Questioning Λ: where can we go?

Transcription

1 Instut für Theoretische Physik - University of Heidelberg Refs: JCAP 1210 (2012) 009, Phys.Rev. D87 (2013) ,

2 New Physics from Cosmology Cosmic microwave Background δt/t 10 6 Cosmic Inflation Large scale structure Dark Matter ρ DM 5 ρ SM Acceleration small Λ G 1 Probes complementary and consistent 3 exotic ingredients revise basic assumptions

3 The Standard Cosmological Model Theory of Gravity R g 16πG

4 The Standard Cosmological Model Metric Ansatz dt 2 + a(t) 2 d x 2 Theory of Gravity R g 16πG

5 The Standard Cosmological Model Metric Ansatz dt 2 + a(t) 2 d x 2 Standard Matter Theory of Gravity R g 16πG

6 The Standard Cosmological Model Initial Conditions Inflation Metric Ansatz dt 2 + a(t) 2 d x 2 Standard Matter Theory of Gravity R g 16πG

7 The Standard Cosmological Model Initial Conditions Inflation Structure formation Dark Matter Metric Ansatz dt 2 + a(t) 2 d x 2 Standard Matter Theory of Gravity R g 16πG

8 The Standard Cosmological Model Initial Conditions Inflation Structure formation Dark Matter Acceleration Λ Metric Ansatz dt 2 + a(t) 2 d x 2 Standard Matter Theory of Gravity R g 16πG

9 Why and How The BAO scale in LTB universes Why inhomogeneous cosmologies?

10 Why and How The BAO scale in LTB universes Precision Cosmology 3 Precission Goals: Search for surprises Gain confidence on the results Model independence 2 1 No Big Bang SC P HZSNS accelerating decelerating The case for Λ: - Ω Λ 0 in flat-frw - w = 1 in flat-frw - w = 1 in curved-frw - Ω Λ 0 for non-frw? 0-1 closed flat open expands forever recollapses eventually Goobar & Leibundgut

11 Why and How The BAO scale in LTB universes Post Planck Cosmology Precission Goals: Search for surprises Gain confidence on the results Model independence ESA and the Planck Collaboration Great support for ΛCDM model, but - Minor discrepancies: H 0 local void (Marra et al. PRL 13) - Anomalies (i.e. statistical anisotropy) fluctuations? include in the model

12 Why and How The BAO scale in LTB universes Spherical Symmetry LTB The Lemaitre-Tolman-Bondi metric (p = 0) ds 2 = dt 2 + A 2 (r, t) 1 k(r) dr2 + A 2 (r, t) dω 2 Two expansion rates: H R = A /A Matter/curvature profile k(r) Ω M (r) A/A = H T

13 Why and How The BAO scale in LTB universes Spherical Symmetry LTB The Lemaitre-Tolman-Bondi metric (p = 0) ds 2 = dt 2 + A 2 (r, t) 1 k(r) dr2 + A 2 (r, t) dω 2 Two expansion rates: H R = A /A Matter/curvature profile k(r) Ω M (r) A/A = H T Expansion rate H 0 (r) time to big-bang t BB (r) t BB (r) = t 0 homogeneous state at early times

14 Why and How The BAO scale in LTB universes Spherical Symmetry LTB The Lemaitre-Tolman-Bondi metric (p = 0) ds 2 = dt 2 + A 2 (r, t) 1 k(r) dr2 + A 2 (r, t) dω 2 Two expansion rates: H R = A /A Matter/curvature profile k(r) Ω M (r) A/A = H T Expansion rate H 0 (r) time to big-bang t BB (r) t BB (r) = t 0 homogeneous state at early times Observations on ds 2 = 0 mix time & space variations time acceleration spatial variation CMB isotropy Central location r 0 ± 10Mpc

15 Why and How The BAO scale in LTB universes A non-copernican void model

16 Why and How The BAO scale in LTB universes A non-copernican void model Can t prove models right we have to disprove alternatives and find observational answers Cosmological Justice: judge models by the facts

