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Ay 127, Winter 2017:
The Early Universe
TheKeyIdeas
•  Pushingbackwardin5metowardstheBigBang,theuniversewas
ho<eranddenserinafairlypredictablemanner(asidefrom
surprising“glitches”suchastheinfla5on…)
•  Atanygiven5me,thetemperaturetranslatesintoacharacteris5c
massofpar5cles,whichdominatethatepoch:theUniverseas
theul5mateaccelerator?
•  Astheenergiesincrease,differentphysicalregimesanddifferent
fundamentalinterac5onscomeintoplay
•  ThecloserwegettotheBigBang(i.e.,furtherawayfromthe
experimentallyprobedregime),thelesscertainthephysics:the
earlyUniverseasthelaboratoryofphysicsbeyondthestandard
model?
•  Ourextrapola5onsmustbreakdownbytheepochof~10-43sec
~Plack5me,wherequantumgravitymustbeimportant
TheCosmicThermalHistory
… on a logarithmic time axis - a theorist’s delight!
The
Planck
Era
(from M. Turner)
AnotherSchema5cOutline:
SomeKeyMoments
intheThermalHistoryoftheUniverse:
•  Planckera,t~10-43sec:quantumgravity,…???…
•  Infla5on,t~10-33sec:vacuumphasetransi5on,exponen5al
expansion
•  GrandUnifica5on,t~10-32sec:strongandelectroweak
interac5onssplit
•  Baryogenesis,t~10-6sec:quark-hadrontransi5on
•  Nucleosynthesis,t~1msto3min:D,He,Li,Beform
•  Radia5ontomaFerdominancetransi5on,t~105yr:structure
beginstoform
•  Recombina5on,t~380,000yr:hydrogenbecomesneutral,
CMBRreleased,darkagesbegin
•  Reioniza5on,t~0.3-1Gyr:firstgalaxiesandQSOsreionizethe
universe,thecosmicrenaissance
ThermalHistoryoftheEarlyUniverse
Age
Temperature
Processes
t < 10-10 s
T > 1015 K GUT
10-10 < t <10-4 s 1015>T>1012K e+, e-,quarks,γ,ν
n, p
t ~ 10-4 s
T ~ 1012K Quarks->
+ −
10
-10
-4
12
10
µ µ > νµ,νµ
e+, e-, n, p, γ,νe
< t <10 s 10 >T>10 K
t ~ 0.01 s
T ~ 1011K assymetry in n, p
t~4s
T ~ 5x109K e+, e-−> νe,νe
t ~ 100 s
t ~ 1011 s
t ~ 1013 s
4
n->p+e-+νe
nucleosynthesis
T ~ 10 K
T ~ 16 500 K Matter
domination
T ~ 3000 K Decoupling
EmpiricalEvidence
•  TheCMBR:probestherecombina5onera,t~105yr,z~1100,
basedonawellunderstoodatomicandmacroscopicphysics
•  Nucleosynthesis:probesthet~10-3-102secera,z~109,
comparethemodelpredic5onswithobservedabundancesof
thelightestelements,basedonawellunderstoodnuclear
physics
•  MaFer-an5maFerasymmetry:probesthebaryogenesisera,
t~10-6sec,z~1012,butonlyinsugges5ngthatsomesymmetry
breakingdidoccur
•  Predic5onsoftheinfla5onaryscenario:flatness,uniformityof
CMBR,absenceofmonopoles,therighttypeofdensity
fluctua5onspectrum-itallsupportstheideathatinfla5ondid
happen,butdoesnotsayalotaboutitsdetailedphysics
•  Cosmologicalobserva5onscanindicateorconstrainphysics
welloutsidethereachoflaboratoryexperiments
CMBRandtheRecombina5onEra
Prediction of CMB is trivial in Hot Big Bang model:
•  Hot, ionised initial state should produce thermal radiation
•  Photons decouple when universe stops being ionised (last
scattering)
•  Expansion by factor a cools a
blackbody spectrum from T to T/a
•  Therefore we should now see
a cool blackbody background
–  Alpher and Herman, 1949,
“A temperature now of the order
of 5 K”
–  Dicke et al., 1965, “<40 K”
•  note that the Gamow, Alpher
& Herman prediction had been
nearly forgotten at this time!
