Tension in the Void AIMS

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Tension in the Void AIMS

  1. 1. A-Void Dark Energy Observational constraints Tension in the Void arXiv:1201.2790 Miguel Zumalac´arregui Institute of Cosmos Sciences, University of Barcelona with Juan Garcia-Bellido and Pilar Ruiz-Lapuente AIMS (Cape Town), January 2012 Miguel Zumalac´arregui Tension in the Void
  2. 2. A-Void Dark Energy Observational constraints Outline 1 A-Void Dark Energy The Standard Cosmological Model Inhomogeneous Universes 2 Observational constraints Cosmological Data MCMC analysis 3) Conclusions Miguel Zumalac´arregui Tension in the Void
  3. 3. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes A-Void Dark Energy Miguel Zumalac´arregui Tension in the Void
  4. 4. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Precission Cosmology and New Physics Cosmic microwave Background δT/T ∼ 10−6 ⇒ Cosmic Inflation Large scale structure ⇒ Dark Matter ρDM ≈ 5 × ρSM Supernovae ⇒ small Λ (Dark Energy, Modified Gravity...) Probes complementary and consistent: New Physics required Miguel Zumalac´arregui Tension in the Void
  5. 5. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Standard Model of Cosmology The ingredients of the Standard Model of Cosmology GR + FRW + Inflation + SM + CDM + Λ Theory of Gravitation: General Relativity Ansatz for the metric: Homogeneous + Isotropic Miguel Zumalac´arregui Tension in the Void
  6. 6. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Standard Model of Cosmology The ingredients of the Standard Model of Cosmology GR + FRW + Inflation + SM + CDM + Λ Theory of Gravitation: General Relativity Ansatz for the metric: Homogeneous + Isotropic Initial conditions: Inflationary perturbations Miguel Zumalac´arregui Tension in the Void
  7. 7. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Standard Model of Cosmology The ingredients of the Standard Model of Cosmology GR + FRW + Inflation + SM + CDM + Λ Theory of Gravitation: General Relativity Ansatz for the metric: Homogeneous + Isotropic Initial conditions: Inflationary perturbations Standard particle content: γ, ν’s, p+, n, e− Miguel Zumalac´arregui Tension in the Void
  8. 8. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Standard Model of Cosmology The ingredients of the Standard Model of Cosmology GR + FRW + Inflation + SM + CDM + Λ Theory of Gravitation: General Relativity Ansatz for the metric: Homogeneous + Isotropic Initial conditions: Inflationary perturbations Standard particle content: γ, ν’s, p+, n, e− Cold Dark Matter: some new particle species Cosmological constant: Λ (energy of the vacuum??) Commercial name: ΛCDM c Miguel Zumalac´arregui Tension in the Void
  9. 9. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Some Popular (and Unpopular) Variations on the SCM GR + FRW + Inflation + SM + CDM + Λ Many models intended to avoid a small cosmological constant Dark Energy: Λ → Scalar φ for acceleration Modified Gravity: GR→ f(R), φR, TeVeS, 5D-DGP. . . Miguel Zumalac´arregui Tension in the Void
  10. 10. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Some Popular (and Unpopular) Variations on the SCM GR + FRW + Inflation + SM + CDM + Λ Many models intended to avoid a small cosmological constant Dark Energy: Λ → Scalar φ for acceleration Modified Gravity: GR→ f(R), φR, TeVeS, 5D-DGP. . . Inflation → Varying speed of light, Horava-Lifschitz... Miguel Zumalac´arregui Tension in the Void
  11. 11. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Some Popular (and Unpopular) Variations on the SCM GR + FRW + Inflation + SM + CDM + Λ Many models intended to avoid a small cosmological constant Dark Energy: Λ → Scalar φ for acceleration Modified Gravity: GR→ f(R), φR, TeVeS, 5D-DGP. . . Inflation → Varying speed of light, Horava-Lifschitz... Neutrinos (mν, Nν), axions... Miguel Zumalac´arregui Tension in the Void