17 Why and How The BAO scale in LTB universes Observations in LTB universes, constant t 0 constant Ρ 12 constant t z t Gyr 6 t z Homogeneous state at early times, large r t z CMB z 1100

18 Why and How The BAO scale in LTB universes Observations in LTB universes, constant t 0 12 We are here constant Ρ constant t z t Gyr 6 t z t z CMB z 1100

19 Why and How The BAO scale in LTB universes Observations in LTB universes, constant t 0 We are here r Gpc t Gyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Ia SNe z 1.5

20 Why and How The BAO scale in LTB universes Observations in LTB universes, constant t 0 We are here r Gpc t Gyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Ia SNe z 1.5 BAO z 0.8

21 Why and How The BAO scale in LTB universes Observations in LTB universes, constant t 0 We are here r Gpc t Gyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Ia SNe z 1.5 BAO z 0.8 Relate to early time and asymptoticvalue

22 Why and How The BAO scale in LTB universes Baryon acoustic oscillations - Standard Rulers -Sound waves in the baryon-photon plasma travel a finite distance -Initial baryon clumps more galaxies -Statistical standard ruler

23 Why and How The BAO scale in LTB universes Baryon acoustic oscillations - Standard Rulers -Sound waves in the baryon-photon plasma travel a finite distance -Initial baryon clumps more galaxies -Statistical standard ruler LTB: Do these clumps/galaxies move? Geodesics [ k r + 2(1 k) + A A ] ṙ 2 A + 2 A ṫṙ = 0 ṫ ṙ Constant coordinate separation (zero order) Supported by N-body simulations (Alonso et al ) and Linear PT (February et al )

24 Why and How The BAO scale in LTB universes Physical BAO scale Early Coordinate BAO scale Coordinates distances: g rr = A 2 (r,t) 1 k(r)r 2, g θθ = A 2 (r, t) Physical BAO scales l R (r, t) = A (r, t) A (r, t e ) l early l A (r, t) = A(r, t) A(r, t e ) l early l early = early physical BAO scale at t e LTB: evolving (t), inhomogeneous (r) and anisotropic l A l R

25 Why and How The BAO scale in LTB universes Observed BAO scale Early Coordinate Physical BAO scale Geometric mean d ( δθ 2 δz ) 1/3 δθ = l A(z) D A (z), δz = (1 + z)h R(z) l R (z) Compare with FRW: d LTB (z) ξ(z) d FRW (z) Rescaling: ξ(z) = (ξ 2 A ξ R) 1/3 Ξ z Radial rescaling ΞR Geom. Average Ξ T 2 ΞR 1 3 Transverse rescaling ΞT 1.0 Inhomogeneous, anisotropic z

26 Why and How The BAO scale in LTB universes Data and models We are here r Gpc t Gyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Ia SNe z 1.5 BAO z GBH model (6 param) - WiggleZ + SDSS + 6dF - Union 2 Compilation - H 0 luminosity prior - CMB peaks information (simplified analysis)

27 Why and How The BAO scale in LTB universes GBH + Homogeneous BB + asymptotically flat Uncalibrated candles & rulers: SNe Ω in 0.1 BAO Ω in 0.3 Ω M (0) 3σ discrepant! Adding calibration: SNe+H0 h in 0.74 BAO+CMB h in 0.62 worse using full CMB! Asymptotically open not any better

28 Why and How The BAO scale in LTB universes Tension in the Void - Bad fit to SNe and BAO Geom. Average Ξ T 2 Ξ R LTB Strongly ruled out! SNe: measure distance BAO: distance + rescaling Ξ z Radial rescaling Ξ R Transverse rescaling Ξ T z

