The Unity of the Universe

Portsmouth UK June 2009

Outline•  Howcurrentandfutureobserva4onsincosmologyand

experimentsinpar4clephysicshaveaffectedandwillaffectourunderstandingof`founda4ons’oftheore4calphysics

•  StringcosmologyOnchao4cinfla4onandB‐modes

•  Standardmodelinfla4onwithandsupersymmetry

•  Recentdrama4cprogressinN=8four‐dimensionalsupergravity

Thehighwayacrossthedesert

Gerard‘tHooH

Today’s Limit …

GUTs

Planck length :

LHC

B‐modesfrominfla6on

Quantum Gravity

SUPERSYMMETRY

Cosmology,ten‐dimensionalsuperstringtheoryandeffec6vefour‐dimensionalsupergravity

Genericpoten4alofN=1supergravitydependsonanumber

ofcomplexscalarfieldswhichhavegeometricmeaningofcoordinatesinKählergeometry

+ D-terms

Kähler potential and the Superpotential

StringTheory•  Stringtheoryisthebestknowncandidateforthetheoryofall

interac4ons,includinggravity.

•  Since1987itwasknownthatstringtheoryhasmany(10500‐101500)solu4onsdefiningstringtheoryvacua(Lerche,Lust,Schellekens1987;Bousso,Polchinsky2000).Thiswasasourceofembarrassmentforstringtheory,a[emp4ngtoexplainouruniverseinthebesttradi4onsoftheoldparadigm:adreamtoexplainjustoneworldwelivein.

•  However,allofthesevacuawereunstable,theyhadnega6veenergydensity,andthereforetheycouldnotdescribeourworld.Thisproblembecameespeciallyurgentwhencosmologistsfoundthatthevacuumenergydensity(thecosmologicalconstant)isposi6ve.

•  Thisproblemwasresolvedin2003intheKKLTscenariobasedonmanyothereffortsofstringcommunityinthisdirec6on.

The volume stabilization problem:

A potential of the theory obtained by compactification in string theory of type IIB:

The potential with respect to X and Y is very steep, these fields rapidly run down, and the potential energy vanishes. We must stabilize these fields.

Volume stabilization: KKLT construction Kachru, RK, Linde, Trivedi 2003

X and Y are canonically normalized field corresponding to the dilaton field and to the volume of the compactified space; φ is the field driving inflation

Dilaton stabilization: Giddings, Kachru, Polchinski 2001

Even now the dilaton was not yet stabilized in heterotic string theory

Long Term Problem of Moduli Stabilisation And Supersymmetry Breaking

4D Compactifications: String theory is consistent in 10D. One of the moduli is the total volume of extra dimensions, it tend to have a runaway behavior. If this volume becomes infinite, we cannot explain the current cosmological observations which require an effective 4D!

Examples of Calabi-Yau 3-folds

Other moduli: size of cycles

1)  Start with a theory with a typical stringy runaway potential 2)  Bend this potential down due to nonperturbative quantum

effects 3)  Uplift the minimum to the state with a positive vacuum

energy by adding a positive energy of a D brane in warped Calabi-Yau geometry

Solvingthecosmologicalconstantproblem

Among10500vacuaonecanalwaysfindmanyvacuawithvacuumenergysmallerthan10‐120.Wecannotliveinthevacuawithvacuumenergymuchgreaterthan10‐120.

Thusacombina4onofinfla4onarytheory,stringtheoryandanthropicreasoningcansolvethecosmologicalconstantproblem.

Atthemoment,wedonothaveanyalterna4vesolu4ons.

Inflation in string theory

To produce a reasonable cosmology in string theory it was necessary to stabilize all moduli but the inflaton (or two, for non-gaussianity). In 4d theory such moduli are scalar fields. In string theory and supergravity they often have physical and geometrical meaning as volumes of extra dimensions and various cycles in topologically non-trivial extra dimensions. The inflaton can also be related to a distance between branes.

Brane inflation with monodromy

Brane inflation

Modular inflation

KKLMMT brane-anti-brane inflation

Hybrid D3/D7 brane inflation (Stringy D-term inflation)

Dirac-Born-Infeld inflation

Two-throat model

ModularInfla4onmodels

Kahler modular inflation Roulette inflation

,

Racetrack inflation

A simple working model of the moduli inflation Blanco-Pilado, Burgess, Cline, Escoda, Gomes-Reino, R.K., Linde, Quevedo

Superpotential:

Kähler potential:

Stringy corrections do not remove terms as originally expected. With fine-tuning one can find an inflection point and slow-roll inflation. “Delicate inflation.”

Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan, Steinhardt:

After that, the model works and has interesting properties, such as light cosmic strings

η-problem ( ) requires fine-tuning of terms

2008 Baumann, Dymarsky, Kachru, Klebanov, McAllister

Improved understanding of quantum corrections

If there are some discrete symmetries, the original KKLMMT scenario with inflaton mass tuned is valid.

2007

2003

Haack, RK, Krause, Linde, Lust, Zagermann 2008

Stringy version of the D-term inflation. Naturally flat inflaton direction, string theory corrections under control, eternal inflation regime, a controllably small amount of cosmic strings.

