THE THE UNIVERSE UNIVERSE

AS A AS A BRANEBRANE

QG05 Sardegna Roy MaartensPortsmouth

why donwhy don’’t we see the extrat we see the extra dimensions?dimensions? cconventionalonventional KaluzaKaluza--Klein Klein ideaidea::

extra dimensions extra dimensions too smalltoo small to be seento be seen

ddiscoveryiscovery of Dof D--branebrane mmatteratter fieldsfields restricted restricted

to to lower dimensional lower dimensional branebrane eexternalxternal bulk felt only bulk felt only

through through gravitygravity extra dimension biggerextra dimension bigger

4D spacetimesmall extra dimension

large extra dimension

gravity

matter

general relativity + particle general relativity + particle physics:physics:

expanding 4D universe modelexpanding 4D universe model

confirmed by observationsscales cosmic sets 1H

WMAP satellite and SDSS telescope

the model fits the high-precision the model fits the high-precision datadata

SDSS

WMAP

3 3 independenindependent data sets t data sets intersectintersect

successfulsuccessful

model model butbut we know we know

GR breaks GR breaks downdown

quantum quantum gravity will gravity will explain (pre-) explain (pre-) inflationinflation

GR + SM particle physics:GR + SM particle physics:inflationary LCDM modelinflationary LCDM model

TeV10~ 16PME

inflation is not the only puzzle ….inflation is not the only puzzle ….

dark energy??dark energy??

maybe an IRmaybe an IR

modification modification to GR?to GR?(as well as UV(as well as UV in the earlyin the early universe)universe)

LCDM is a framework seeking a LCDM is a framework seeking a fundamental theoryfundamental theory

moremore puzzles to come from observations? puzzles to come from observations?

inflation is crucial – what underlies it?inflation is crucial – what underlies it? what is dark energy – matter or gravity?what is dark energy – matter or gravity? GR must break down in the UVGR must break down in the UV

we need quantum gravity in the early we need quantum gravity in the early universe universe

+… +… maybe also in the late universe/ IR? maybe also in the late universe/ IR? candidate theories candidate theories (Kiefer (Kiefer

2004)2004)

quantum GR quantum GR (Williams, (Williams, Markopolou talks)Markopolou talks)

string theorystring theory

is high-is high-precision precision

cosmology cosmology probing the probing the limits of GR?limits of GR?

removes the infinities of QFT removes the infinities of QFT

and includes the graviton and includes the graviton

but there is a price … but there is a price …

9 space dimensions!!9 space dimensions!!

string theorystring theory

6 compact

3

simple observation: we live in a large 3D world simple observation: we live in a large 3D world

why don’t we see the extrawhy don’t we see the extra dimensions?dimensions?

cconventional onventional Kaluza-Klein Kaluza-Klein ideaidea:: extra dimensions extra dimensions too smalltoo small to be seen to be seen

ddiscovery of D-braneiscovery of D-brane

mmatter fieldsatter fields restricted restricted to to lower dimensional branelower dimensional brane eexternal bulk felt only xternal bulk felt only through through gravitygravity extra dimensions canextra dimensions can

be much largerbe much larger

4D spacetimesmall extra dimension ~ Lp

large extra dimension >> Lp

gravity

matter

Kaluza-Klein extra dimensions

have SM fields

Braneworldextra dimensions

are “dark”

Flux lines of gravity

Electric flux line

(Tanaka)

1+9 D universe 1+9 D universe has branes and has branes and stringsstrings

some of the some of the 6D may be 6D may be smallsmall 5 string theories + 5 string theories +

supergravity =supergravity =

limits of 1+10 D limits of 1+10 D theorytheory

M THEORYM THEORY

(Bousso, Nicolai, Stelle, Zanelli talks)(Bousso, Nicolai, Stelle, Zanelli talks)

string theory -string theory -the cosmologist’s wish-listthe cosmologist’s wish-list

** a natural mechanism for 3 dimensions to a natural mechanism for 3 dimensions to grow grow very large/ 6 dimensions to compactifyvery large/ 6 dimensions to compactify

* * a natural mechanism for inflationa natural mechanism for inflation

* * or … an alternative - eg brane collisionor … an alternative - eg brane collision