TheCMBRDisoveries
Firstseenin1941(yes,1941!)
•  Linesseeninstellarspectra
iden5fiedasinterstellarCHand
CN(AndrewMcKellar,theory;
WalterAdams,spectroscopy)
•  Comparisonoflinesfrom
differentrota5onalstatesgave
“rota5onaltemperature”of2-3K
CH
CN
•  Unfortunately Gamow et al. did not have known about this
•  Hoyle made the connection in 1950:
"[the Big Bang model] would lead to a temperature of the radiation at
present maintained throughout the whole of space much greater than
McKellar's determination for some regions within the Galaxy."
•  So, Penzias & Wilson made the recognized discovery in 1964
DiscoveryoftheCosmicMicrowave
Background(CMBR):ADirectEvidence
fortheBigBang
Arno Penzias &
Robert Wilson (1965)
Nobel Prize, 1978
TheCMBRSpectrum:
ANearlyPerfectBlackbody
Residuals from the BB
strongly limit possible
energy injection (e.g., from
hypothetical decaying DM
particles) during and after
the recombination - no new
physics here…
TemperatureofRecombina5on
Mean photon energy:
E ~ 3k BT
E = 13.6 eV
13.6 eV
Photoionisation Temperature: T =
= 50000K
3k B
Ionisation energy of H:
But there are many more photons than H ions:
9
nγ ≈ 10 n p
Thus, the T can be lower and have enough photons with high
enough energies to ionize H!
&
#
−
E
nγ (> E ) ∝ exp$
Boltzmann distribution:
k T!
So the actual T of recombination is:
And thus, zrec
~ 1100
%
B
"
13.6 eV
T=
= 2500K
3k B 9 ln (10 )
TheExtentofRecombina5on
This phase transition (ionized
to neutral gas) has a finite
thickness: most of the plasma
recombines before the last
scattering, which is the CMBR
photosphere we see
IntotheNucleosynthesisEra
•  Inthepre-nucleosynthesisuniverse,theradia5onproduces
pairsofelectronsandpositrons,aswellasprotonsand
an5protons,neutronsandan5neutrons,andtheycan
annihilate;e+e-reac5onsproduceelectronneutrinos(νe)and
an5neutrinos:
e-+e+←→νe+νe
e-+p←→n+νe,νe+p←→n+e+
n←→p+e-+νe
e-+e+←→γ+γ
•  Thisoccursun5lthetemperaturedropstoT~1010K,t~1sec
•  Inequilibriumtherewillslightlymoreprotonsthanneutrons
sincetheneutronmassisslightly(1.293MeV)larger
•  Thisleadstoanasymmetrybetweenprotonsandneutrons…
AsymmetryinNeutron/ProtonRa5o
Mass difference between n and p causes
an asymmetry via reactions:
n +ν e ↔ p + e−
n + e+ ↔ p +ν e
It is slightly easier (requires less energy)
to produce p than n:
n → p + e− +ν e
p → n + e+ +ν e
Thus, once e+, e- annihilation occurs only neutrons can decay
We can calculate the equilibrium ratio of n to p via the
Boltzmann equation,
Nn
⎛
t ⎞
Xn =
~ 0.16 exp⎜ −
⎟
Nn + N p
⎝ 1013s ⎠
at T~ 1012 K, n/p = 0.985
The n/p ratio is “frozen” at the value it had at when T= 1010 K ,
n/p = 0.223, i.e., for every 1000 protons, there are 223 neutrons
BigBangNucleosynthesis(BBNS)
Free neutrons are unstable to beta decay, with mean lifetime = 886
sec, n → p + e- + νe . This destroys ~ 25% of them, before
they can combine with the protons
2
When the temperature drops to ~ 109 K
(t=230s), neutrons and protons combine
to form deuterium, and then helium:
Note that these are not the same reactions
as in stars (the pp chain)!
n + p↔ H + γ
2
H + 2H ↔ 3He + n
3
3
He + n ↔ 3H + p
H + 2H ↔ 4He + n
Photons break the newly created nuclei, but as the temperature
drops, the photodissociation stops
At t ~ 103 sec and T < 3Í108 K, the density also becomes too
low for fusion, and BBN ends. This is another “freeze-out”, as
no new nuclei are created and none are destroyed
The actual reactions network
is a tad more complicated…
But the simplified version is pretty
close, and conveys the important
parts of the story
StableMassGapsinthePeriodicTable
9Be
7Li
6Li
4He
3He
2H
No stable nuclei
1H
Since there are no stable mass-5 nuclides, combining He and
tritium to get Li requires overcoming the Coulomb repulsion.
