N-body simulations in f(R) gravity Kazuya Koyama University of - - PowerPoint PPT Presentation

Kazuya Koyama University of Portsmouth

N-body simulations in f(R) gravity

with Gong-bo Zhao (Portsmouth), Baojiu Li (Durham)

General picture of modified gravity models

 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

 Small scales (solar system)

GR is recovered

*

r

Modified gravity Scalar tensor GR

1

H 

Example – f(R) gravity

 Chameleon mechanism

suppress modification at high densities parameter

4

( ), ( ) S d x g f R f R   



2 2 2

1 4 2 1 8 ( ) 3 3

R R R

G f G f R f                

4

( ) 16

m

R f R S d x g L G           



( )

R

df R f dR 

( )

n R

R f R f R         

| |

R

f

: the fifth force

Behaviour of gravity

There regimes of gravity Understandings of non-linear clustering require N-body simulations Scalar tensor GR

GR "

"  

k

linear LCDM

P P 

z

eff

w

G 4G/3

Constraints on fR0

By Lucas Lombriser

N-body Simulations

 MLAPM code  ECOSMOG code (based on RAMSES)

Li, Zhao 0906.3880, Li, Barrow 1005.4231 Zhao, Li, Koyama 1011.1257 Li, Zhao, T eyssier, Koyama 1110.1379 Li et.al.

Snapshots at z=0

 If the fifth force is not suppressed, we have

Chameleon is working Fifth force is not suppressed

Snapshots

Chameleon is working Chameleon stops working Chameleon starts to hibernate

4

| | 10

R

f





Power spectrum (z=0)

full Non- Chameleon

4

| | 10

R

f





6

| | 10

R

f





5

| | 10

R

f





Zhao, Li, KK 1011.1257 Li, Hellwing, KK, Zhao, Jennings, Baugh 1206.4317

Velocity divergence

 redshift distorion

Power spectrum in redshift space become anisotropic

F4 linear GR linear F4 GR

( , ) ( ) ( ) P k P k L   

Linear enhancement Non-linear damping Jennings, Baugh, Li, Zhao, Koyama, 1205.2698 Li, Hellwing, KK, Zhao, Jennings, Baugh 1206.4317

Mass function

4

| | 10

R

f





5

| | 10

R

f





6

| | 10

R

f





full Non- Chameleon

 If Chameleon is not working, strong

gravity creates more and more heavy halos and the abundance of massive halos is enhanced

 Cluster abundance gives the tightest

constraint so far

 Chameleon works better for heavier

halos and it suppresses the abundance of large halos

4

| | 1.65 10

R

f



 

5

| | 10

R

f





Conclusion

 Modification of GR

generally introduce the fifth force, which should be screened 1) break equivalence principle and remove coupling to baryons

Einstein frame - interacting dark energy models 2) Environmentally (density) dependent screening Chameleon/Symmetron/dilaton models 3) Vainshtein mechanism massive gravity, Galileon models, braneworld models Non-linearity of the Poisson equation for the fifth force plays an essential role