29 Why and How The BAO scale in LTB universes Tension in the Void - Bad fit to SNe and BAO Geom. Average Ξ T 2 Ξ R LTB Strongly ruled out! SNe: measure distance BAO: distance + rescaling Ξ z Radial rescaling Ξ R Transverse rescaling Ξ T z Other problems of LTB models with Λ = 0: H0: CMB vs Local - Moss et al 10 ksz bounds - Zhang & Stebbins 10 Standard clocks - De Putter et al 12 Geometrical result, whatever Luminosity & BAO scale Standard Rulers vs Standard Candles

30 Most general scalar-tensor theory May the Force not be with you The Standard Cosmological Model Initial Conditions Structure formation Acceleration Inflation Dark Matter Λ Metric Ansatz Standard Matter Theory of Gravity dt 2 + a(t) 2 d x 2 R g 16πG

31 Most general scalar-tensor theory May the Force not be with you Why alternative gravities? Inflation again? Einstein s gravity not final: QG surprises at low energy? Classical Λ tuning: EW phase transition Test gravity on cosmological scales Focus: Most general theory? Compatible with Local Gravity tests? Other: Acceleration, make Λ small, cosmological signatures...

32 Most general scalar-tensor theory May the Force not be with you What is the most general theory of gravity? (that deserves our attention)

33 Most general scalar-tensor theory May the Force not be with you Ostrogradski s Theorem (1850) Theories with L n q, n 2 are unstable tn L(q(t), q, q) L q d L dt q + d2 L dt 2 q q, q, q,... q Q 1, Q 2, P 1, P 2 = 0 H = P 1 Q 2 + terms independent of P 1 Assumes... q, q P 2, Q 2

34 Most general scalar-tensor theory May the Force not be with you Ostrogradski s Theorem (1850) Theories with L n q, n 2 are unstable tn L(q(t), q, q) L q d L dt q + d2 L dt 2 q q, q, q,... q Q 1, Q 2, P 1, P 2 = 0 H = P 1 Q 2 + terms independent of P 1 Assumes... q, q P 2, Q 2

35 Most general scalar-tensor theory May the Force not be with you Ostrogradski s Theorem (1850) Theories with L n q, n 2 are unstable tn L(q(t), q, q) L q d L dt q + d2 L dt 2 q q, q, q,... q Q 1, Q 2, P 1, P 2 = 0 H = P 1 Q 2 + terms independent of P 1 Assumes... q, q P 2, Q 2 loophole for Degenerate Theories: 2 nd order equations Implicit constraints / reduced phase space

36 Most general scalar-tensor theory May the Force not be with you Lovelock s Theorem (1971) g µν + Local + 4-D + Lorentz Theory with 2 nd order Eqs. Add a scalar field φ: g 1 16πG (R 2Λ) + gl m (g µν, ψ M ) simple, isotropic seem to exist arise in other theories (e.g. extra dimensions) Jordan-Brans-Dicke R φr Modify Einstein-Hilbert action Bekenstein g µν φg µν Modify the metric in L m

37 Most general scalar-tensor theory May the Force not be with you Horndeski s Theory (1974) g µν + φ + Local + 4-D + Lorentz Theory with 2 nd order Eqs. L H = G 2 (X, φ) G 3 (X, φ) φ +G 4 R + G 4,X [ ( φ) 2 φ ;µν φ ;µν] + G 5 G µν φ ;µν G [ ] 5,X ( φ) 3 3( φ)φ ;µν φ ;µν + 2φ ;µ ;ν φ ;ν ;λ φ ;µ 6 ;λ 4 free functions of φ, X 1 2 φ,µφ,µ Jordan-Brans-Dicke: G 4 = φ 16πG, G 2 = X ω(φ) V (φ)