So almost all of the neutrons end up in He instead!
There is another gap at mass-8, so BBN ends with Li, with
only trace amounts of Be produced
TheEvolu5onofAbundancesinBBNS
BigBangNucleosynthesisEnd
At this point n/p ratio has dropped to ~ 0.14. The excess protons
account for about 75% of the total mass, and since essentially all
neutrons are incorporated into He nuclei, the predicted primordial
He abundance is ~ 25% - about as measured
Thus neutron/proton asymmetry caused by their mass difference
and the beta decay of neutrons determines primordial abundance
of He and other light elements
Because all the neutrons are tied up in He, its abundance is not
sensitive to the matter density. In contrast, the abundances of
other elements produces in the early universe, D, 3He, and 7Li are
dependent on the amount of baryonic matter in the universe
The universe expanded to rapidly to build up heavier elements!
BBNSPredic5ons
•  TheBBNSmakesdetailedpredic5onsoftheabundancesof
lightelements:2D,3He,4He,7Li,8Be
•  Thesearegenerallygivenasafunc5onofthebaryontophoton
ra5oη=nn/nγ,usuallydefinedinunitsof1010,anddirectly
relatedtothebaryondensityΩb:η10=1010(nn/nγ)=274Ωbh2
•  Astheuniverseevolvesηispreserved,sothatwhatwe
observetodayshouldreflectthecondi5onsintheearly
universe
•  Comparisonwithobserva5ons(consistentamongthedifferent
elements)gives:
2
Ωbaryonsh = 0.021 → 0.025
•  Thisisinaspectacularlygoodagreementwiththevaluefrom
2
theCMBfluctua5ons:
Ωbaryonsh = 0.024 ± 0.001
€
BBNSPredic5ons
4He:
the higher the density,
the more of it is made ➙
2D, 3He:
easily burned into
4He, so abundances are
lower at higher densities ➙
7Li:
… complicated ➙
Boxes indicate observed values
Helium-4Measurements
•  Heisalsoproducedin
stars,butthis“secondary”
abundanceisexpectedto
correlatewithabundances
ofothernucleosynthe5c
products,e.g.,oxygen
•  Observe 4He from
recombination lines in
extragalactic HII regions
in low-metallicity
starforming galaxies
•  The intercept at the zero oxygen abundance should represent the
primordial (BBNS) value
•  The result is: YBBNS = 0.238 +/- 0.005
DeuteriumMeasurements
Deuterium is easily destroyed in
stars, and there is no known
astrophysical process where it
can be created in large amounts
after the BBNS
Thus, we need to measure it in a
“pristine” environment, e.g., in
QSO absorption line systems
It is a tricky measurement and it
requires high resolution spectra
from 8-10 m class telescopes
The result is: D
H
= 2.74 ×10−5
BBNSandPar5clePhysics
BBNS predictions also depend on the number of lepton
(neutrino) families. Indeed, only 3 are allowed:
TheIdeaofInfla5on
•  AlanGuth(1980);precursors:D.Kazanas,A.Starobinsky
•  Explainsanumberoffundamentalcosmologicalproblems:
flatness,horizon,originofstructure,absenceoftopological
defects…
•  Developed further
by P. Steinhardt,
A. Albrecht, A.
Linde, and many
others
A page from
Guth’s notebook
A. Guth
A. Starobinsky
A. Linde
TheInfla5onaryScenario
Itsolves3keyproblemsoftheBigBangcosmology:
1.  Theflatnessproblem:whyistheuniversesocloseto
beingflattoday?
2.  Thehorizonproblem:howcomestheCMBRisso
uniform?
3.  Themonopoleproblem:wherearethecopious
amountsofmagne5cmonopolespredictedtoexistin
theBBcosmology?