Silverstein, Westphal, 2008, McAllister, Silverstein, Westphal 2008

Type IIA string

Type IIB, CY

Type IIB CY

MEASUREMENT OF CMB POLARIZATION POWER SPECTRA FROM TWO YEARS OF BICEP DATA

June 2009

IMPROVED MEASUREMENTS OF THE TEMPERATURE AND POLARIZATION OF THE CMB FROM QUAD

B-mode spectrum is consistent with zero Directly from CMB B-mode polarization

WMAP+ACBAR +QUaD

From CMB alone

r =0.1

+…

Add

Where is dark matter and how supersymmetry will affect this conclusion ???

StandardModel+Supersymmetry:impossiblewith1Higgs,minimum2Higgsfields

Standard model Higgs inflation with non-minimal + supersymmetry

1. It is not possible to simply add to standard supergravity action

+ fermions

2. Need many new terms in the action proportional to

Work in progress

Quantum Gravity???

Duringthelastfewyearsstudiesofmul4‐par4cleamplitudesinQCD(N=0)weresimplifiedusingN=4superYang‐Millstheory.This,inturn,ledtosignificantprogressincomputa4onofQFTamplitudesinN=8supergravity.Somespectacularcancella4onsofUVdivergenceswerediscoveredatthe3‐looplevelin2007andatthe4‐looplevelin2009.

IsN=8supergravityUVfinite?Iftheansweris"yes"whatwoulditmeanforQuantumGravity?

N=8 supergravity in four dimensions during the last 25 years was believed to be UV divergent: all-loop geometric counterterms, candidates for UV divergences, are known RK; Howe, Lindstrom (1981). The onset of divergences was less clear.

•  Majorsurprise:

•  The3‐loopand4‐loopcomputa4onshowmuchbe[erUVthanexpected

•  Argumentsaboutall‐loopfiniteness

Bern, Carrasco, Dixon, Johansson, Kosower, Roiban (2007)

Bern, Carrasco, Dixon, Johansson, Roiban (2008, 2009)

•  Dc = 6 at L=3 same as for N=4 SYM!

•  Will the same happen at higher loops, so that the formula

continues to be obeyed by N=8 supergravity as well?

•  If so, N=8 supergravity may represent a perturbatively finite, pointlike theory of quantum gravity

N=4 SYM

At 3 loops N=8 supergravity seems to have the same UV behavior as N=4 SYM gauge theory.

Severalstrikingfeaturesofthe3‐loop4‐pointamplitudeanswer

•  TherearenoUVlogdivergenttermsoftheform

logΛ (R….)4

•  Therearenotermsoftheform

1/Λ2 D2(R….)4 •  Therearenotermsoftheform

1/Λ4 D4(R….)4

•  Thefirstnon‐vanishingtermsareoftheform1/Λ6 D6(R….)4

+higherderiva4ves

4‐loopcomputa4on

Predic4on:ifN=8SGatthe4‐looplevelbehavesasN=4SYM

theymustfind3‐typesofcancella4on:

logΛ

1/Λ2

1/Λ4

Superfiniteness is not a necessary condition for the all-loop UV finiteness in d=4, however, it is extremely unlikely to be accidental

If the last term is not vanishing, it indicates that D=5 L=4 maximal SG is divergent

Howe, Stelle: UV divergent

Computation: UV finite

This single 5-loop diagram has terms prior to evaluating any integrals. More terms than atoms in the brain!

terms in 3-loop diagram. There is a reason why this hasn’t been evaluated.

Brute force computations are totally hopeless!

Maximalsupergravity

•  Theory has 28 = 256 massless states. •  Multiplicity of states, vs. helicity, from coefficients in binomial expansion of (x+y)8 – 8th row of Pascal’s triangle

SUSY charges Qa, a=1,2,…,8 shift helicity by 1/2

DeWit, Freedman (1977); Cremmer, Julia, Scherk (1978); Cremmer, Julia (1978,1979); De Wit, Nicolai (1982)

Two-particle cut:

Generalized unitarity:

Three- particle cut:

Apply decomposition of cut amplitudes in terms of product of tree amplitudes.

Bern, Dixon, Dunbar and Kosower, 1994

3 loop N=8 supergravity computation, 2007

4 loop N=8 supergravity computation, May 2009

It continues to be as well behaved as N=4 SYM gauge theory.

What is next? Understanding the reason for cancellation of UV divergences, use light-cone superfields, E7(7) symmetry

Atpresentweareunawareofanynaturalwaytoaccommodateinstringtheoryafuturedetec4onofB‐modesand,simultaneously,apossiblefutureexperimentaliden4fica4onofthegravi4noaspar4cleswithmassmuchsmallerthan1013GeV.

EvenifB‐modesarenotdetected,thereiss4llatensionbetweenstringcosmologyandlightgravi4no,par4cularlyifitformsdarkma[er.

Newideasarerequired.

•  Supersymmetry?

•  Isdarkenergyacosmologicalconstant?•  Non‐gaussianity•  Moreonspectralindex

•  Cosmicstrings•  B‐modes?•  Massofgravi4no?

• Testofsuperstringtheory? We are waiting for LHC and Planck, dark matter and B-mode experiments data