38 Most general scalar-tensor theory May the Force not be with you Horndeski s Theory (1974) g µν + φ + Local + 4-D + Lorentz Theory with 2 nd order Eqs. L H = G 2 (X, φ) G 3 (X, φ) φ +G 4 R + G 4,X [ ( φ) 2 φ ;µν φ ;µν] + G 5 G µν φ ;µν G [ ] 5,X ( φ) 3 3( φ)φ ;µν φ ;µν + 2φ ;µ ;ν φ ;ν ;λ φ ;µ 6 ;λ 4 free functions of φ, X 1 2 φ,µφ,µ Jordan-Brans-Dicke: G 4 = φ 16πG, G 2 = X ω(φ) V (φ) Kinetic Gravity Braiding - Deffayet et al. JCAP 2010

39 Most general scalar-tensor theory May the Force not be with you Horndeski s Theory (1974) g µν + φ + Local + 4-D + Lorentz Theory with 2 nd order Eqs. L H = G 2 (X, φ) G 3 (X, φ) φ +G 4 R + G 4,X [ ( φ) 2 φ ;µν φ ;µν] + G 5 G µν φ ;µν G [ ] 5,X ( φ) 3 3( φ)φ ;µν φ ;µν + 2φ ;µ ;ν φ ;ν ;λ φ ;µ 6 ;λ 4 free functions of φ, X 1 2 φ,µφ,µ Jordan-Brans-Dicke: G 4 = φ 16πG, G 2 = X ω(φ) V (φ) Kinetic Gravity Braiding - Deffayet et al. JCAP 2010 Deriv. couplings G 4 (X)

40 Most general scalar-tensor theory May the Force not be with you Horndeski s Theory (1974) g µν + φ + Local + 4-D + Lorentz Theory with 2 nd order Eqs. L H = G 2 (X, φ) G 3 (X, φ) φ +G 4 R + G 4,X [ ( φ) 2 φ ;µν φ ;µν] + G 5 G µν φ ;µν G [ ] 5,X ( φ) 3 3( φ)φ ;µν φ ;µν + 2φ ;µ ;ν φ ;ν ;λ φ ;µ 6 ;λ 4 free functions of φ, X 1 2 φ,µφ,µ Jordan-Brans-Dicke: G 4 = φ 16πG, G 2 = X ω(φ) V (φ) Kinetic Gravity Braiding - Deffayet et al. JCAP 2010 Deriv. couplings G 4 (X), G 5 0

41 Most general scalar-tensor theory May the Force not be with you Disformal Relation - Bekenstein (PRD 1992) Matter sector gl m ( g µν,...) with g µν = C(X, φ)g µν +D(X, φ)φ,µ φ,ν }{{}}{{} conformal disformal 2 nd order eqs. X = 1 2 ( φ)2 L H C,X,D,X =0 L H C,X,D,X 0 L H C,X, D,X 0 non-horndeski!

42 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0

43 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 2Ω(g µν Ω Ω ;µν ) + Ω 2 G µν g µν Ω,α Ω,α + 4Ω,µ Ω,ν (ΩR 6 Ω)Ω,X φ,µ φ,ν = 8πGT µν

44 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 Take trace with g µν : 2Ω(g µν Ω Ω ;µν ) + Ω 2 G µν g µν Ω,α Ω,α + 4Ω,µ Ω,ν (ΩR 6 Ω)Ω,X φ,µ φ,ν = 8πGT µν

45 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 Take trace with g µν : 2Ω(3 Ω) + Ω 2 G µν g µν Ω,α Ω,α + 4Ω,µ Ω,ν (ΩR 6 Ω)Ω,X φ,µ φ,ν = 8πGT µν

46 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 Take trace with g µν : 2Ω(3 Ω) + Ω 2 ( R) g µν Ω,α Ω,α + 4Ω,µ Ω,ν (ΩR 6 Ω)Ω,X φ,µ φ,ν = 8πGT µν

47 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 Take trace with g µν : 2Ω(3 Ω) + Ω 2 ( R) 0 (ΩR 6 Ω)Ω,X φ,µ φ,ν = 8πGT µν

