Large distance modification of gravity and dark energy Kazuya Koyama ICG, University of Portsmouth ICG, University of Portsmouth.
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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
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)
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