  12. 12. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Some Popular (and Unpopular) Variations on the SCM GR + FRW + Inflation + SM + CDM + Λ Many models intended to avoid a small cosmological constant Dark Energy: Λ → Scalar φ for acceleration Modified Gravity: GR→ f(R), φR, TeVeS, 5D-DGP. . . Inflation → Varying speed of light, Horava-Lifschitz... Neutrinos (mν, Nν), axions... Backreacktion: Nonlinearity of GR, inhomogeneous effects Miguel Zumalac´arregui Tension in the Void
  13. 13. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Some Popular (and Unpopular) Variations on the SCM GR + FRW + Inflation + SM + CDM + Λ Many models intended to avoid a small cosmological constant Dark Energy: Λ → Scalar φ for acceleration Modified Gravity: GR→ f(R), φR, TeVeS, 5D-DGP. . . Inflation → Varying speed of light, Horava-Lifschitz... Neutrinos (mν, Nν), axions... Backreacktion: Nonlinearity of GR, inhomogeneous effects Large underdensity: FRW→ inhomogeneous metric Miguel Zumalac´arregui Tension in the Void
  14. 14. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Beyond Homogeneity Homogeneity + Isotropy ⇒ FRW ds2 = −dt2 + a(t)2 dr2 1 − k + [a(t) r]2 dΩ2 Spherical Symmetry ⇒ LTB The Lemaitre-Tolman-Bondi metric ds2 = −dt2 + A 2(r, t) 1 − k(r) dr2 + A2 (r, t) dΩ2 Miguel Zumalac´arregui Tension in the Void
  15. 15. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Beyond Homogeneity Homogeneity + Isotropy ⇒ FRW ds2 = −dt2 + a(t)2 dr2 1 − k + [a(t) r]2 dΩ2 Spherical Symmetry ⇒ LTB The Lemaitre-Tolman-Bondi metric ds2 = −dt2 + A 2(r, t) 1 − k(r) dr2 + A2 (r, t) dΩ2 CMB isotropy ⇒ Central location r ≈ 0 ± 10Mpc Miguel Zumalac´arregui Tension in the Void
  16. 16. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Beyond Homogeneity Homogeneity + Isotropy ⇒ FRW ds2 = −dt2 + a(t)2 dr2 1 − k + [a(t) r]2 dΩ2 Spherical Symmetry ⇒ LTB The Lemaitre-Tolman-Bondi metric ds2 = −dt2 + A 2(r, t) 1 − k(r) dr2 + A2 (r, t) dΩ2 CMB isotropy ⇒ Central location r ≈ 0 ± 10Mpc Observations from ds2 = 0 ⇒ mix time & space variations Miguel Zumalac´arregui Tension in the Void
  17. 17. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Beyond Homogeneity Homogeneity + Isotropy ⇒ FRW ds2 = −dt2 + a(t)2 dr2 1 − k + [a(t) r]2 dΩ2 Spherical Symmetry ⇒ LTB The Lemaitre-Tolman-Bondi metric ds2 = −dt2 + A 2(r, t) 1 − k(r) dr2 + A2 (r, t) dΩ2 CMB isotropy ⇒ Central location r ≈ 0 ± 10Mpc Observations from ds2 = 0 ⇒ mix time & space variations Trade Λ for living in the center of a ∼ Gpc underdensity Miguel Zumalac´arregui Tension in the Void
  18. 18. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Inhomogeneous Cosmologies LTB metric: ds2 = −dt2 + A 2(r,t) 1−k(r) dr2 + A2(r, t) dΩ2 Two expansion rates: HL = ˙A /A = ˙A/A = HT Miguel Zumalac´arregui Tension in the Void
  19. 19. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Inhomogeneous Cosmologies LTB metric: ds2 = −dt2 + A 2(r,t) 1−k(r) dr2 + A2(r, t) dΩ2 Two expansion rates: HL = ˙A /A = ˙A/A = HT Three free functions of r: Miguel Zumalac´arregui Tension in the Void
  20. 20. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Inhomogeneous Cosmologies LTB metric: ds2 = −dt2 + A 2(r,t) 1−k(r) dr2 + A2(r, t) dΩ2 Two expansion rates: HL = ˙A /A = ˙A/A = HT Three free functions of r: Local curvature k(r) −→ Matter profile: ΩM (r) Miguel Zumalac´arregui Tension in the Void
  21. 21. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Inhomogeneous Cosmologies LTB metric: ds2 = −dt2 + A 2(r,t) 1−k(r) dr2 + A2(r, t) dΩ2 Two expansion rates: HL = ˙A /A = ˙A/A = HT Three free functions of r: Local curvature k(r) −→ Matter profile: ΩM (r) Initial “position” A(r, t0) −→ Gauge choice: A0(r) Miguel Zumalac´arregui Tension in the Void