48 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 Take trace with g µν : 2Ω(3 Ω) + Ω 2 ( R) 0 (ΩR 6 Ω)Ω,X ( 2X) = 8πGT µν

49 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 Take trace with g µν : 2Ω(3 Ω) + Ω 2 ( R) 0 (ΩR 6 Ω)Ω,X ( 2X) = 8πGT

50 Most general scalar-tensor theory May the Force not be with you Pure conformal: g µν = C(X, φ)g µν = Ω 2 R + 6Ω,α Ω,α ( µ (ΩR 6 Ω)Ω,X φ,µ) + Ω,φ (ΩR 6 Ω) + 1 δl φ 2 δφ = 0 Take trace with g µν : 2Ω(3 Ω) + Ω 2 ( R) 0 (ΩR 6 Ω)Ω,X ( 2X) = 8πGT Implicit Constraint - MZ, García-Bellido (ΩR 6 Ω) = 8πGΩ,XT Ω 2Ω,X X T K φ Trace of metric eqs solves high derivs!

51 Most general scalar-tensor theory May the Force not be with you Implicit Constraint - MZ, García-Bellido T K 8πGΩ,XT Ω 2Ω,X X = (ΩR 6 Ω) Scalar Field eqs: µ (φ,µ T K ) + Ω,φ T K 1 δl φ Ω,X 2 δφ = 0 Metric eqs: δl δg µν g µν Ω Ω ;µν = g kα Ω ;kα Ω ;0i Ω ;0i g ij Ω Ω ;ij No higher time derivatives in Jordan frame

52 Most general scalar-tensor theory May the Force not be with you How to satisfy local gravity tests?

53 Most general scalar-tensor theory May the Force not be with you Scalar-tensor theories scalar mediated force Point Particle, coupled to g µν [φ]: ẍ α = ( Γ α µν + Kµν α )ẋµẋ ν }{{} γ αλ ( (µ γ ν)λ 1 2 λγ µν) F i φ f[φ] i φ + O(v i /c)

54 Most general scalar-tensor theory May the Force not be with you Subtle the Force can be F i φ f[φ] i φ You must feel the Force around you; here, between you, me, the tree, the rock, everywhere, yes Master Yoda

55 Most general scalar-tensor theory May the Force not be with you Subtle the Force can be F i φ f[φ] i φ You must feel the Force around you; here, between you, me, the tree, the rock, everywhere, yes Master Yoda Screening Mechanisms F φ F G { ρ 1 when ρ0 r H 1 0

56 Most general scalar-tensor theory May the Force not be with you May the force not be with you ρ ρ 0 Chameleon Screening - Khoury & Weltman (PRL 2004) Yukawa force: φ 1 r e φ/m φ with m φ (ρ) increases with ρ (see also Symmetron - Pietroni PRD 05, Hinterbichler Khoury PRL 10)

57 Most general scalar-tensor theory May the Force not be with you May the force not be with you ρ ρ 0 Chameleon Screening - Khoury & Weltman (PRL 2004) Yukawa force: φ 1 r e φ/m φ with m φ (ρ) increases with ρ (see also Symmetron - Pietroni PRD 05, Hinterbichler Khoury PRL 10) r H 0 1 Vainshtein Screening - Vainshtein (PLB 1972) L ( φ) + φx/m 2 + αφt m Non-linear derivative interactions φ + m ( 2 ( φ) 2 φ ;µνφ ;µν) = αmδ(r) φ { r 1 if r r V r if r rv Vainshtein radius r V (GM/m 2 ) 1/3

58 Most general scalar-tensor theory May the Force not be with you May the force not be with you ρ ρ 0 Chameleon Screening - Khoury & Weltman (PRL 2004) Yukawa force: φ 1 r e φ/m φ with m φ (ρ) increases with ρ (see also Symmetron - Pietroni PRD 05, Hinterbichler Khoury PRL 10) r H 0 1 Vainshtein Screening - Vainshtein (PLB 1972) L ( φ) + φx/m 2 + αφt m Non-linear derivative interactions φ + m ( 2 ( φ) 2 φ ;µνφ ;µν) = αmδ(r) φ { r 1 if r r V r if r rv Vainshtein radius r V (GM/m 2 ) 1/3

