O slideshow foi denunciado.
Utilizamos seu perfil e dados de atividades no LinkedIn para personalizar e exibir anúncios mais relevantes. Altere suas preferências de anúncios quando desejar.
IntroductionResultsMay the force not be with youScreening Modifications of Gravity and Disformal CouplingsMiguel Zumalac´ar...
IntroductionResultsTheories of GravityScreening MechanismsThe Frontiers of GravityOstrogradski’s Theorem (1850)Theories wi...
IntroductionResultsTheories of GravityScreening MechanismsThe Frontiers of GravityOstrogradski’s Theorem (1850)Theories wi...
IntroductionResultsTheories of GravityScreening MechanismsEinstein’s TheoryLovelock’s Theorem (1971)gµν + Local + 4-D + Lo...
IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Loc...
IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Loc...
IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Loc...
IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Loc...
IntroductionResultsTheories of GravityScreening MechanismsFrames and Forcesf(R) + Lm ,vvφ=f , V =R((φR + Lm + Lφ ,uugµν ↔φ...
IntroductionResultsTheories of GravityScreening MechanismsFrames and Forcesf(R) + Lm ,vvφ=f , V =R((φR + Lm + Lφ ,uugµν ↔φ...
IntroductionResultsTheories of GravityScreening MechanismsSubtle the Force can beFiφ ≈ f[φ] iφ“You must feel the Force aro...
IntroductionResultsTheories of GravityScreening MechanismsSubtle the Force can beFiφ ≈ f[φ] iφ“You must feel the Force aro...
IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Velt...
IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Velt...
IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Velt...
IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Velt...
IntroductionResultsTheories of GravityScreening MechanismsForm of the Matter Metric√−g R16πG +√−γLm γµν[φ, gµν]matter metr...
IntroductionResultsTheories of GravityScreening MechanismsForm of the Matter Metric√−g R16πG +√−γLm γµν[φ, gµν]matter metr...
IntroductionResultsTheories of GravityScreening MechanismsForm of the Matter Metric√−g R16πG +√−γLm γµν[φ, gµν]matter metr...
IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 201...
IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 201...
IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 201...
IntroductionResultsDisformally Related FramesScreening the ForceThe Galileon FrameCompute√−γ ¯R[γµν] for§¦¤¥γµν = gµν + π,...
IntroductionResultsDisformally Related FramesScreening the ForceThe Galileon FrameCompute√−γ ¯R[γµν] for§¦¤¥γµν = gµν + π,...
IntroductionResultsDisformally Related FramesScreening the ForceThe Galileon FrameCompute√−γ ¯R[γµν] for§¦¤¥γµν = gµν + π,...
IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 201...
IntroductionResultsDisformally Related FramesScreening the ForceThe Einstein FrameLEF =√−gR16πG+ Lφ +√−γLM (γµν, ψ)γµν = C...
IntroductionResultsDisformally Related FramesScreening the ForceThe Einstein FrameLEF =√−gR16πG+ Lφ +√−γLM (γµν, ψ)γµν = C...
IntroductionResultsDisformally Related FramesScreening the ForceThe Einstein FrameLEF =√−gR16πG+ Lφ +√−γLM (γµν, ψ)γµν = C...
IntroductionResultsDisformally Related FramesScreening the ForceConsequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2...
IntroductionResultsDisformally Related FramesScreening the ForceConsequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2...
IntroductionResultsDisformally Related FramesScreening the ForceConsequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2...
IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Stati...
IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Stati...
IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Stati...
IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Stati...
IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Stati...
IntroductionResultsDisformally Related FramesScreening the ForceThe Vainshtein Radius - Vainshtein (PLB 1972)Non-linear de...
IntroductionResultsDisformally Related FramesScreening the ForceThe Vainshtein Radius - Vainshtein (PLB 1972)Non-linear de...
IntroductionResultsDisformally Related FramesScreening the ForceThe Vainshtein Radius - Vainshtein (PLB 1972)Non-linear de...
IntroductionResultsConclusionsLife beyond the conformal coupling: Dφ,µφ,ν→ don’t be a conformist!New frames: Galileon  Dis...
IntroductionResultsBackup SlidesMiguel Zumalac´arregui May the force not be with you
IntroductionResultsProperties of the Field EquationCanonical scalar field Lφ = X − V , solve for φMµνµ νφ +CC − 2DXQµνTµνm ...
IntroductionResults(Some) Cosmology˙ρ + 3Hρ = Q0˙φ ,- Pure Conformal Q(c)0 = C2C ρ- Pure Disformal Q(d)0 ≈ ρφD2D (1 + wφ) ...
Próximos SlideShares
Carregando em…5
×
Próximos SlideShares
Key pages from 3 to 5
Avançar
Transfira para ler offline e ver em ecrã inteiro.