  22. 22. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Inhomogeneous Cosmologies LTB metric: ds2 = −dt2 + A 2(r,t) 1−k(r) dr2 + A2(r, t) dΩ2 Two expansion rates: HL = ˙A /A = ˙A/A = HT Three free functions of r: Local curvature k(r) −→ Matter profile: ΩM (r) Initial “position” A(r, t0) −→ Gauge choice: A0(r) Initial velocity ˙A(r, t0) −→ Expansion rate: H0(r) Miguel Zumalac´arregui Tension in the Void
  23. 23. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Inhomogeneous Cosmologies LTB metric: ds2 = −dt2 + A 2(r,t) 1−k(r) dr2 + A2(r, t) dΩ2 Two expansion rates: HL = ˙A /A = ˙A/A = HT Three free functions of r: Local curvature k(r) −→ Matter profile: ΩM (r) Initial “position” A(r, t0) −→ Gauge choice: A0(r) Initial velocity ˙A(r, t0) −→ Expansion rate: H0(r) If pressure negligible: H2 T (r, t) = H2 0 (r) ΩM (r) (A/A0(r))3 + 1 − ΩM (r) (A/A0(r))2 Miguel Zumalac´arregui Tension in the Void
  24. 24. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Less Inhomogeneous Cosmologies No pressure: H2 T = 1 A dA dt = H2 0 (r) ΩM (r) (A/A0(r))3 + 1−ΩM (r) (A/A0(r))2 t(A, r) = A 0 dA A H2 T (r, A ) allows the construction of an implicit solution for A(r, t) Miguel Zumalac´arregui Tension in the Void
  25. 25. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Less Inhomogeneous Cosmologies No pressure: H2 T = 1 A dA dt = H2 0 (r) ΩM (r) (A/A0(r))3 + 1−ΩM (r) (A/A0(r))2 t(A, r) = A 0 dA A H2 T (r, A ) allows the construction of an implicit solution for A(r, t) Homogeneous Big-Bang tBB(r) = t(A0, r) = t0 Miguel Zumalac´arregui Tension in the Void
  26. 26. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Less Inhomogeneous Cosmologies No pressure: H2 T = 1 A dA dt = H2 0 (r) ΩM (r) (A/A0(r))3 + 1−ΩM (r) (A/A0(r))2 t(A, r) = A 0 dA A H2 T (r, A ) allows the construction of an implicit solution for A(r, t) Homogeneous Big-Bang tBB(r) = t(A0, r) = t0 Relates H0(r) ↔ ΩM (r) up to a constant H0 ↔ t0 ¶¶ Evolution from very homogeneous state at early times Miguel Zumalac´arregui Tension in the Void
  27. 27. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes Less Inhomogeneous Cosmologies No pressure: H2 T = 1 A dA dt = H2 0 (r) ΩM (r) (A/A0(r))3 + 1−ΩM (r) (A/A0(r))2 t(A, r) = A 0 dA A H2 T (r, A ) allows the construction of an implicit solution for A(r, t) Homogeneous Big-Bang tBB(r) = t(A0, r) = t0 Relates H0(r) ↔ ΩM (r) up to a constant H0 ↔ t0 ¶¶ Evolution from very homogeneous state at early times + ρb ∝ ρm → growth of an spherical adiabatic perturbation Miguel Zumalac´arregui Tension in the Void
  28. 28. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Constrained GBH: A0(r), H0(r), ΩM (r) Adiabatic / Constrained models Homogeneous Big-Bang: ΩM (r) determines H0(r) up to normalization H0 → t0 Constant baryon-DM ratio: ρb(r, t) = fbρm(r, t) ΩM (r) → GBH parameterization 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 r Mr GBH Profile in out R0 R 1Gpc R 0.5 R 1.5 Miguel Zumalac´arregui Tension in the Void
  29. 29. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Constrained GBH: A0(r), H0(r), ΩM (r) Adiabatic / Constrained models Homogeneous Big-Bang: ΩM (r) determines H0(r) up to normalization H0 → t0 Constant baryon-DM ratio: ρb(r, t) = fbρm(r, t) ΩM (r) → GBH parameterization Depth of void Ωin Asymptotic curvature Ωout 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 r Mr GBH Profile in out R0 R 1Gpc R 0.5 R 1.5 Miguel Zumalac´arregui Tension in the Void
  30. 30. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Constrained GBH: A0(r), H0(r), ΩM (r) Adiabatic / Constrained models Homogeneous Big-Bang: ΩM (r) determines H0(r) up to normalization H0 → t0 Constant baryon-DM ratio: ρb(r, t) = fbρm(r, t) ΩM (r) → GBH parameterization Depth of void Ωin Asymptotic curvature Ωout Shape of the void R0, ∆R 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 r Mr GBH Profile in out R0 R 1Gpc R 0.5 R 1.5 Miguel Zumalac´arregui Tension in the Void