59 Most general scalar-tensor theory May the Force not be with you May the force not be with you ρ ρ 0 Chameleon Screening - Khoury & Weltman (PRL 2004) Yukawa force: φ 1 r e φ/m φ with m φ (ρ) increases with ρ (see also Symmetron - Pietroni PRD 05, Hinterbichler Khoury PRL 10) r H 0 1 Vainshtein Screening - Vainshtein (PLB 1972) L ( φ) + φx/m 2 + αφt m Non-linear derivative interactions φ + m ( 2 ( φ) 2 φ ;µνφ ;µν) = αmδ(r) φ { r 1 if r r V r if r rv Vainshtein radius r V (GM/m 2 ) 1/3

60 Most general scalar-tensor theory May the Force not be with you Einstein gravity + disformal coupling L EF = ( ) R g 16πG + L φ + gl M ( g µν, ψ) g µν = C(φ)g µν + D(φ)φ,µ φ,ν G µν = 8πG(T µν m + T µν φ ) Matter-field interaction: µ T µν m = Qφ,ν

61 Most general scalar-tensor theory May the Force not be with you Einstein gravity + disformal coupling L EF = ( ) R g 16πG + L φ + gl M ( g µν, ψ) g µν = C(φ)g µν + D(φ)φ,µ φ,ν G µν = 8πG(T µν m + T µν φ ) Matter-field interaction: µ T m µν = Qφ,ν Q = D ( ) C µ (T m µν φ,ν ) C D 2C T m + 2C DC C 2 φ,µ φ,ν T m µν Kinetic mixing Conformal Disformal

62 Most general scalar-tensor theory May the Force not be with you Consequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2012) Static matter ρ( x) + non-rel. p = 0 [ ] Dρ 1 + φ + F( φ C 2DX,µ, φ,µ, ρ) = 0

63 Most general scalar-tensor theory May the Force not be with you Consequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2012) Static matter ρ( x) + non-rel. p = 0 [ ] Dρ 1 + φ + F( φ C 2DX,µ, φ,µ, ρ) = 0 Disformal Screening Mechanism φ D 2D φ 2 + C ( φ2 C 1 2D ) (If Dρ )

64 Most general scalar-tensor theory May the Force not be with you Consequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2012) Static matter ρ( x) + non-rel. p = 0 [ ] Dρ 1 + φ + F( φ C 2DX,µ, φ,µ, ρ) = 0 Disformal Screening Mechanism φ D 2D φ 2 + C ( φ2 C 1 2D φ( x, t) independent of ρ( x) and i φ ) (If Dρ ) No φ between massive bodies No fifth force!

65 Most general scalar-tensor theory May the Force not be with you Consequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2012) Static matter ρ( x) + non-rel. p = 0 [ ] Dρ 1 + φ + F( φ C 2DX,µ, φ,µ, ρ) = 0 Disformal Screening Mechanism φ D 2D φ 2 + C ( φ2 C 1 2D φ( x, t) independent of ρ( x) and i φ ) (If Dρ ) No φ between massive bodies No fifth force! Signatures: fast matter, pressure, strong gravity, cosmic gradients

66 Most general scalar-tensor theory May the Force not be with you Kinetic Screening mechanisms: Vainshtein screening: within r V (GM/m 2 ) 1/3 Disformal coupling + canonical field φ + Q µνδt m µν C + D(φ,r ) 2 = 0 { asymptotic φ = S r breaks down at r V = ( ) DS 2 1/4 C Different screening mechanisms - MZ, Koivisto, Mota - PRD 2013 D > 0 stable disformal screening, complex r V D < 0 Positive r V, but unstable (if canonical)