…Italsoaccountsnaturallyfortheobservedpower
spectrumoftheiniCaldensityperturbaCons
…Itpredictsasimilar,scale-invariantspectrumforthe
cosmicgravita5onalwavebackground
…Anditimpliesamuch,much(!)biggeruniversethanthe
observableone
TheFlatnessProblem
The expanding universe
evolves away from Ωtot = 1:
H 02 (1 − Ω 0 )
kc 2
1 − Ω(t ) = −
=
2
2 2
H (t ) a(t ) R0 H (t ) 2 a(t ) 2
2
⎛ H (t ) ⎞
Ω r0 Ω m0
⎜⎜
⎟⎟ = 4 + 3
a
a
⎝ H0 ⎠
This creates an
enormous fine-tuning
problem: the early
universe must have
been remarkably close
to Ωtot = 1 in order to
have Ωtot ~ 1 today !
(from N. Wright)
TheHorizonProblem
3.5
Considerma<er-onlyuniverse:
d/ct
•  HorizondistancedH(t)=3ct
•  Scalefactora(t)=(t/t0)2/3
•  Thereforehorizonexpandsfaster
thantheuniverse,sonew”objects
areconstantlycomingintoview
ConsiderCMBR:
Itdecouplesat1+z~1000
i.e.,tCMB=t0/104.5
ThendH(tCMB)=3ct0/104.5
Nowthishasexpandedbyafactor
of1000to3ct0/101.5
•  Buthorizondistancenowis3ct0
•  Soanglesubtendedonskybyone
CMBhorizondistanceisonly~2°
• 
• 
• 
• 
3
2.5
distance to object at
dhor for a =1.0
2
horizon
distance
1.5
1
distance to object at
dhor for a =0.1
0.5
0
0
0.25
0.5
0.75
t/t0
➙ Patches of CMB sky
> 2° apart should not be
causally connected!
1
-6
CMBRisUniformto∆T/T~10 Yettheprojectedsizeofthepar5clehorizonatthedecouplingwas
~2°-theseregionswerecausallydisconnected-sohowcome?
TheMonopoleProblem
•  Magne5cmonopolesarebelievedtobean
inevitableconsequenceofGrandUnifica5on
Theories(GUTs)
–  Point-liketopologicaldefectsarisingduringthephase
transi5onwhenthestrongandtheelectroweakforces
decouple
•  Expectenormousnumbersofthem
–  Mass~1016mp;dominateallotherma<erdensitybya
factorof~1012andthusclosetheuniverseanddriveitto
aBigCrunchalong5meago…
•  Notobserved!So,wherearethey?
Infla5onaryUniverseScenario
•  IfthereisaTheoryofEverything(TOE)thatunifiesallfourforces
itwillbreakspontaneouslyatthePlanck5me(t~10-43sec)into
thegravita5onandaunifiedversionofthemagne5c,
electroweak,andstrongforces–aGrandUnifiedTheory(GUT)
•  TheGUTwillholdun5lT~1028K,ort~10-34sec.Atthispointthe
universeenteredaperiodof“falsevacuum”:theenergylevel
higherthanthelowest,“ground”state
•  SymmetrybreakinginGUTtheoriesisassociatedwithmassive
Higgsbosons,whicharequantaofascalarfieldthathasan
associatedpoten5alwhichdescribestheenergyofthefield
•  Thefalsevacuumisametastablestate,withit’svacuumenergy
ac5ngasa“nega5vepressure”causingtheuniversetoexpand
exponen5allyasit“rollsdownthescalarfield”
Infla5onWithaScalarField
•  Needpoten5alUwithbroadnearlyflatplateaunearφ=0
•  Thisisthemetastablefalsevacuum
•  Inflation occurs as φ moves
Potential U(φ) of
slowly away from 0
ö
a scalar field φ
•  It stops at drop to minimum
U - the true vacuum
•  Decay of inflaton field φ at U False vacuum
this point reheats universe,
producing photons, quarks,
etc. - all of the matter/energy
content of the universe is
created in this process
True vacuum
φ
•  This is equivalent to latent
<
= <=
heat of a phase transition
Inflation
Reheating
TheCosmicInfla5on
Recall that the energy density of the physical vacuum is described
as the cosmological constant. If this is the
dominant density term, the Friedmann Eqn. is:
The solution is obviously:
In the model where the GUT phase transition drives the inflation,
the net expansion factor is:
The density parameter evolves as:
Thus:
TheInfla5onaryScenario
Inflationary
Period
The universe inflates
by > 40 orders of
magnitude!