  31. 31. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Constrained GBH: A0(r), H0(r), ΩM (r) Adiabatic / Constrained models Homogeneous Big-Bang: ΩM (r) determines H0(r) up to normalization H0 → t0 Constant baryon-DM ratio: ρb(r, t) = fbρm(r, t) ΩM (r) → GBH parameterization Depth of void Ωin Asymptotic curvature Ωout Shape of the void R0, ∆R Local expansion rate Hin Baryon fraction fb 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 r Mr GBH Profile in out R0 R 1Gpc R 0.5 R 1.5 Miguel Zumalac´arregui Tension in the Void
  32. 32. A-Void Dark Energy Observational constraints The Standard Cosmological Model Inhomogeneous Universes The Constrained GBH: A0(r), H0(r), ΩM (r) Adiabatic / Constrained models Homogeneous Big-Bang: ΩM (r) determines H0(r) up to normalization H0 → t0 Constant baryon-DM ratio: ρb(r, t) = fbρm(r, t) ΩM (r) → GBH parameterization Depth of void Ωin Asymptotic curvature Ωout Shape of the void R0, ∆R Local expansion rate Hin Baryon fraction fb 0 2 4 6 8 10 0.2 0.4 0.6 0.8 1.0 r Gpc M r Ρ r ,t0 Ρ t0 Ρ r ,t10 Ρ t10 HT r ,t0 HL r ,t0 These are just parameters → physical quantities ρ, HL, HT ... Miguel Zumalac´arregui Tension in the Void
  33. 33. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Observational constraints Miguel Zumalac´arregui Tension in the Void
  34. 34. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Supernova Ia - Standard Candles Standar(izable) Candles: ≈ Same (corrected) Luminosity DL(z) = Luminosity 4π Flux = H−1 0 f(z, ΩΛ, ΩM ) (FRW) difficult to model SNe ⇒ Intrinsic Luminosity unknown!! For any L, comparison of low and high z SNe very useful Miguel Zumalac´arregui Tension in the Void
  35. 35. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Supernova Ia - Standard Candles Standar(izable) Candles: ≈ Same (corrected) Luminosity DL(z) = Luminosity 4π Flux = H−1 0 f(z, ΩΛ, ΩM ) (FRW) difficult to model SNe ⇒ Intrinsic Luminosity unknown!! For any L, comparison of low and high z SNe very useful FRW: Luminosity degenerate with Hubble rate ⇒ need L to determine H0 Miguel Zumalac´arregui Tension in the Void
  36. 36. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Supernova Ia - Standard Candles Standar(izable) Candles: ≈ Same (corrected) Luminosity DL(z) = Luminosity 4π Flux = H−1 0 f(z, ΩΛ, ΩM ) (FRW) difficult to model SNe ⇒ Intrinsic Luminosity unknown!! For any L, comparison of low and high z SNe very useful FRW: Luminosity degenerate with Hubble rate ⇒ need L to determine H0 In LTB not quite true ⇒ convert constraint H0 = 73.8 ± 2.4 Mpc/Km/s ↔ L = −0.120 ± 0.071 Mag Miguel Zumalac´arregui Tension in the Void
  37. 37. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Baryon acoustic oscillations - Standard Rulers -CMB light released when H forms -Sound waves in the baryon-photon plasma travel a finite distance -Initial baryon clumps → more galaxies Miguel Zumalac´arregui Tension in the Void
  38. 38. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Baryon acoustic oscillations - Standard Rulers -CMB light released when H forms -Sound waves in the baryon-photon plasma travel a finite distance -Initial baryon clumps → more galaxies Same logic as SNe: Distance vs Length (well determined!) Miguel Zumalac´arregui Tension in the Void
  39. 39. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Baryon acoustic oscillations - Standard Rulers -CMB light released when H forms -Sound waves in the baryon-photon plasma travel a finite distance -Initial baryon clumps → more galaxies Same logic as SNe: Distance vs Length (well determined!) LTB: Do these clumps/galaxies move? Geodesics Miguel Zumalac´arregui Tension in the Void
