Large distance modification Large distance modification of gravity and dark energyof gravity and dark energy

Kazuya KoyamaKazuya Koyama

ICG, University of PortsmouthICG, University of Portsmouth

Cosmic accelerationCosmic acceleration

Cosmic accelerationCosmic acceleration

Big surprise in cosmologyBig surprise in cosmology

Simplest best fit model Simplest best fit model

LCDMLCDM

4D general relativity + cosmological const.4D general relativity + cosmological const.

22

8

3 3m

G KH

a

1 m K

3 independent 3 independent data sets data sets intersect intersect

Problem of LCDMProblem of LCDM

Huge difference in scales (theory vs observation)Huge difference in scales (theory vs observation)

vacuum energy =0 from fundamental theoryvacuum energy =0 from fundamental theory

(1) tiny vacuum energy is left somehow(1) tiny vacuum energy is left somehow

(2) Potential energy of quintessence field(2) Potential energy of quintessence field

fundamental

2 2 33 2 19 2 47 40

4 3 4 12 4

(10 eV) (10 GeV) 10 GeV8

(10 GeV) 10 GeV

plobs

theory

H MG

M

Alternative modelsAlternative models Tiny energy scale Tiny energy scale

unstable under quantum correctionsunstable under quantum corrections

Alternative - modified gravityAlternative - modified gravity

dark energy is important only at late timesdark energy is important only at late times

large scales / low energy modificationslarge scales / low energy modifications

cf. cf.

from Newton to GRfrom Newton to GR

Is cosmology probing breakdown of Is cosmology probing breakdown of GR on large (IR) scales ?GR on large (IR) scales ?

OptionsOptions

Modify the Friedmann equation empiricallyModify the Friedmann equation empirically

or or

how to perturb?how to perturb? Modify the Einstein-Hilbert action Modify the Einstein-Hilbert action

cf. cf.

2 8( )

3 m

GH f

8( )

3 m

Gf H

4 ( , , )S d x g f R R R R R

( )f R RR

(Carol et.al., …)

(Freese, …)(Dvali and Turner, …)

Problems of IR modificationProblems of IR modification Modified gravityModified gravity

graviton has a scalar mode graviton has a scalar mode

Solar system constraints - theory must be GRSolar system constraints - theory must be GR

cf. cf.

difficult to explain dark energy purely from modified difficult to explain dark energy purely from modified gravitygravity

24 ( )S d x g R V

2 2010000, ( )plV H M

( )f R RR

0 (Chiba)

DGP modelDGP model

Crossover scaleCrossover scale

4D Newtonian gravity4D Newtonian gravity

5D Newtonian gravity5D Newtonian gravitycr r

5 (5) (5) 41 1

32 16 mc

S d x g R d x g R LG r G

cr

Infinite extra-dimension

gravity leakage

cr rcr

(Dvali, Gabadadze,Porrati)

Consistent with local experiments?Consistent with local experiments?

DGP also has a scalar mode of gravitonDGP also has a scalar mode of graviton

:4D Newtonian but not 4D GR!:4D Newtonian but not 4D GR!

(Scalar-Tensor theory)(Scalar-Tensor theory)

Non-linear shieldingNon-linear shielding

theory becomes GR attheory becomes GR at

solar-system solar-system

constraints can be evaded if constraints can be evaded if

1

2 3* g cr r r r

gr

cr r

2 3kmgr GM 1 28

0 10 cmcr H

*r

cr 5D

ST

GR

4D(Deffayet et.al.)

Cosmology of DGPCosmology of DGP

Friedmann equationFriedmann equation

early times 4D Friedmannearly times 4D Friedmann

late timeslate times

As simple as LCDM modelAs simple as LCDM model

and as fine-tuned as LCDM and as fine-tuned as LCDM

(stability against quantum corrections can be different)(stability against quantum corrections can be different)

2 8

3c

H GH

r

10

c

c

Hr

Hr

10cr H

(Deffayet)

4

4

1

16

m

d x g RG

d x L

5 (5) (5)1

32 c

d x g RG r

LCDM vs DGP LCDM vs DGP

Can we distinguish between DGP and LCDM ?Can we distinguish between DGP and LCDM ?

Friedmann equationFriedmann equation

cf. LCDMcf. LCDM

2

22 2

1 1 8

2 4 3 mc c

G KH

r r a

2

2 20

11 ,

4c c cr r m K rcr H

22

8

3 3m

G KH

a

1 m K

SNe + baryon oscillationSNe + baryon oscillation

SNLS + SDSS ‘Gold’ set + SDSSSNLS + SDSS ‘Gold’ set + SDSS(Fairbairn and Goobar astro-ph/0511029)

(cf. Alam and Sahni, astro-ph/0511473)

(Maartens and Majerotto in preperation)

Why baryon oscillation?Why baryon oscillation?