** solve the dark energy problem solve the dark energy problem

…. then we test the answers…. then we test the answers COSMOLOGY AS A PROBE OF STRING COSMOLOGY AS A PROBE OF STRING THEORYTHEORY

but … but … string theory is tough!string theory is tough!

no convincing stringy no convincing stringy inflation yetinflation yet

no convincing stringy dark no convincing stringy dark energy yetenergy yet

no convincing progress on no convincing progress on perturbationsperturbations

some progress in string some progress in string brane inflationbrane inflation ** D/ anti-D brane models D/ anti-D brane models * * higher-Dhigher-D cosmic strings can cosmic strings can be be producedproduced * * … but still a long way to go… but still a long way to go

the practical cosmologist’s the practical cosmologist’s approachapproach

while waiting for progress in string while waiting for progress in string cosmologycosmology

… … develop phenomenologydevelop phenomenology

** it’s what we do with inflation it’s what we do with inflation * * and QG phenomenologyand QG phenomenology (Liberati talk)(Liberati talk)

use string theory ideas in cosmologyuse string theory ideas in cosmology

* * in fact this can help string theory …in fact this can help string theory …

** brings high-precision data into the picture brings high-precision data into the picture

experimental tests of experimental tests of gravitygravity

CavendishCavendish neutrons neutrons (Bertolami talk)(Bertolami talk)

colliders colliders (Cavaglia)(Cavaglia)

solar systemsolar system perihelionperihelion bending of lightbending of light

binary pulsarsbinary pulsars gravitational lensinggravitational lensing BHs and GWsBHs and GWs cosmologycosmology

BBN, SNeBBN, SNe LSS, CMBLSS, CMB

cosmology probes gravity on vast cosmology probes gravity on vast scalesscales

(Tegmark)(Tegmark)

eg - SDSS test of Newton’s laweg - SDSS test of Newton’s law

0.8 0.9 cccc

(Shirata et (Shirata et al)al)

extra-dimensional gravity brings extra-dimensional gravity brings newnew features features

extra polarizations of the graviton (KK modes)extra polarizations of the graviton (KK modes)

new fields (dilaton, moduli, radion, form fields)new fields (dilaton, moduli, radion, form fields)

shadow mattershadow matter

holography (AdS/CFT) holography (AdS/CFT) (Bianchi (Bianchi talk)talk)

precision data precision data constrains constrains extra-dimensional extra-dimensional gravitygravity

… … hopefully rule out some modelshopefully rule out some models

signature of extra dimensionssignature of extra dimensions

in observations?in observations?

5D gravitons – effective mass on 5D gravitons – effective mass on branebrane

(massive KK modes)(massive KK modes)

polarizations:polarizations: 5 = 2+2+15 = 2+2+1

graviton KK modes graviton KK modes graviton KK modes graviton KK modes

)5(ap

an

p

2)5(2 a

a npmpp

5D spin-2 (5) = 4D spin-2 (2) + 4D spin-1 (2) + 4D spin-0 (1)

0 (gauge) and

0 , )5()5()5(

b

ab

aa

abbababab

nh

hhhgg

start with simple modelsstart with simple models similar to inflation and dark energy modelssimilar to inflation and dark energy models

simplest models with simplest models with predictivepredictive power power

focus on one or two key aspects at a timefocus on one or two key aspects at a time

KK modes of gravitonKK modes of graviton

scalar fields – dilaton, radion, moduliscalar fields – dilaton, radion, moduli

… …..

motivate by string theorymotivate by string theory 2 branes with large separation + small internal 2 branes with large separation + small internal space space (Horava-Witten)(Horava-Witten)

AdSAdS55 X M models: 1 large dimension, warped X M models: 1 large dimension, warped

… …..

small extra dimensions

(moduli stabilised)

large extra dimension

visible brane

shadow brane

L

TeV1colliders

/~

true,

3/12true,

P

PPP

M

MLMM

exp(-y/L)

anti de Sitter 5D (infinite extra

dimension)

brane

all extra dimensions large

TeV1colliders

/~

4

)2/(1 24

n

P

nnPn

M

MLMM

(Antoniadis, Arkani-Hamed, Dimopoulos, Dvali 1998)

identify

brane

n-torus

(…. Antoniadis talk)

