AlanGuth,In ationaryCosmology:IsOurUniversePartofaMultiverse,Part2,8.286Lecture2,September10,2018,p.1.

SUMMARYOFLASTLECTURE

TheStandardBigBang:Reallydescribesonlytheaftermathofa

bang,beginningwithahotdenseuniformsoupofparticles�lling

anexpandingspace.

CosmicIn ation:Theprequel,describeshowrepulsivegravity|

aconsequenceofnegativepressure|

couldhavedrivenatiny

patchoftheearlyuniverseintoexponentialexpansion.Thetotal

energywouldbeverysmallormaybezero,withthenegative

energyofthecosmicgravitational�eldcancelingtheenergyof

matter.

AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{1{

Summaryp.2:EvidenceforInflation

1)In ationcanexplainthelarge-scaleuniformityoftheuniverse.

(Cosmicmicrowavebackground(CMB)uniform

to1partin

100,000.)

AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{2{

2)\Flatnessproblem:"

WhywastheearlyuniversesoFLAT?

Whatismeantby\ at"?

Flatdoesnotmean2-dimensional.

FlatmeansEuclidean,asopposedtothe

non-Euclideancurvedspacesthatarealso

allowedbyEinstein'sgeneralrelativity.

3-dimensionalcurvedspacesarehardto

visualize,buttheyareanalogoustothe

2-dimensionalcurvedsurfacesshownonthe

right.AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{3{

AlanGuth,In ationaryCosmology:IsOurUniversePartofaMultiverse,Part2,8.286Lecture2,September10,2018,p.2.

Accordingtogeneralrelativity,the atness

oftheuniverseisrelatedtoitsmassdensity:

(Omega)=

actualmassdensity

criticalmassdensity;

wherethe\criticaldensity"dependsonthe

expansionrate.=1is at,greater

than1isclosed,lessthan1isopen.

AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{4{

Auniverseatthecriticaldensityislikeapencilbalancingonits

tip:Ifintheearlyuniversewasslightlybelow1,itwouldrapidly

falltozero|

andnogalaxieswouldform.

Ifwasslightlygreaterthan1,itwouldrapidlyrisetoin�nity,

theuniversewouldrecollapse,andnogalaxieswouldform.

Tobeasclosetocriticaldensityaswemeasuretoday,atone

secondafterthebigbang,musthavebeenequaltooneto15

decimalplaces!

{5{

InflationarySolution:

Sincein ationmakesgravitybecome

repulsive,theevolutionofchanges,too.isdriventowards

one,extremelyrapidly.Itcouldbeginatalmostanyvalue.

Sincethemechanismbywhichin ationexplainsthe atnessof

theearlyuniversealmostalwaysovershoots,itpredictsthateven

todaytheuniverseshouldhaveacriticaldensity.

Until1998,observationpointedto�

0:2{0.3.

LatestobservationbyPlancksatellite(combinedwithother

astronomicalobservations):

=0:999�

0:004(95%con�dence)

Newingredient:DarkEnergy.In1998itwasdiscoveredthatthe

expansionoftheuniversehasbeenacceleratingforaboutthelast

5billionyears.The\DarkEnergy"istheenergycausingthisto

happen.

AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{6{

3)Smallscalenonuniformity:

Canbemeasuredinthecosmic

backgroundradiation.Theintensityisalmostuniformacrossthe

sky,buttherearesmallripples.Althoughtheseripplesareonly

atthelevelof1partin100,000,thesenonuniformitiesarenow

detectable!Wheredotheycomefrom?

InflationarySolution:

In ationattributestheseripplesto

quantum

uctuations.

In ationmakesgenericpredictionsfor

thespectrumoftheseripples(i.e.,howtheintensityvarieswith

wavelength).Thedatameasuredsofaragreebeautifullywith

in ation.

AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{7{

AlanGuth,In ationaryCosmology:IsOurUniversePartofaMultiverse,Part2,8.286Lecture2,September10,2018,p.3.

RipplesintheCosmicMicrowaveBackground{

8{

CMB:

Comparison

ofTheory

and

Experiment

GraphbyMaxTegmark,

forA.Guth&D.Kaiser,

Science307,884

(Feb11,2005),updated

toincludeWMAP

7-yeardata.

AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{9{

CMB:

Comparison

ofTheory

and

Experiment

GraphbyMaxTegmark,

forA.Guth&D.Kaiser,

Science307,884

(Feb11,2005),updated

toincludeWMAP

7-yeardata.

AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{10{

SpectrumofCMBRipples

{11{

AlanGuth,In ationaryCosmology:IsOurUniversePartofaMultiverse,Part2,8.286Lecture2,September10,2018,p.4.

GravitationalWaves:CameandWent

March17,2014:TheBICEP2pressconferenceannouncedthe

detectionofswirlypatterns(B-modes)inthepolarizationofthe

CMB,indicatinggravitationalwavesfromtheearlyuniverse,in

agreementwithin ation.

Result:Afteraccountingfortheirbestestimateofcontaminationdue

todust,theyfoundatensor/scalarratior=

0:16+0:

06

�

0:

05 ,with

r=0disfavoredat5.9�.

Translation:theprobabilitythattherearenoprimordialgravitational

wavesisonlyaboutoneinabillion.

April14,2015:AJointAnalysisofBICEP2/KeckArrayandPlanck

Data:\We�ndstrongevidencefordustandnostatistically

signi�cantevidencefortensormodes."

AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{12{

ThesearchforB-modesisstillon,andiftheyarefoundtheywill

provideadditionalstrongevidenceforin ation,andatoolfor

probingthedetailsofin ation.

Currentlimit:r<

0:07.Futuresensitivity:ifr>

0:001,itcanbe

foundbyabout2024(CMBStage4).

IfB-modesarenotfound,thatisnotevidenceagainstin ation:many

in ationarymodelspredictaB-modeintensitymuchsmallerthan

0.001.AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{13{

InflationSuggestsaMultiverse

Almostalldetailedmodelsofin ationleadto\eternalin ation,"and

hencetoamultiverse.

Roughlyspeaking,in ationisdrivenbyametastablestate,which

decayswithsomehalf-life.

Afteronehalf-life,halfofthein atingmaterialhasbecomenormal,

nonin atingmatter,butthehalfthatremainshascontinued

toexpandexponentially.Itisvastlylargerthanitwasatthe

beginning.

Oncestarted,thein ationgoesonFOREVER,withpiecesofthe

in atingregionbreakingo�andproducing\pocketuniverses."

Wewouldbelivinginoneofthein�nityofpocketuniverses.

AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{14{

TheCosmologicalConstantProblem

In1998,twogroupsofastronomersdiscoveredthatforthepast5{

6billionyears,theexpansionoftheuniversehasbeenaccelerating.

AccordingtoGR,thisrequiresarepulsivegravitymaterial,which

isdubbed\DarkEnergy".

Simplestexplanation:darkenergyisvacuumenergy|theenergy

densityofemptyspace.Thephysicist'svacuumisfarfromempty,

soanonzeroenergydensityisexpected.

ValueofVacuumEnergyDensityMakesNoSense:Wecannot

calculatethevacuum

energydensity,butthenaturalparticle

physicsestimateiscalledthePlanckscale|

theenergyscale

atwhichthee�ectsofquantumgravityareexpectedtobecome

important.ButitisMUCHlargerthantheobservedvalue:

Itislargerby120ordersofmagnitude!

{15{

AlanGuth,In ationaryCosmology:IsOurUniversePartofaMultiverse,Part2,8.286Lecture2,September10,2018,p.5.

TheMultiverseandthe

CosmologicalConstantProblem

Oneofthethorniestproblemsinparticletheoryistounderstand

whytheenergydensityofthevacuum(equivalenttothecos-

mologicalconstant)is120ordersofmagnitudesmallerthanthe

(expected)Planckscale.

Themultiverseo�ersapossible(althoughcontroversial)solution.

Ifthereare10500

di�erenttypesofvacuum(asinstringtheory),

therewillbemanywithenergydensitiesintherangeweobserve.

Thevacuumenergya�ectscosmicevolution:ifitistoolargeand

positive,theuniverse iesaparttoofastforgalaxiestoform.If

toolargeandnegative,theuniverseimplodes.

Itisthereforeplausiblethatlifeonlyformsinthosepocketuni-

verseswithincrediblysmallvacuumenergies,soalllivingbeings

wouldobserveasmallvacuumenergy.(Anthropicprinciple,or

observationalselectione�ect.)

{16{

SUMMARY

TheInflationaryParadigmisinGreatShape!

Explainslargescaleuniformity.

Predictsthemassdensityoftheuniversetobetterthan1%

accuracy.

Explainstheripplesweseeinthecosmicbackgroundradiationas

theresultofquantum uctuations.

AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{17{

ThreeWindsBlowingUsTowardstheMultiverse

1)Almostallin ationarymodelsareeternalintothefuture.Once

in ationstarts,itneverstops,butgoesonforeverproducing

pocketuniverses.

2)Astronomershavediscoveredthattheuniverseisaccelerating,

whichprobablyindicatesavacuumenergythatisnonzero,but

incrediblymuchsmallerthanwecanunderstand.

Whatis

happening?

3)Stringtheoristsmostlyagreethatstringtheoryhasnounique

vacuum,butinsteadalandscapeofperhaps10500

long-lived

metastablestates,anyofwhichcouldbeourvacuum.With

themultiverse,thisallowsthesmallvacuumenergydensityto

beexplainedasaselectione�ect:perhapsweseeasmallvacuum

energydensitybecauseconsciousbeingsonlyforminthoseparts

ofthemultiversewherethevacuumenergydensityissmall.

AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{18{

DoPhysicistsTakethe

MultiverseSeriously?

Martin

Rees(AstronomerRoyalofGreatBritainand(former)

PresidentoftheRoyalSociety)hassaidthatheissuÆciently

con�dentaboutthemultiversetobethisdog'slifeonit.

AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{19{

AlanGuth,In ationaryCosmology:IsOurUniversePartofaMultiverse,Part2,8.286Lecture2,September10,2018,p.6.

DoPhysicistsTakethe

MultiverseSeriously?

AndreiLinde(StanfordUniversity,majorroleindevelopingin ation-

arycosmology,sharedinthe2002DiracPrize,the2004Gruber

Prize,the2012FundamentalPhysicsPrize,andthe2014Kavli

Prize)hassaidthatheissocon�dentthathewouldbethisown

life.AlanGuth

Massachusetts

InstituteofTechnology

8.286Lecture

2,September10,2018

{20{

DoPhysicistsTakethe

MultiverseSeriously?

StevenWeinberg(1979NobelPrizeinPhysics):\Ihavejustenough

con�denceaboutthemultiversetobetthelivesofbothAndrei

LindeandMartinRees'sdog."

AlanGuth

MassachusettsInstituteofTechnology

8.286Lecture

2,September10,2018

{21{