Baryon oscillationBaryon oscillation

angular diameter at z=0.3 angular diameter at z=0.3

+ shape parameter of power spectrum + shape parameter of power spectrum

K=0K=0

equivalent to dark energy model withequivalent to dark energy model with

2 8

3 mc

G HH

r

1

1 ( )m

wa

m

1w

(Lue.et.al)

(LCDM)VS

DGP Cosmology DGP Cosmology

As simple as LCDMAs simple as LCDM

a falsifiable modela falsifiable model

now the model is under pressure from the datanow the model is under pressure from the data

measurements of is crucialmeasurements of is crucial

Fit to SNe assuming flat universeFit to SNe assuming flat universe

A parameter is fixed! A parameter is fixed!

101.4cr H

m

Dark energy vs DGPDark energy vs DGP Can we distinguish between dark energy in GR Can we distinguish between dark energy in GR

and DGP ?and DGP ?

0.7w

1w

DGP

1

0( ) ( )

zr z dz H z

DGP model is fitted by

0

0

( ) (1 ),

0.78, 0.32a

a

w a w w a

w w

(Linder)

Dvali and Turner

Cosmology as a probe of DGP Cosmology as a probe of DGP gravitygravity

CMB ISW

LSS

4D 5D

Scalar tensorEinstein

CMB

SNe

Weak lensing

linearNon-linear

Expansion historyGrowth rate

cr

Non-linear mapping

Growth rate of structure formationGrowth rate of structure formation

Evolution of CDM over-densityEvolution of CDM over-density GRGR

If there is no dark energyIf there is no dark energy dark energy suppresses the gravitational collapsedark energy suppresses the gravitational collapse

DGPDGP

an additional modification from the scalar modean additional modification from the scalar mode

a 2 4H G

2 4 ( )cH GF Hr

Expansion history vs growth rateExpansion history vs growth rate

Growth rate resolves the degeneracyGrowth rate resolves the degeneracy

LCDM

dark energy

DGP

( )g aa

(Lue.et.al, Linder)

ExperimentsExperiments ASSUME our universe is DGP braneworldASSUME our universe is DGP braneworld

but you do not want to believe this,but you do not want to believe this,

so fit the data using dark energy modelso fit the data using dark energy model

Inconsistent!

m(z): apparent magnitude

R:CMB shift parameter

G(a):Growth rate

SNe+CMB

SNe+weak lensing

OR

(Ishak et.al, astro-ph/0507184)

Consistent 5D analysis of growth Consistent 5D analysis of growth factorfactor

Use correct 5D physicsUse correct 5D physics growth rate is sensitive to truncation of 5D physics growth rate is sensitive to truncation of 5D physics

Consistency in 5D physics Consistency in 5D physics (1)(1) Analysis based on Analysis based on (2)(2) must be revisited must be revisited

a

(1) Lue.et.al astro-ph/0401515

(2) Song astro-ph/0407489

KK and R.Maartens astro-ph/0511634

LCDM

Dark energy

a

Solutions for metric perturbationsSolutions for metric perturbations

Scalar tensor theory with Brans-Dick parameter Scalar tensor theory with Brans-Dick parameter

Solutions for metric perturbationsSolutions for metric perturbations

2 2 2 2(1 2 ) ( ) (1 2 )ds dt a t dx

21 2 1

3c

Hr H

H

3( 1)

2

(Lue et.al, KK and R,Maartens)

2

2

2

2

14 1 ,

3

14 1 ,

3

kG

a

kG

a

a

ISW effects and weak lensingISW effects and weak lensing

Growth rate is determined by Growth rate is determined by

ISW effects and weak lensing effects depends on ISW effects and weak lensing effects depends on

the same as GR!the same as GR!

Difference comes from growth rate of Difference comes from growth rate of

2

28

kG

a

2

22

kH

a

12 4 1

3H G

2

2

2

2

14 1 ,

3

14 1 ,

3

kG

a

kG

a

CMB ISW

LSS

4D 5D

Scalar tensorEinstein

CMB

SNe Weak lensing

linearNon-linear cr

Need 5D solutions

Large scale ISWNon-linear P(k)

Need non-linear mapping

SummarySummary

Alternative to LCDM from large scale modificationAlternative to LCDM from large scale modification

DGP model as an exampleDGP model as an example The model is already in tension with the data The model is already in tension with the data Structure formation is different from GRStructure formation is different from GR 5D study of perturbations is crucial5D study of perturbations is crucial

cf. Theoretical difficulties of DGP model cf. Theoretical difficulties of DGP model

strong coupling / a ghost in de Sitter spacetimestrong coupling / a ghost in de Sitter spacetime(Luty, Porrati, Rattazi) (Nicolis, Rattati; KK hep-th/0503191

Gorbunov, KK, Sibiryakov; to appear)

Lessons from DGPLessons from DGP

Gravity is subtleGravity is subtle

modification at present day horizon scale does modification at present day horizon scale does

not mean no modification under horizonnot mean no modification under horizon

structure formation is different from GR structure formation is different from GR

great opportunity to exploit future observationsgreat opportunity to exploit future observations

Build consistent modelsBuild consistent models

Structure formation is sensitive to underlying theoryStructure formation is sensitive to underlying theory

Build consistent theory (ghost free etc.)Build consistent theory (ghost free etc.)

Address fundamental questions (fine-tuning, coincidence)Address fundamental questions (fine-tuning, coincidence)