)4()4(4

416

1 nnn

n

RgydxdG

S

testing gravity in the testing gravity in the laboratorylaboratory

extra dimension changes Newton’s lawextra dimension changes Newton’s law

L

mm1.0 experiment

)/(~D extra1 22

L

Vr

GMmV

rLOV

torsion pendulum

warped geometrywarped geometry extra dimension shrinksextra dimension shrinks

toward infinitytoward infinity finite volume bulkfinite volume bulk curvature scalecurvature scale

4D GR is recovered 4D GR is recovered

on large scaleson large scales

exp( / )y

r

0.1mm

5D solution of

Einstein equations

(Randall & Sundrum 1999)

222/22 dyxddteds y

y

222/1 )(),()( mzUktezzh z

Discrete spectrum m=0: zero mode for tensors no zero-mode for scalars/ vectors

Continuous spectrum m>0: massive KK modes of the graviton same massive modes for scalar/ vector/ tensor

U(z)

z

～ z –2

KK modes of the KK modes of the gravitongraviton

22 /~/ rVV

rV /1~

bran

e

(Garriga, (Garriga, Tanaka)Tanaka)

(de Risi talk)(de Risi talk)

cosmic expansion = movement of cosmic expansion = movement of branebrane

time

3D space

deviation from 4D GR in the early deviation from 4D GR in the early universeuniverse

modified Friedmann equationmodified Friedmann equation

gravity leakage:gravity leakage:

gravity becomes 5Dgravity becomes 5D

gravity leakage

1H

HH

GGH

1

3

21

3

8 22

(Binetruy, Deffayet, Langlois)(Binetruy, Deffayet, Langlois)

(Shiromizu, Maeda, Sasaki)(Shiromizu, Maeda, Sasaki)

RS inflationRS inflation

modified Friedmannmodified Friedmann boosts 4D perturbationsboosts 4D perturbations but also creates 5D GWbut also creates 5D GW

* * back-reaction of 5D back-reaction of 5D

metric perturbationsmetric perturbations

* * loss of powerloss of power large scales boostedlarge scales boosted but small scales?but small scales?

H

5D metric

perturbation

* Vinf lowered

* AS and AT boosted

* but AT/ AS suppressed

(RM et al)(RM et al)

(Langlois, RM, Wands)(Langlois, RM, Wands)

(Koyama,Mizuno,Wand(Koyama,Mizuno,Wands)s)

L I S A

?

g r a v i t a t i o n a l w a v e s i n h i g h - e n e r g y u n i v e r s e

- s i g n a t u r e o f e x t r a d i m e n s i o n s ?

a d v L I G O

41 0 H z ( f o r = 0 . 1 m m )f

• modified background modified background boosts 4D GWboosts 4D GW

• but 5D GW emission but 5D GW emission damps 4D GWdamps 4D GW

• competing effects – competing effects – cancel!cancel!recover GR resultrecover GR result

(Hiramatsu,Koyama,Taruy(Hiramatsu,Koyama,Taruya)a)

5D BH induces “dark radiation” on the 5D BH induces “dark radiation” on the branebrane

perturbation isocurvature perturbationperturbation isocurvature perturbation

5D anisotropy induces anisotropic stress5D anisotropy induces anisotropic stress

time

bulk

brane

BH

CMB anisotropiesCMB anisotropies

BH

simple modelsimple model

constraint on small BH massconstraint on small BH mass

in 5D bulk spacetimein 5D bulk spacetime

BH massS

pectral index

probability

00

(Koyama)(Koyama)

is dark energy a gravitational is dark energy a gravitational effect?effect?

general relativity general relativity

observations (nearly) flat, accelerating observations (nearly) flat, accelerating universe, with sub-critical matteruniverse, with sub-critical matter

field equations imply dark energyfield equations imply dark energy

example from historyexample from history Mercury perihelion – Newton + missing Mercury perihelion – Newton + missing mattermatter??

no:no: modified gravity modified gravity

)3( pa

a

GTGG

GTGTG

8

versus

88

dark

dark

modify Einstein’s equations?modify Einstein’s equations?

