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

2. Cosmic acceleration Cosmic acceleration Big surprise in cosmology
Simplest best fit model
LCDM
4D general relativity + cosmological const.

3. 3 independent data sets intersect

4. Problem of LCDM Huge difference in scales (theory vs observation)
vacuum energy =0 from fundamental theory
(1) tiny vacuum energy is left somehow
(2) Potential energy of quintessence field

5. Alternative models Tiny energy scale
unstable under quantum corrections
Alternative - modified gravity
dark energy is important only at late times
large scales / low energy modifications
cf.
from Newton to GR

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

7. Options Modify the Friedmann equation empirically or how to perturb?
Modify the Einstein-Hilbert action
cf.
(Freese, …)
(Dvali and Turner, …)
(Carol et.al., …)

8. Problems of IR modification
Modified gravity
graviton has a scalar mode
Solar system constraints - theory must be GR
cf.
difficult to explain dark energy purely from modified gravity
(Chiba)

9. DGP model Crossover scale 4D Newtonian gravity 5D Newtonian gravity
(Dvali, Gabadadze,Porrati)
Crossover scale
4D Newtonian gravity
5D Newtonian gravity
gravity leakage
Infinite extra-dimension

10. Consistent with local experiments?
DGP also has a scalar mode of graviton
:4D Newtonian but not 4D GR!
(Scalar-Tensor theory)
Non-linear shielding
theory becomes GR at
solar-system
constraints can be evaded if 5D ST GR 4D
(Deffayet et.al.)

11. Cosmology of DGP Friedmann equation early times 4D Friedmann
late times
As simple as LCDM model
and as fine-tuned as LCDM
(stability against quantum corrections can be different)
(Deffayet)

12. LCDM vs DGP Can we distinguish between DGP and LCDM ?
Friedmann equation
cf. LCDM

13. SNe + baryon oscillation
SNLS + SDSS ‘Gold’ set + SDSS
(Maartens and Majerotto in preperation)
(Fairbairn and Goobar astro-ph/ )
(cf. Alam and Sahni, astro-ph/ )

14. Why baryon oscillation?
angular diameter at z=0.3
+ shape parameter of power spectrum
K=0
equivalent to dark energy model with
(Lue.et.al) VS
(LCDM)

15. DGP Cosmology As simple as LCDM a falsifiable model
now the model is under pressure from the data
measurements of is crucial
Fit to SNe assuming flat universe
A parameter is fixed!

16. Dark energy vs DGP
Can we distinguish between dark energy in GR and DGP ?
DGP model is fitted by
DGP
(Linder)
Dvali and Turner

17. Cosmology as a probe of DGP gravity
Non-linear
linear
Einstein
Scalar tensor 4D 5D
CMB ISW
LSS
CMB
SNe
Weak lensing
Non-linear mapping
Growth rate
Expansion history

18. Growth rate of structure formation
Evolution of CDM over-density GR
If there is no dark energy
dark energy suppresses the gravitational collapse
DGP
an additional modification from the scalar mode

19. Expansion history vs growth rate
Growth rate resolves the degeneracy
(Lue.et.al, Linder)
LCDM
dark energy
DGP

20. Experiments ASSUME our universe is DGP braneworld
(Ishak et.al, astro-ph/ )
ASSUME our universe is DGP braneworld
but you do not want to believe this,
so fit the data using dark energy model
m(z):
apparent magnitude R:
CMB shift parameter
G(a):
Growth rate OR
SNe+CMB
SNe+weak lensing
Inconsistent!

21. Consistent 5D analysis of growth factor
KK and R.Maartens astro-ph/
Use correct 5D physics
growth rate is sensitive to truncation of 5D physics
Consistency in 5D physics
(1)
Analysis based on (2)
must be revisited
(1) Lue.et.al astro-ph/
(2) Song astro-ph/
LCDM
Dark energy

22. Solutions for metric perturbations
(Lue et.al, KK and R,Maartens)
Solutions for metric perturbations
Scalar tensor theory with Brans-Dick parameter

23. ISW effects and weak lensing
Growth rate is determined by
ISW effects and weak lensing effects depends on
the same as GR!
Difference comes from growth rate of

24. Einstein Scalar tensor 4D 5D Non-linear P(k) Large scale ISW
Need 5D solutions
Need non-linear mapping
Non-linear
linear
Einstein
Scalar tensor 4D 5D
CMB ISW
LSS
CMB
SNe
Weak lensing

25. Summary Alternative to LCDM from large scale modification
DGP model as an example
The model is already in tension with the data
Structure formation is different from GR
5D study of perturbations is crucial
cf. Theoretical difficulties of DGP model
strong coupling / a ghost in de Sitter spacetime
(Luty, Porrati, Rattazi) (Nicolis, Rattati; KK hep-th/
Gorbunov, KK, Sibiryakov; to appear)

26. Lessons from DGP Gravity is subtle
modification at present day horizon scale does
not mean no modification under horizon
structure formation is different from GR
great opportunity to exploit future observations
Build consistent models
Structure formation is sensitive to underlying theory
Build consistent theory (ghost free etc.)
Address fundamental questions (fine-tuning, coincidence)