0

Compartilhar

Baixar para ler offline

May the Force NOT be with you

Baixar para ler offline

Alternative theories of gravity may have considerable impact on cosmological scales while remaining compatible with Solar System tests by means of screening mechanism. I describe the natural emergence of such mechanisms in scalar-tensor theories featuring a coupling to matter of the disformal type.

Livros relacionados

Gratuito durante 30 dias do Scribd

Ver tudo

Audiolivros relacionados

Gratuito durante 30 dias do Scribd

Ver tudo
  • Seja a primeira pessoa a gostar disto

May the Force NOT be with you

  1. 1. IntroductionResultsMay the force not be with youScreening Modifications of Gravity and Disformal CouplingsMiguel Zumalac´arreguiInstituto de F´ısica Te´orica (IFT-UAM-CSIC) → ITP - Uni. HeidelbergRefs: PRL 109 241102 (1205.3167) and PRD 87 083010 (1210.8016)with Tomi S. Koivisto and David F. MotaUniversity of Geneva (May 2013)Miguel Zumalac´arregui May the force not be with you
  2. 2. IntroductionResultsTheories of GravityScreening MechanismsThe Frontiers of GravityOstrogradski’s Theorem (1850)Theories with L ⊃∂nq∂tn, n ≥ 2 are unstable∗L(q(t), ˙q, ¨q) →∂L∂q−ddt∂L∂ ˙q+d2dt2∂L∂¨q= 0q, ˙q, ¨q,...q → Q1, Q2, P1,P2H = P1Q2 + terms independent of P1Miguel Zumalac´arregui May the force not be with you
  3. 3. IntroductionResultsTheories of GravityScreening MechanismsThe Frontiers of GravityOstrogradski’s Theorem (1850)Theories with L ⊃∂nq∂tn, n ≥ 2 are unstable∗L(q(t), ˙q, ¨q) →∂L∂q−ddt∂L∂ ˙q+d2dt2∂L∂¨q= 0q, ˙q, ¨q,...q → Q1, Q2, P1,P2H = P1Q2 + terms independent of P1∗ Loophole: Th’s with second order equations of motionMiguel Zumalac´arregui May the force not be with you
  4. 4. IntroductionResultsTheories of GravityScreening MechanismsEinstein’s TheoryLovelock’s Theorem (1971)gµν + Local + 4-D + Lorentz Theory with 2nd order Eqs.√−g116πG(R − 2Λ)Ways out - Clifton et al. (Phys.Rept. 2012)Additional fields −→£¢ ¡φ , Aµ, hµν...“Higher derivatives” −→ f(R)...Extra dimensions −→ DGP, Kaluza-Klein...Weird stuff −→ Non-local, Lorentz violating...Scalars fields: Simple + certain limits from other theoriesMiguel Zumalac´arregui May the force not be with you
  5. 5. IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Local + 4-D + Lorentz Theory with 2nd order Eqs.⇒ 4 free functions Gi(φ, X), X ≡ −12φ,µφ,µLH = G2 − G3 φ + G4R + G4,X ( φ)2− φ;µνφ;µν+ G5Gµνφ;µν−G5,X6( φ)3− 3( φ)φ;µνφ;µν+ 2φ ;ν;µ φ ;λ;ν φ ;µ;λJordan-Brans-Dicke: G4 = φ16πG, G2 = Xω(φ) − V (φ)Miguel Zumalac´arregui May the force not be with you
  6. 6. IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Local + 4-D + Lorentz Theory with 2nd order Eqs.⇒ 4 free functions Gi(φ, X), X ≡ −12φ,µφ,µLH = G2 − G3 φ + G4R + G4,X ( φ)2− φ;µνφ;µν+ G5Gµνφ;µν−G5,X6( φ)3− 3( φ)φ;µνφ;µν+ 2φ ;ν;µ φ ;λ;ν φ ;µ;λJordan-Brans-Dicke: G4 = φ16πG, G2 = Xω(φ) − V (φ)Kinetic Gravity Braiding - Deffayet et al. JCAP 2010Miguel Zumalac´arregui May the force not be with you
