Nonlinear Probes of Screening Mechanisms in Modified Gravity

Transcription

1 Nonlinear Probes of Screening Mechanisms in Modified Gravity David F. Mota Institute for Research in Fundamental Sciences IPM-Tehran 2016

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3 Structure formation in GR

4 Structure formation in f(r)

5 Chameleon f(r)-gravity Hu & Sawicki (2007) Effective potential (Einstein frame) Free parameters f R0,n

6 Hinterbichler & Khoury (2010) The Symmetron S = Z d 4 x p g apple R 16 G 1 2 (@')2 V (') + S m ( g µ, ) Effective potential Free parameters Range Symmetry breaking Coupling strength

7 Structure formation probes deviations from GR f(r) GR Llinares, DFM & Winther, ApJ

8 Snapshots at z=0 If the fifth force is not suppressed, we have Fifth force is not suppressed Fifth Force not suppressed Chameleon is working Compton wavelength is short Compton wavelength short

9 Snapshots at z=0 If the fifth force is not suppressed, we have Fifth force is not suppressed Fifth Force not suppressed Chameleon is working Chameleon working Compton wavelength is short Chameleon not working

10 Time evolution full screen no screen 10 f R 0 4

11 Structure formation dependence on coupling and range tronger coupling -> bigger deviations from LCDM Larger range -> large scale deviations from LCDM r r Short range Long range Scales larger than Compton wavelength: recovers GR Llinares, DFM & Winther, ApJ

12 Structure formation dependence on the screening scale critical scale Chameleon screening Symmetron screening screening at high densities screening at high densities screening at low densities screening at low densities screening at high densities => deviations from GR easier to detect Gronke, Llinares, DFM, A&A

13 Probing the critical screening density with Tomography critical scale screening at low densities screening at high densities Screening at higher densities => fifth force acts for longer time Llinares, DFM & Winther, ApJ

14 Large scale observables are not ideal to probe Screening Mechanisms

15 Fifth Force in a galaxy cluster Screened Unscreened

16 Probing Screening Mechanisms Lensing Mass vs. Dynamical Mass

17 Mass measured via gravitational lensing Conformal Invariance: photons not affected by Modified Gravity Lensing Mass in (conformal) Modified Gravity same as GR

18 Lensing'Mass'' COSMO12,'Beijing'China' September'13,'2012'

19 Lensing'Mass'' COSMO12,'Beijing'China' September'13,'2012'

20 Lensing'Mass'' Spherical symmetry COSMO12,'Beijing'China' September'13,'2012'

21 Mass measured via dynamics M D = F N + F a Modified Gravity enhances mass inferred via dynamical methods

22 Structure formation in f(r) s

23 Dynamical)Mass)) COSMO12,)Beijing)China) September)13,)2012)

24 Dynamical)Mass)) COSMO12,)Beijing)China) September)13,)2012)

25 Dynamical)Mass)) Spherical symmetry COSMO12,)Beijing)China) September)13,)2012)

26 Mass Difference In GR, Δ M = 0 In MG, Δ M [0,1/ 3] COSMO12, Beijing China September(13,(2012(

27 Modified Gravity with Screening Mechanisms: Dynamical mass depends on position in environment Screened Unscreened Dynamical mass is same in GR Dynamical mass differs from GR Dynamical Mass depends on distance to high/low dense environment

28 Modified Gravity with Screening Mechanisms: Dynamical Mass depends on size of cluster Dynamical Mass same as in GR Dynamical Mass differs from GR Dynamical Mass depends on size/density of cluster

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30 In underdense environment

31 In underdense environment

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33 In dense environment

34 In dense environment The halos are screened so that they cannot feel the enhancement of gravity!

35 Smoking gun for Screening Mechanisms Lensing Mass vs. Environmental dependent Dynamical Mass Lensing Mass same as in GR Dynamical Mass depends on environment GR : M =0 M M D M L 1 F (R) : M 2 [0, 1 3 ] Chameleon/Symmetron : M 2 [0, 2 2 ]

36 dynamical vs. lensing masses of halos in clusters M M D M L 1 f(r) Max deviation Winther, DFM, Li ApJ ; Zhao, Li, Koyama ;

