1. Institute of Cosmology and Gravitation, University of Portsmouth
Cosmological Tests of Modified Gravity
Kazuya Koyama
Institute of Cosmology and Gravitation,
University of Portsmouth
“Cosmological Tests of Modified Gravity” KK,
Report of Progress of Physics 79 (2016) no.4, , arXiv:

2. Cosmic acceleration
Many independent data sets indicate the expansion of the Universe is accelerating
Standard cosmology requires
70% of unknown ‘dark’ energy

3. Dark energy v Dark gravity
Cosmological constant is the simplest candidate
but the theoretical prediction is more than 50 orders of magnitude larger than the observed values
“Most embarrassing observation in physics”
Standard model of cosmology is based on GR
but we have never tested GR on cosmological scales
cf. precession of perihelion
dark planet v GR

4. Is cosmology probing breakdown of GR on large scales ?

5. Assuming GR Dark Matter Dark Energy curvature potential Curvature
Psaltis Living Rev. Relativity 11 (2008), 9
curvature
Grav Probe B
Hulse-Taylor
1 Rsun
Moon
Mercury
1 AU
potential
10 kpc
Curvature
10 Mpc
Dark Matter
Dark Energy
Gravitational potential

6. General Relativity Modified Gravity Screening mechanism
Grav Probe B
General Relativity
Hulse-Taylor
1 Rsun
Moon
Mercury
1 AU
Screening mechanism
Curvature
10 kpc
10 Mpc
Dark Matter
Cosmological tests of gravity
Modified Gravity
Gravitational potential

7. General picture Largest scales
gravity is modified so that the universe
accelerates without dark energy
Large scale structure scales
gravity is still modified by a
fifth force from scalar graviton
model independent tests of GR
Small scales (solar system)
GR is recovered
Modified gravity
Scalar tensor GR
Linear scales
Clifton, Ferreira, Padilla & Skordis Phys. Rept. 513 (2012) 1

8. Why we need screening mechanism?
Brans-Dicke gravity
quasi-static approximations (neglecting time derivatives)
: fifth force

9. Constraints on BD parameter
Solutions
PPN parameter
This constraint excludes any detectable modifications in cosmology

10. Screening mechanism Require screening mechanism to restore GR
recovery of GR must be environmental dependent
make the scalar short-ranged using (chameleon)
make the kinetic term large to suppress coupling to matter
using (dilaton/symmetron) or (k-mouflage)
(Vainshtein)
Break equivalence principle
remove the fifth force from baryons
(interacting DE models in Einstein frame)

11. Chameleon mechanism Scalar is coupled to matter
Depending on density, the mass can change
It is easier to understand the dynamics in Einstein frame

12. Chameleon mechanism
Khoury & Weltman astro-ph/

13. Thin shell condition
Khoury & Weltman astro-ph/
If the thin shell condition is satisfied, only the shell of the size contributes to the fifth force
Screening is determined by the gravitational potential of the object
Silvestri

14. Behaviour of gravity There regimes of gravity
Understandings of non-linear clustering require N-body simulations
where the non-linear scalar equation needs to be solved
In most models, the scalar mode obeys non-linear equations describing the transition from the scalar tensor theory on large scales to GR on small scales
Scalar tensor GR

15. N-body simulations GR Modified gravity models superposition of forces
the non-linear nature of the scalar field equation implies that the superposition rule does not hold
It is required to solve the non-linear scalar equation directly on a mesh
a computational challenge!
The breakdown of the superposition rule has interesting consequences

16. N-body Simulations for MG
Multi-level adaptive mesh refinement
solve Poisson equation using a linear Gauss-Seidel relaxation
add a scalar field solver using a non-linear Gauss Seidel relaxation
ECOSMOG Li, Zhao, Teyssier, KK JCAP1201 (2012) 051
MG-GADGET Puchwein, Baldi, Springel MNRAS (2013)
ISIS Llinares, Mota, Winther A&A (2014) 562 A78
DGPM, Schmidt PRD80,
Modified Gravity Simulations comparison project
Winther, Shcmidt, Barreira et.al. arXiv:

17. Where to test GR GR is recovered in high dense regions Scalar tensor
(we consider the chameleon mechanism here)
GR is recovered in high dense regions
GR is restored in massive dark matter halos
Environmental effects
Even if dark matter halo itself is small, if it happens to live near massive halos, GR is recovered
Using simulations, we can develop criteria to identify the places
where GR is not recovered
Scalar tensor GR
Zhao, Li, KK Phy. Rev. Lett. 107 (2011)

18. Environmental effects
Zhao, Li, Koyama
GR is recovered even in
small halos nearby big halos
Large bubbles =better screened (GR is recovered)

19. Environmental dependence
Difference between lensing and dynamical mass
environment:
O(1) difference
no difference
O(1) difference
no difference

20. Testing chameleon gravity
Outskirt of clusters
Terukina. et.al. PRD , JCAP
48 X-ray clusters from XCS compared with
lensing (shear) from CFHTLS
Dynamical mass can be inferred from X-ray and SZ
Wilcox et.al ,

21. Creating a screening map
It is essential to find places where GR is not recovered
Small galaxies in underdense regions
SDSS galaxies within 200 Mpc
Cabre, Vikram, Zhao, Jain, KK
JCAP (2012) 034
(we consider the chameleon mechanism here)
GR is recovered

22. Tests of chameleon gravity
dwarf galaxies in voids
strong modified gravity effects
Galaxies are brighter
Cerpheid periods change
Various other tests
Jain & VanderPlas JCAP 1110 (2011) 032
Davis et.al. Phys. Rev. D85
(2012)
Jain et.al. ApJ 779 (2013) 39
Vikram et.al. JCAP1308
(2013) 020
Hui, Nicolis & Stubbs Phys. Rev. D80 (2009)

23. Constraints on chameleon gravity
Non-linear regime is powerful for constraining chameleon gravity
Astrophysical tests could give better constraints than the solar system tests and can be done by “piggybacking” ongoing surveys
Jain et.al
Interaction range of the extra force that modifies GR in the cosmological background GR

24. Summary
In the next decade, we may be able to detect the failure of GR on cosmological scales
Linear scales
model independent tests of gravity
Non-linear scales
novel astrophysical tests of gravity
(in a model dependent way)
It is required to develop theoretical models from fundamental theory
SUMIRE
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