  7. 7. IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Local + 4-D + Lorentz Theory with 2nd order Eqs.⇒ 4 free functions Gi(φ, X), X ≡ −12φ,µφ,µLH = G2 − G3 φ + G4R + G4,X ( φ)2− φ;µνφ;µν+ G5Gµνφ;µν−G5,X6( φ)3− 3( φ)φ;µνφ;µν+ 2φ ;ν;µ φ ;λ;ν φ ;µ;λJordan-Brans-Dicke: G4 = φ16πG, G2 = Xω(φ) − V (φ)Kinetic Gravity Braiding - Deffayet et al. JCAP 2010Deriv. couplings G4(X)Miguel Zumalac´arregui May the force not be with you
  8. 8. IntroductionResultsTheories of GravityScreening MechanismsScalar Tensor-TheoriesHorndenski’s Theory (1974)gµν +£¢ ¡φ + Local + 4-D + Lorentz Theory with 2nd order Eqs.⇒ 4 free functions Gi(φ, X), X ≡ −12φ,µφ,µLH = G2 − G3 φ + G4R + G4,X ( φ)2− φ;µνφ;µν+ G5Gµνφ;µν−G5,X6( φ)3− 3( φ)φ;µνφ;µν+ 2φ ;ν;µ φ ;λ;ν φ ;µ;λJordan-Brans-Dicke: G4 = φ16πG, G2 = Xω(φ) − V (φ)Kinetic Gravity Braiding - Deffayet et al. JCAP 2010Deriv. couplings G4(X), G5 = 0Miguel Zumalac´arregui May the force not be with you
  9. 9. IntroductionResultsTheories of GravityScreening MechanismsFrames and Forcesf(R) + Lm ,vvφ=f , V =R((φR + Lm + Lφ ,uugµν ↔φ−1˜gµν**˜R + Lm[φ−1˜gµν] + ˜LφJordan frame Einstein frame√−gR16πG+√−γLm γµν[φ, gµν]matter metric, · · · +√−gLφMiguel Zumalac´arregui May the force not be with you
  10. 10. IntroductionResultsTheories of GravityScreening MechanismsFrames and Forcesf(R) + Lm ,vvφ=f , V =R((φR + Lm + Lφ ,uugµν ↔φ−1˜gµν**˜R + Lm[φ−1˜gµν] + ˜LφJordan frame Einstein frame√−gR16πG+√−γLm γµν[φ, gµν]matter metric, · · · +√−gLφPoint Particle:¨xα= − Γαµν + Kαµνγαλ( (µγν)λ−12 λγµν )˙xµ˙xν⇒ Fiφ = Ki00 +O(vi/c) ≈ f[φ] iφMiguel Zumalac´arregui May the force not be with you
  11. 11. IntroductionResultsTheories of GravityScreening MechanismsSubtle the Force can beFiφ ≈ f[φ] iφ“You must feel the Force around you;here, between you, me, the tree, the rock,everywhere, yes”Master YodaMiguel Zumalac´arregui May the force not be with you
  12. 12. IntroductionResultsTheories of GravityScreening MechanismsSubtle the Force can beFiφ ≈ f[φ] iφ“You must feel the Force around you;here, between you, me, the tree, the rock,everywhere, yes”Master YodaNo Fφ observed in Solar SystemScreening MechanismsFφFG1 whenρ ρ0r H−10Miguel Zumalac´arregui May the force not be with you
  13. 13. IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Veltman (PRL 2004)Yukawa force: φ ∝ 1r e−φ/mφ with mφ(ρ) increases with ρ(cf. Symmetron - Hinterbichler & Khoury PRL 2010)Miguel Zumalac´arregui May the force not be with you
  14. 14. IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Veltman (PRL 2004)Yukawa force: φ ∝ 1r e−φ/mφ with mφ(ρ) increases with ρ(cf. Symmetron - Hinterbichler & Khoury PRL 2010)§¦¤¥r H−10 Vainshtein Screening - Vainshtein (PLB 1972)L ⊃ (∂φ) + φX/m2+ αφTm Non-linear derivative interactions⇒ φ + m−2( φ)2− φ;µν φ;µν= αMδ(r)φ ∝r−1 if r rV√r if r rVVainshtein radius rV ∝ (GM/m2)1/3Miguel Zumalac´arregui May the force not be with you
