not doing; instead, space

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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

relativity, as t → 0 s, the size of the universe approaches zero, while its temperature and density

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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 higher-

dimensional 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 gcm2/s, & G = 6.67 x 10-8 cm3/(gs2)Then, to find tp, we must combine the constants to obtain seconds units, i.e., c A hBGD=s⟹ ( cm

s )A( g∙ cm2

s )B

( cm3

g ∙ s2 )D

=s .

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The result is a system of linear equations that may be solved using Gaussian elimination to find that A=−5

2, B=1

2, D=1

2⟹ t p=c

−52 h

12 G

12=√ hG

c5 ≈ 10−43 seconds .

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 )= 11+z

⟺ z (a )=1a−1 , T γ (a )=2.7 a−1⟺T γ ( 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∝ t2 /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

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(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 force-

carriers 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

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

Retrieved from: http://www.hep.ucl.ac.uk/theory//unification.png

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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 pre-

inflationary 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

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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−.022+.018),

initial conditions for the

universe where Ω deviates from

one by any amount at all (positive or

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−2 H inf 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

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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.

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Their

reasoning

explains the process of 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 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

(Retrieved from: [6])

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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

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

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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

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

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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

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 ≤ 3min ,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)

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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 → He3 +n→ H

3 + p∧ H3 +d → He

4 +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

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

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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.

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.

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References

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863, 98-103.

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universe-end-in-a-big-slurp-higgs-like-particle-suggests-it-might

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