67 Most general scalar-tensor theory May the Force not be with you Scalar-tensor Generations Jordan-Brans-Dicke Horndeski Implicit Constraints

68 The Standard Cosmological Model Initial Conditions Inflation Structure formation Dark Matter Acceleration Λ Metric Ansatz dt 2 + a(t) 2 d x 2 Standard Matter Theory of Gravity R g 16πG

69 Conclusions Model independence & cosmological justice Spherically symmetric models without Λ don t work (perhaps if very involved) Scalar-tensor gravity as alternative to Λ: can mimick Einstein s locally through screening Vainshten & disformal: related but different and have cosmological effects Ostrogradski s theorem understand all the alternatives 3 theoretical generations

70 Backup Slides

71 Disformally Related Theories - MZ, Koivisto, Mota (PRD 2013) γ µν = C(φ)g µν + D(φ)φ,µ φ,ν Einstein Frame: L EF = gr[g µν ] + gl M ( g µν, ψ) Einstein D matter g µν g µν D C φ,µφ,ν g µν C 1 g µν Galileon g µν 1 C g µν D C φ,µφ,ν Disformal D gravity Jordan Jordan Frame: L JF = gr[ g µν ] + gl M (g µν, ψ)

72 Disformally Related Theories - MZ, Koivisto, Mota (PRD 2013) γ µν = C(φ)g µν + D(φ)φ,µ φ,ν Einstein Frame: L EF = gr[g µν ] + gl M ( g µν, ψ) Einstein D matter g µν g µν D C φ,µφ,ν g µν C 1 g µν Galileon g µν 1 C g µν D C φ,µφ,ν Disformal D gravity Jordan Jordan Frame: L JF = gr[ g µν ] + gl M (g µν, ψ)

73 Disformally Related Theories - MZ, Koivisto, Mota (PRD 2013) γ µν = C(φ)g µν + D(φ)φ,µ φ,ν Einstein Frame: L EF = gr[g µν ] + gl M ( g µν, ψ) Einstein D matter g µν g µν D C φ,µφ,ν g µν C 1 g µν Galileon g µν 1 C g µν D C φ,µφ,ν Disformal D gravity Jordan Jordan Frame: L JF = gr[ g µν ] + gl M (g µν, ψ)

74 Disformally Related Theories - MZ, Koivisto, Mota (PRD 2013) γ µν = C(φ)g µν + D(φ)φ,µ φ,ν Einstein Frame: L EF = gr[g µν ] + gl M ( g µν, ψ) Einstein D matter g µν g µν D C φ,µφ,ν g µν C 1 g µν Galileon g µν 1 C g µν D C φ,µφ,ν Disformal D gravity Jordan Jordan Frame: L JF = gr[ g µν ] + gl M (g µν, ψ)

75 Disformal screening - assumptions: Static t ρ = 0, Pressureless Dp < X C 2DX ( Neglect p ρ, p φ ) 2 ρ tφ, X Dρ, X Dρ V / φ, Γ µ 00 φ,µ/ φ 0 Potential Signatures: Matter velocity flows: T 0i v/c Binary pulsars? Pressure: effects on radiation Strong gravitational fields: Γ µ 00 φ,µ Compact objects? Frozen cosmic gradients: Evolution independent of i φ

76 Properties of the Field Equation Canonical scalar field L φ = X V, solve for φ M µν µ ν φ + C C 2DX Q µνt µν m V = 0 M µν g µν D T m µν ( C 2DX, Q µν C C 2C g D µν + C 2 D 2C Coupling to (Einstein F) perfect fluid T µ ν = diag(ρ, p, p, p) M 0 0 = 1 + M i i = 1 Dρ C 2DX, D, ρ > 0 no ghosts ) φ,µ φ,ν Dp C 2DX, potential instability if p > C/D X - Does it occur dynamically? - Consider non-relativistic coupled species M i i > 0