  40. 40. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Baryon acoustic oscillations - Standard Rulers -CMB light released when H forms -Sound waves in the baryon-photon plasma travel a finite distance -Initial baryon clumps → more galaxies Same logic as SNe: Distance vs Length (well determined!) LTB: Do these clumps/galaxies move? Geodesics ¨r + k 2(1 − k) + A A ˙r2 + 2 ˙A A ˙t ˙r = 0 ˙t ˙r ⇒ Constant coordinate separation (zero order) Miguel Zumalac´arregui Tension in the Void
  41. 41. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Observations in LTB universes (Constrained case) 2 0 2 4 6 8 10 0 2 4 6 8 10 12 r Gpc tGyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Homogeneous state at early times, large r Miguel Zumalac´arregui Tension in the Void
  42. 42. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Observations in LTB universes (Constrained case) We are here 2 0 2 4 6 8 10 0 2 4 6 8 10 12 r Gpc tGyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Miguel Zumalac´arregui Tension in the Void
  43. 43. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Observations in LTB universes (Constrained case) We are here 2 0 2 4 6 8 10 0 2 4 6 8 10 12 r Gpc tGyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Ia SNe z 1.5 Miguel Zumalac´arregui Tension in the Void
  44. 44. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Observations in LTB universes (Constrained case) We are here 2 0 2 4 6 8 10 0 2 4 6 8 10 12 r Gpc tGyr constant t z 0 t z 1 t z 100 constant Ρ CMB z 1100 Ia SNe z 1.5 BAO z 0.8 Miguel Zumalac´arregui Tension in the Void
  45. 45. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Observations in LTB universes (Constrained case) We are here 2 0 2 4 6 8 10 0 2 4 6 8 10 12 r Gpc tGyr 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 Miguel Zumalac´arregui Tension in the Void
  46. 46. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis The physical BAO scale BAO scale at early times ≈ homogeneous and isotropic Fix early time BAO scale with r → ∞ value (FRW limit) Miguel Zumalac´arregui Tension in the Void
  47. 47. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis The physical BAO scale BAO scale at early times ≈ homogeneous and isotropic Fix early time BAO scale with r → ∞ value (FRW limit) LTB geodesics ⇒ baryon clumps remain at constant r, θ, φ Miguel Zumalac´arregui Tension in the Void
  48. 48. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis The physical BAO scale BAO scale at early times ≈ homogeneous and isotropic Fix early time BAO scale with r → ∞ value (FRW limit) LTB geodesics ⇒ baryon clumps remain at constant r, θ, φ Physical distances given by grr = A 2(r,t) 1−k(r) , gθθ = A2(r, t) Miguel Zumalac´arregui Tension in the Void
  49. 49. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis The physical BAO scale BAO scale at early times ≈ homogeneous and isotropic Fix early time BAO scale with r → ∞ value (FRW limit) LTB geodesics ⇒ baryon clumps remain at constant r, θ, φ Physical distances given by grr = A 2(r,t) 1−k(r) , gθθ = A2(r, t) lL(r, t) = A (r, t) A (r, te) learly, lT (r, t) = A(r, t) A(r, te) learly Miguel Zumalac´arregui Tension in the Void
  50. 50. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis The physical BAO scale BAO scale at early times ≈ homogeneous and isotropic Fix early time BAO scale with r → ∞ value (FRW limit) LTB geodesics ⇒ baryon clumps remain at constant r, θ, φ Physical distances given by grr = A 2(r,t) 1−k(r) , gθθ = A2(r, t) lL(r, t) = A (r, t) A (r, te) learly, lT (r, t) = A(r, t) A(r, te) learly LTB: evolving (t), inhomogeneous (r) and anisotropic lT = lL FRW → only time evolution! Miguel Zumalac´arregui Tension in the Void
  51. 51. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis The observed BAO scale Observations → galaxy correlation in angular and redshift space Geometric mean d ≡ δθ2δz 1/3 δθ = lT (z) DA(z) , δz = (1 + z)HL(z) lL(z) Miguel Zumalac´arregui Tension in the Void