  15. 15. IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Veltman (PRL 2004)Yukawa force: φ ∝ 1r e−φ/mφ with mφ(ρ) increases with ρ(cf. Symmetron - Hinterbichler & Khoury PRL 2010)§¦¤¥r H−10 Vainshtein Screening - Vainshtein (PLB 1972)L ⊃ (∂φ) + φX/m2+ αφTm Non-linear derivative interactions⇒ φ + m−2( φ)2− φ;µν φ;µν= αMδ(r)φ ∝r−1 if r rV√r if r rVVainshtein radius rV ∝ (GM/m2)1/3Miguel Zumalac´arregui May the force not be with you
  16. 16. IntroductionResultsTheories of GravityScreening MechanismsScreening Mechanisms§¦¤¥ρ ρ0 Chameleon Screening - Khoury & Veltman (PRL 2004)Yukawa force: φ ∝ 1r e−φ/mφ with mφ(ρ) increases with ρ(cf. Symmetron - Hinterbichler & Khoury PRL 2010)§¦¤¥r H−10 Vainshtein Screening - Vainshtein (PLB 1972)L ⊃ (∂φ) + φX/m2+ αφTm Non-linear derivative interactions⇒ φ + m−2( φ)2− φ;µν φ;µν= αMδ(r)φ ∝r−1 if r rV√r if r rVVainshtein radius rV ∝ (GM/m2)1/3Miguel Zumalac´arregui May the force not be with you
  17. 17. IntroductionResultsTheories of GravityScreening MechanismsForm of the Matter Metric√−g R16πG +√−γLm γµν[φ, gµν]matter metric, · · · +√−gLφDisformal Relations - Bekenstein (PRD 1992)γµν = C(φ)gµνconformal+ D(φ)φ,µφ,νdisformald¯s2γ = Cds2g + D(φ,µdxµ)2C = 1 local rescaling, same causal structureMiguel Zumalac´arregui May the force not be with you
  18. 18. IntroductionResultsTheories of GravityScreening MechanismsForm of the Matter Metric√−g R16πG +√−γLm γµν[φ, gµν]matter metric, · · · +√−gLφDisformal Relations - Bekenstein (PRD 1992)γµν = C(φ)gµνconformal+ D(φ)φ,µφ,νdisformald¯s2γ = Cds2g + D(φ,µdxµ)2C = 1 local rescaling, same causal structureD = 0 modified causal structureMiguel Zumalac´arregui May the force not be with you
  19. 19. IntroductionResultsTheories of GravityScreening MechanismsForm of the Matter Metric√−g R16πG +√−γLm γµν[φ, gµν]matter metric, · · · +√−gLφDisformal Relations - Bekenstein (PRD 1992)γµν = C(φ)gµνconformal+ D(φ)φ,µφ,νdisformald¯s2γ = Cds2g + D(φ,µdxµ)2C = 1 local rescaling, same causal structureD = 0 modified causal structure¯γ00 ∝ 1 − DC˙φ2 → Slow roll - MZ, Koivisto et al. (JCAP 2010)+ relativistic MOND, VSL, Galileons...Miguel Zumalac´arregui May the force not be with you
  20. 20. IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 2013)γµν = C(φ)gµν + D(φ)φ,µφ,νEinstein Frame: LEF =√−gR[gµν] +√−γLM (γµν, ψ)Einsteingµν → 1C gµν − DC φ,µφ,νJordanJordan Frame: LJF =√−γR[γµν] +√−gLM (gµν, ψ)Miguel Zumalac´arregui May the force not be with you
  21. 21. IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 2013)γµν = C(φ)gµν + D(φ)φ,µφ,νEinstein Frame: LEF =√−gR[gµν] +√−γLM (γµν, ψ)Einsteingµν → 1C gµν − DC φ,µφ,νJordanJordan Frame: LJF =√−γR[γµν] +√−gLM (gµν, ψ)Miguel Zumalac´arregui May the force not be with you