)( 44 RfgxdRgxd trytry

GR + light scalar field – same as DE fieldGR + light scalar field – same as DE field

trytry,...),(4

RRRfgxd ghostsghosts

try infinite extra degrees of freedom?try infinite extra degrees of freedom?

try try massive graviton (Pauli-Fierz)massive graviton (Pauli-Fierz)

unstable theoryunstable theory

braneworld models braneworld models with late-time accelerationwith late-time acceleration

Randall-Sundrum modifies GR in UV (early Randall-Sundrum modifies GR in UV (early universe)universe)

- via gravity leakage off the brane at early - via gravity leakage off the brane at early timestimes

recover GR in recover GR in IRIR

DGP model is an alternative DGP model is an alternative (Dvali, Gabadadze, (Dvali, Gabadadze, Porrati 2000)Porrati 2000)

- gravity leakage off the brane at late times- gravity leakage off the brane at late times

recover GR in recover GR in UVUV

3

82 G

L

HH LL = crossover scale = crossover scale

3

21

3

8 22 GG

H

LL = crossover scale: = crossover scale:

5D gravity dominates at late times5D gravity dominates at late times no graviton zero-mode: no graviton zero-mode:

4D gravity recovered at high energy via lightest KK 4D gravity recovered at high energy via lightest KK modesmodes

‘metastable graviton’

5D Minkowski bulk:

infinite volume extra dimension

gravity leakage

35

2

4

5

)5()5(5

5

2 :scale Planck 4D

16

16

1

LMM

RgxdG

LRgxd

GS

p

2

1

1

rVLr

rVLr

brane

10 Lm

DGP cosmologyDGP cosmology

3

8 :searly time

10 : timeslate

3

8

21

2

GHLH

LH

G

L

HH

FriedmannFriedmann

early universeearly universe – recover GR dynamics – recover GR dynamics

late universelate universe – acceleration – acceleration withoutwithout dark dark energyenergy

* from leakage of gravity* from leakage of gravity

* but fine-tuned* but fine-tuned 1331

0 eV10~HL

(Deffayet)

need to test this against SNe need to test this against SNe redshiftsredshifts

comparison with SNe observationscomparison with SNe observations

2

2

20

3

0

2

1

4

1)(

m

c

mcc

L

H

zH

zH

(Deffayet et al)(Sahni et al)(Song)(Bento talk)

structure formationstructure formation

degeneracy between DGP and GR+DE:degeneracy between DGP and GR+DE:

both can fit SNe observationsboth can fit SNe observations

but this is broken but this is broken

by structure formationby structure formation

how to distinguish DGP from how to distinguish DGP from GR+DE?GR+DE?structure formation is suppressed:structure formation is suppressed:

** in GR – because DE dominates over matter in GR – because DE dominates over matter

* * in DGP – because gravity weakensin DGP – because gravity weakens

need to compute LSS and compare with SDSSneed to compute LSS and compare with SDSS

L~1/HL~1/H00

m

m

tot

mH

2

2

3

term5D21

1

2

3 2

m

m

LH

LHH

CMB – the ISW effectCMB – the ISW effect

difference in LSS formation will leave an difference in LSS formation will leave an imprintimprint

(Nichol)

ISW effectISW effect

gravity leakage must be taken into accountgravity leakage must be taken into account … …. SNe+SDSS+CMB may rule out DGP. SNe+SDSS+CMB may rule out DGP

DGP (4D)

LCDM

Dark Energy

DE curve:

scalar field model with the same background evolution as DGP

DGP(4D) curve:

neglects 5D term

(Takahashi)

brane cosmology brings new brane cosmology brings new ideasideas ** new effects in inflation, CMB, dark energy new effects in inflation, CMB, dark energy - even in the simplest models - even in the simplest models * * RS + DGP models – extra-DRS + DGP models – extra-D gravity gravity is central is central

(unlike string brane inflation models)(unlike string brane inflation models) * * probe stringy ideas via gravity – and test probe stringy ideas via gravity – and test

against observationsagainst observations

exciting challenges for theorists!exciting challenges for theorists!

conclusion -conclusion -the universe as a branethe universe as a brane

• string theory demands extra dimensions• this may explain the beginning of the universe• this may explain what inflation is

• this may explain what the dark energy is

• ….. but not yet - brane models can help