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

N-body simulations in f(R) gravity Kazuya Koyama University of Portsmouth with Gong-bo Zhao (Portsmouth), Baojiu Li (Durham)

General picture of modified gravity models  Largest scales Modified H  1 gravity is modified so that the universe gravity 0 accelerates without dark energy r Scalar * tensor  Large scale structure scales gravity is still modified by a GR fifth force from scalar graviton  Small scales (solar system) GR is recovered

Example – f(R) gravity    ( ) R f R     4 S d x g L       4  ( ), ( ) 0 m S d x g f R  f R  16 G 1         2 2 4 G f R 2  1 8 ( ) df R G         2 ( ) f : the fifth force f R f R R R dR 3 3  Chameleon mechanism suppress modification at high densities n   R    0 ( )   f R f parameter | | f 0 R   R 0 R

Behaviour of gravity w eff There regimes of gravity   GR " " Scalar z tensor GR  P linear G 4G/3 P LCDM k Understandings of non-linear clustering require N-body simulations

Constraints on f R0 By Lucas Lombriser

N-body Simulations  MLAPM code Li, Zhao 0906.3880, Li, Barrow 1005.4231 Zhao, Li, Koyama 1011.1257  ECOSMOG code (based on RAMSES) 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

Chameleon Snapshots Chameleon starts Chameleon is working to hibernate stops working   4 | | 10 f 0 R

full Non- Power spectrum (z=0) Chameleon   4 | | 10 f 0 R   5 | | 10 f 0 R   6 | | 10 f 0 R Zhao, Li, KK 1011.1257 Li, Hellwing, KK, Zhao, Jennings, Baugh 1206.4317

Velocity divergence Li, Hellwing, KK, Zhao, Jennings, Baugh 1206.4317 Non-linear damping F4 linear GR linear Linear enhancement GR F4  redshift distorion Power spectrum in redshift space become anisotropic     ( , ) ( ) ( ) P k P k L Jennings, Baugh, Li, Zhao, Koyama, 1205.2698

full Non- Mass function Chameleon  If Chameleon is not working, strong   4 | | 10 f gravity creates more and more heavy 0 R halos and the abundance of massive halos is enhanced  Cluster abundance gives the tightest   5 | | 10 f R 0 constraint so far    4 | | 1.65 10 f 0 R   5 | | 10  f  6 | | 10 f 0 R 0 R  Chameleon works better for heavier halos and it suppresses the abundance of large halos

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