  22. 22. IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 2013)γµν = C(φ)gµν + D(φ)φ,µφ,νEinstein Frame: LEF =√−gR[gµν] +√−γLM (γµν, ψ)Einsteingµν →C−1gµν))gµν →gµν − DCφ,µφ,νuugµν → 1C gµν − DC φ,µφ,νD ⊂ matteroo§¦¤¥Galileon))DisformaluuD ⊂ gravity //OOJordanJordan Frame: LJF =√−γR[γµν] +√−gLM (gµν, ψ)Miguel Zumalac´arregui May the force not be with you
  23. 23. IntroductionResultsDisformally Related FramesScreening the ForceThe Galileon FrameCompute√−γ ¯R[γµν] for§¦¤¥γµν = gµν + π,µπ,ν (π ≡ D(φ)dφ)Miguel Zumalac´arregui May the force not be with you
  24. 24. IntroductionResultsDisformally Related FramesScreening the ForceThe Galileon FrameCompute√−γ ¯R[γµν] for§¦¤¥γµν = gµν + π,µπ,ν (π ≡ D(φ)dφ)Disformal Curvature√−γR[γµν] =√−g1˜γR[gµν] − ˜γ ( π)2− π;µνπ;µν+ µξµwith ˜γ−1 ≡ g/γ = 1 + π,µπ,µMiguel Zumalac´arregui May the force not be with you
  25. 25. IntroductionResultsDisformally Related FramesScreening the ForceThe Galileon FrameCompute√−γ ¯R[γµν] for§¦¤¥γµν = gµν + π,µπ,ν (π ≡ D(φ)dφ)Disformal Curvature√−γR[γµν] =√−g1˜γR[gµν] − ˜γ ( π)2− π;µνπ;µν+ µξµwith ˜γ−1 ≡ g/γ = 1 + π,µπ,µQuartic DBI Galileonπ = brane coordinate in 5th dim.- De Rham Tolley (JCAP 2010)Miguel Zumalac´arregui May the force not be with you
  26. 26. IntroductionResultsDisformally Related FramesScreening the ForceDisformally Related Theories - MZ, Koivisto, Mota (PRD 2013)γµν = C(φ)gµν + D(φ)φ,µφ,νEinstein Frame: LEF =√−gR[gµν] +√−γLM (γµν, ψ)§¦¤¥Einsteingµν →C−1gµν))gµν →gµν − DCφ,µφ,νuugµν → 1C gµν − DC φ,µφ,νD ⊂ matterooGalileon))DisformaluuD ⊂ gravity //OOJordanJordan Frame: LJF =√−γR[γµν] +√−gLM (gµν, ψ)Miguel Zumalac´arregui May the force not be with you
  27. 27. IntroductionResultsDisformally Related FramesScreening the ForceThe Einstein FrameLEF =√−gR16πG+ Lφ +√−γLM (γµν, ψ)γµν = C(φ)gµν + D(φ)φ,µφ,νGµν = 8πG(Tµνm + Tµνφ )Matter-field interaction: µTµνm = −Qφ,νMiguel Zumalac´arregui May the force not be with you
  28. 28. IntroductionResultsDisformally Related FramesScreening the ForceThe Einstein FrameLEF =√−gR16πG+ Lφ +√−γLM (γµν, ψ)γµν = C(φ)gµν + D(φ)φ,µφ,νGµν = 8πG(Tµνm + Tµνφ )Matter-field interaction: µTµνm = −Qφ,νQ =DCµ (Tµνm φ,ν) −C2CTm +D2C−DCC2φ,µφ,νTµνmMiguel Zumalac´arregui May the force not be with you
  29. 29. IntroductionResultsDisformally Related FramesScreening the ForceThe Einstein FrameLEF =√−gR16πG+ Lφ +√−γLM (γµν, ψ)γµν = C(φ)gµν + D(φ)φ,µφ,νGµν = 8πG(Tµνm + Tµνφ )Matter-field interaction: µTµνm = −Qφ,νQ =DCµ (Tµνm φ,ν) −C2CTm +D2C−DCC2φ,µφ,νTµνmKinetic mixing Conformal DisformalMiguel Zumalac´arregui May the force not be with you
  30. 30. IntroductionResultsDisformally Related FramesScreening the ForceConsequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2012)Static matter ρ(x) + non-rel. p = 01 +DρC − 2DX¨φ + F( φ,µ, φ,µ, ρ) = 0Miguel Zumalac´arregui May the force not be with you