37 dynamical vs. lensing masses of halos in clusters Fifth force not screened M M D M L 1 f(r) Max deviation Winther, DFM, Li ApJ ; Zhao, Li, Koyama ;

38 dynamical vs. lensing masses of halos in clusters M M D M L 1 f(r) Max deviation Max screening Core screened Winther, DFM, Li ApJ ; Zhao, Li, Koyama ;

39 Dynamical vs. Lensing masses Position in the cluster M M D 1 M L Screened purely by environment f(r) Max deviation Winther, DFM, Li ApJ ; Zhao, Li, Koyama ;

40 Dynamical vs. Lensing masses Position in the cluster M M D M L 1 f(r) Max deviation Radial screening environmental dependence! Winther, DFM, Li ApJ ; Zhao, Li, Koyama ;

41 V eff HfL Screened V eff HfL Unscreened! f f Symmetron Unique Feature

42 V eff HfL V eff HfL f Symmetron Domain Walls f Llinares & DFM, PRL

43 Probing Symmetron Unique Signature Domain Walls have a small impact (P full -P static )/P static k (h/mpc) Llinares & DFM, PRL

44 Modified Gravity leads to time variations of the coupling constants Screening Mechanisms imply variations occur in both time and space

45 Variations of fine structure constant in both time and space z = 0 (Symmetron case) z = 1 z = 2 Silva, Winther, DFM, Martins, PRD

46 Signatures may be detected via spectroscopic measurements (ALMA and ELT-HIRES) model E Model A Model C Model E model C 0.5 P α (k) (10-5 β γ 2 ) 2 (Mpc/h) k (h/mpc) model A 0.66 Silva, Winther, DFM, Martins, PRD

47 Gravitational redshift photons climbing out of the potential well of the cluster are redshifted Measurement of (r)

48 Cluster of galaxies Gravitational redshift of a cluster Gravitational redshift of a cluster for CDM -2 v (km s 1 ) ( )M h 1 ( )M h 1 ( )M h 1 ( )M h 1 NFW fit R in Mpc/h! Same for all models & parameters and use relative deviation 11

49 Cluster of galaxies Gravitational redshift of a cluster 12 Expected results CDM < mod expected ====) (Relative deviation) v g,mod v g, CDM 1 > 0

50 Gravitational redshift measurements simple expectation without screening Wojtak et al. (2011)

51 Discussion & conclusions 20 The three screening regimes Full screening! v g v g, CDM fofr4 fofr5 fofr6 fofr4~24 Mpc fofr5~7 Mpc fofr6~2 Mpc

52 Discussion & conclusions 20 The three screening regimes No screening! v g > v g, CDM fofr4 fofr5 fofr6

53 Discussion & conclusions 20 The three screening regimes Partial screening! v g < v g, CDM fofr4 fofr5 fofr6

54 Discussion & conclusions The three screening regimes Full screening! v g v g, CDM fofr4 fofr5 fofr6 fofr4~24 Mpc fofr5~7 Mpc fofr6~2 Mpc Gronke, DFM, Winter, A&A 20

55 Discussion & conclusions The three screening regimes No screening! v g > v g, CDM fofr4 fofr5 fofr6 fofr4~24 Mpc fofr5~7 Mpc fofr6~2 Mpc Gronke, DFM, Winter, A&A 20

56 Discussion & conclusions The three screening regimes Partial screening fofr4 fofr5 fofr6! v g < v g, CDM fofr4~24 Mpc fofr5~7 Mpc fofr6~2 Mpc Gronke, DFM, Winter, A&A 20

57 Discussion & conclusions The three screening regimes Overview Full screening! v g v g, CDM No screening! v g > v g, CDM Partial screening! v g < v g, CDM Gronke, DFM, Winter, A&A fofr4 fofr5 fofr6 21

58 Summary } Modified Gravity affects structure formation both in the linear and the nonlinear regime } Effects are stronger within the fifth force range and proportional to the coupling: } Screening mechanisms to recover GR play a crucial role on the nonlinear regime } The power spectrum tends to go back to the one in GR with the same expansion history } Details of the recovery of GR depend on screening mechanisms } It is crucial to distinguish among screening mechanisms } Global observables may not do the job } Only local observables and environmental dependence can probe the differences