Stan
dard
Big B
ang
… and then the
standard expansion resumes
Infla5onSolvestheFlatnessProblem
As the universe inflates, the local curvature effects become
negligible in comparison to the vastly increased “global”
radius of curvature: the universe becomes extremely close
to flat locally (which is the observable region now). Thus,
at the end of the inflation, Ω = 1 ± ε
Infla5onSolvestheHorizonProblem
Regions of the universe which
were causally disconnected at
the end of the inflation used to
be connected before the
inflation - and thus in a
thermal equilibrium
Note that the inflationary
expansion is superluminal:
the space can expand
much faster than c
Infla5onandStructureForma5on
•  UncertaintyPrinciplemeansthatinquantummechanics
vacuumconstantlyproducestemporarypar5cle-an5par5cle
pairs
–  Thiscreatesminutedensityfluctua5ons
–  Infla5onblowstheseupto
macroscopicsize
–  Theybecometheseedsfor
structureforma5on
•  Expectthemassspectrumofthese
densityfluctua5onstobeapproximately
scaleinvariant
–  Thisisindeedasobserved!
–  Nota“proof”ofinfla5on,butawelcomeconsistencytest
TheInfla5onasaPhaseTransi5on
The universe undergoes a phase
transition from a state of a false
vacuum, to a ground state; this
releases enormous amounts of
energy (“latent heat”) which
drives an exponential expansion
Regions of non-inflating universe are created through the
nucleation of bubbles of true vacuum. When two such
bubbles collide, the vast energy of the bubble walls is
converted into the particles. This process is called reheating
PhysicalInterac5onsintheEarlyUniverse
Aswegetclosertot→0andT→∞,weprobephysicalregimes
inwhichdifferentfundamentalinterac5onsdominate.Their
strengthisafunc5onofenergy,andatsufficientlyhighenergies
theybecomeunified
TheElectroweakEra:upto10-10sec
•  AtT~1028K,threedis5nctforcesintheuniverse:Gravity,
Strong,andElectroweak:unifiedElectromagne5smandWeak
nuclearforce
•  AtT<1015K,Electromagne5smandWeaknuclearforcesplit;
thisistheElectroweakphasetransi5on
•  Limitofwhatwecantestinpar5cleaccelerators
TheGUTEra:upto10-35sec
•  AtT>1029K,electroweakforceandstrongnuclearforcejointo
formtheGUT(grandunifiedtheory)interac5on
•  Rela5velysolidtheore5calframework(butmaybewrong),but
notdirectlytestableinexperiments
•  ThisGUTphasetransi5onmaybedrivingtheInfla5on(but
thereareothercandidates)
Ma<er-An5ma<erAsymmetry
Matter
Particles
Antimatter
Particles
10,000,000,001
10,000,000,000
q
q
They basically have all annihilated away
except a tiny difference between them
Thisprocessleadstothepreponderanceofphotonsoverthe
lezoverbaryonstodaybythesamefactor…
Wheredoesitcomefrom?
TheCosmicBaryogenesis
•  Thecondi5onsrequiredforthecrea5onofmorema<erthan
an5-ma<erwerefirstderivedbyA.Sakharovin1967:
1.  Baryonnumberviola5on
•  Otherwisehavesameno.ofpar5clesandan5par5cles
•  Neverbeenobserved
•  PredictedtooccurinseveralGUTtheories
2.  CandCPviola5on
•  Parityofan5par5clesisoppositetothatofpar5cles
•  CPviola5ondiscoveredin1964(CroninandFitch)
3.  Departurefromnon-thermalequilibrium
•  Otherwiseallreac5onsgobothways
•  Providedbytheexpansionoftheuniverse
•  Nowbelievedtobethemechanismresponsibleforthema<er
-an5ma<erasymmetry
PlanckUnits
Proposedin1899byM.Planck,asthe“natural”systemofunits
basedonthephysicalconstants:
Theymaybeindica5veofthephysicalparametersandcondi5onsatthe
erawhengravityisunifiedwithotherforces…assumingthatG,c,andh
donotchange…andthattherearenootherequallyfundamental
constants
“Derived”PlanckUnits