  31. 31. IntroductionResultsDisformally Related FramesScreening the ForceConsequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2012)Static matter ρ(x) + non-rel. p = 01 +DρC − 2DX¨φ + F( φ,µ, φ,µ, ρ) = 0Disformal Screening Mechanism¨φ ≈ −D2D˙φ2+ C˙φ2C−12D(If Dρ → ∞)Miguel Zumalac´arregui May the force not be with you
  32. 32. IntroductionResultsDisformally Related FramesScreening the ForceConsequences of Kinetic Mixing - Koivisto, Mota, MZ (PRL 2012)Static matter ρ(x) + non-rel. p = 01 +DρC − 2DX¨φ + F( φ,µ, φ,µ, ρ) = 0Disformal Screening Mechanism¨φ ≈ −D2D˙φ2+ C˙φ2C−12D(If Dρ → ∞)φ(x, t)§¦¤¥independent of ρ(x) and ∂iφ⇒ No φ between M1, M2 ⇒§¦¤¥No fifth force!Miguel Zumalac´arregui May the force not be with you
  33. 33. IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Static ∂tρ = 0Pressureless Dp X ≡ C − 2DXNeglect pρ , pρ∂φ∂tφ2, XDρ , XDρV /¨φ , Γµ00φ,µ/¨φ ∼ 0Miguel Zumalac´arregui May the force not be with you
  34. 34. IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Static ∂tρ = 0Pressureless Dp X ≡ C − 2DXNeglect pρ , pρ∂φ∂tφ2, XDρ , XDρV /¨φ , Γµ00φ,µ/¨φ ∼ 0Potential SignaturesMatter velocity flows: T0i → Terms ∝ φ;0i and ˙φ φ,iSuppressed by v/c → Binary pulsars?Miguel Zumalac´arregui May the force not be with you
  35. 35. IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Static ∂tρ = 0Pressureless Dp X ≡ C − 2DXNeglect pρ , pρ∂φ∂tφ2, XDρ , XDρV /¨φ , Γµ00φ,µ/¨φ ∼ 0Potential SignaturesMatter velocity flows: T0i → Terms ∝ φ;0i and ˙φ φ,iSuppressed by v/c → Binary pulsars?Pressure: Instability and effects on radiationMiguel Zumalac´arregui May the force not be with you
  36. 36. IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Static ∂tρ = 0Pressureless Dp X ≡ C − 2DXNeglect pρ , pρ∂φ∂tφ2, XDρ , XDρV /¨φ , Γµ00φ,µ/¨φ ∼ 0Potential SignaturesMatter velocity flows: T0i → Terms ∝ φ;0i and ˙φ φ,iSuppressed by v/c → Binary pulsars?Pressure: Instability and effects on radiationStrong gravitational fields: Γµ00φ,µ not suppressed by DρΓr00 = GMr3 (r − 2GM) → Black holes?Miguel Zumalac´arregui May the force not be with you
  37. 37. IntroductionResultsDisformally Related FramesScreening the ForceDisformal Screening: Potential SignaturesAssumptions:Static ∂tρ = 0Pressureless Dp X ≡ C − 2DXNeglect pρ , pρ∂φ∂tφ2, XDρ , XDρV /¨φ , Γµ00φ,µ/¨φ ∼ 0Potential SignaturesMatter velocity flows: T0i → Terms ∝ φ;0i and ˙φ φ,iSuppressed by v/c → Binary pulsars?Pressure: Instability and effects on radiationStrong gravitational fields: Γµ00φ,µ not suppressed by DρΓr00 = GMr3 (r − 2GM) → Black holes?Spatial Field Gradients: Evolution independent of ∂iφMiguel Zumalac´arregui May the force not be with you
  38. 38. IntroductionResultsDisformally Related FramesScreening the ForceThe Vainshtein Radius - Vainshtein (PLB 1972)Non-linear derivative interactions L ⊃ + φX/m2+ αφTm⇒ φ + m−2( φ)2− φ;µν φ;µν= αMδ(r)φ ∝r−1 if r rV√r if r rVVainshtein radius rV ∝ (GM/m2)1/3Disformal coupling: L ⊃ −˜γ ( φ)2− φ;µν φ;µν(Jordan Fr.)φ = 0 ⇒ φ =SrEinstein Fr.Miguel Zumalac´arregui May the force not be with you
  39. 39. IntroductionResultsDisformally Related FramesScreening the ForceThe Vainshtein Radius - Vainshtein (PLB 1972)Non-linear derivative interactions L ⊃ + φX/m2+ αφTm⇒ φ + m−2( φ)2− φ;µν φ;µν= αMδ(r)φ ∝r−1 if r rV√r if r rVVainshtein radius rV ∝ (GM/m2)1/3Disformal coupling: L ⊃ −˜γ ( φ)2− φ;µν φ;µν(Jordan Fr.)φ =−QµνδTµνmC + D(φ,r)2⇒ φ =Sr(if r → ∞)Miguel Zumalac´arregui May the force not be with you
  40. 40. IntroductionResultsDisformally Related FramesScreening the ForceThe Vainshtein Radius - Vainshtein (PLB 1972)Non-linear derivative interactions L ⊃ + φX/m2+ αφTm⇒ φ + m−2( φ)2− φ;µν φ;µν= αMδ(r)φ ∝r−1 if r rV√r if r rVVainshtein radius rV ∝ (GM/m2)1/3Disformal coupling: L ⊃ −˜γ ( φ)2− φ;µν φ;µν(Jordan Fr.)φ =−QµνδTµνmC + D(φ,r)2⇒ φ =Sr(if r → ∞)D 0 ⇒ asymptotic φ0 = Sr breaks down at ˜rV = DS2C1/4Miguel Zumalac´arregui May the force not be with you
  41. 41. IntroductionResultsConclusionsLife beyond the conformal coupling: Dφ,µφ,ν→ don’t be a conformist!New frames: Galileon DisformalEinstein Frame: simpler Eqs. physical insightScreening mechanisms:Disformal: Dρ → ∞ field eq. independent of ρVainshtein: r rV ⇒ Fφ FGOpen questions potential applications (e.g. Cosmology)May the force not be with you!Miguel Zumalac´arregui May the force not be with you
  42. 42. IntroductionResultsBackup SlidesMiguel Zumalac´arregui May the force not be with you
  43. 43. IntroductionResultsProperties of the Field EquationCanonical scalar field Lφ = X − V , solve for φMµνµ νφ +CC − 2DXQµνTµνm − V = 0Mµν≡ gµν−D TµνmC − 2DX, Qµν ≡C2Cgµν +C DC2−D2Cφ,µφ,νCoupling to (Einstein F) perfect fluid Tµν = diag(ρ, p, p, p)M00 = 1 + DρC−2DX , D, ρ 0 ⇒ no ghostsMii = 1 − DpC−2DX , ⇒ potential instability if p C/D − X- Does it occur dynamically?- Consider non-relativistic coupled species Mii 0Miguel Zumalac´arregui May the force not be with you
  44. 44. IntroductionResults(Some) Cosmology˙ρ + 3Hρ = Q0˙φ ,- Pure Conformal Q(c)0 = C2C ρ- Pure Disformal Q(d)0 ≈ ρφD2D (1 + wφ) − V2V (1 − wφ)Simple models givegood background expansion with Λ = 0too much growth:GeffG− 1 =Q204πGρ2But much room for viable modelsMiguel Zumalac´arregui May the force not be with you

Alternative theories of gravity may have considerable impact on cosmological scales while remaining compatible with Solar System tests by means of screening mechanism. I describe the natural emergence of such mechanisms in scalar-tensor theories featuring a coupling to matter of the disformal type.

Vistos

Vistos totais

440

No Slideshare

0

De incorporações

0

Número de incorporações

3

Ações

Baixados

4

Compartilhados

0

Comentários

0

Curtir

0

×