  52. 52. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis The observed BAO scale Observations → galaxy correlation in angular and redshift space Geometric mean d ≡ δθ2δz 1/3 δθ = lT (z) DA(z) , δz = (1 + z)HL(z) lL(z) Different result than FRW dLTB(z) = ξ(z) dFRW(z) ξ(z) = rescaling = (ξ2 T ξL)1/3 Inhomogeneous, anisotropic 0.0 0.2 0.4 0.6 0.8 1.0 1.0 1.1 1.2 1.3 1.4 z Ξz Transverse rescaling Longitudinal rescaling Miguel Zumalac´arregui Tension in the Void
  53. 53. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC data and models Observations: WiggleZ BAO: 3 × d measurements + Carnero et al.: 1 × δθ 4 new points at 0.4 < z < 0.8 → lBAO in broad range Miguel Zumalac´arregui Tension in the Void
  54. 54. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC data and models Observations: WiggleZ BAO: 3 × d measurements + Carnero et al.: 1 × δθ 4 new points at 0.4 < z < 0.8 → lBAO in broad range Union 2 Supernovae Compilation: 557 Ia SNe z 1.5 H0 = 73.8 ± 2.4 → Prior on the SNe luminosity Miguel Zumalac´arregui Tension in the Void
  55. 55. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC data and models Observations: WiggleZ BAO: 3 × d measurements + Carnero et al.: 1 × δθ 4 new points at 0.4 < z < 0.8 → lBAO in broad range Union 2 Supernovae Compilation: 557 Ia SNe z 1.5 H0 = 73.8 ± 2.4 → Prior on the SNe luminosity CMB peaks position (simplified analysis): 1% error on first peak, 3% on second and third Fixes the BAO scale Miguel Zumalac´arregui Tension in the Void
  56. 56. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC data and models Observations: WiggleZ BAO: 3 × d measurements + Carnero et al.: 1 × δθ 4 new points at 0.4 < z < 0.8 → lBAO in broad range Union 2 Supernovae Compilation: 557 Ia SNe z 1.5 H0 = 73.8 ± 2.4 → Prior on the SNe luminosity CMB peaks position (simplified analysis): 1% error on first peak, 3% on second and third Fixes the BAO scale Monte Carlo Markov Chain Analysis of FRW reference model: ΛCDM LTB models with homogeneous BB: Ωout = 1 and Ωout ≤ 1 Miguel Zumalac´arregui Tension in the Void
  57. 57. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC: FRW-ΛCDM reference model Using BAO scale, CMB peaks, Supernovae and H0+BAO+CMB+SNe BAO ∼ SNe: Arbitrary length/luminosity (before adding CMB/H0) CMB constraints much weaker than usual 1 − Ωk 1% ⇒ don’t take our CMB constraints too seriously Miguel Zumalac´arregui Tension in the Void
  58. 58. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC: constrained GBH, Ωout = 1 Filled: SNe+H0, BAO+CMB, Dashed: BAO , CMB peaks, Supernovae Depth of the Void: SNe → Ωin ≈ 0.1 (< 0.18) BAO → Ωin ≈ 0.3 (> 0.2) New: 3σ Away!!! Miguel Zumalac´arregui Tension in the Void
  59. 59. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC: constrained GBH, Ωout = 1 Filled: SNe+H0, BAO+CMB, Dashed: BAO , CMB peaks, Supernovae Depth of the Void: SNe → Ωin ≈ 0.1 (< 0.18) BAO → Ωin ≈ 0.3 (> 0.2) New: 3σ Away!!! Local Expansion Rate: SNe+H0 → hin ≈ 0.74 BAO+CMB → hin ≈ 0.62 known, worse if full CMB used Do asymptotically open models work better? Miguel Zumalac´arregui Tension in the Void
  60. 60. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis MCMC: constrained GBH, Ωout ≤ 1 Filled: SNe+H0, BAO+CMB, Dashed: BAO , CMB peaks, Supernovae Depth of the Void: SNe → Ωin ≈ 0.1 BAO → Ωin ≈ 0.3 Still 3σ Away!!! Local Expansion Rate: Ωout ≈ 0.85 ↔ higher Hin t0 ∝ 1/Hin → t0 12Gyr Only better H0, but Universe too young Miguel Zumalac´arregui Tension in the Void
  61. 61. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Best fit models Tension in the Void Bad fit to SNe and BAO SNe measure distance BAO: distance+rescaling complementary probes 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 r Gpc Mr constrained GBH Profile, out 1 BAO: in 0.18 SNe: in 0.18 Miguel Zumalac´arregui Tension in the Void
  62. 62. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Best fit models Tension in the Void Bad fit to SNe and BAO SNe measure distance BAO: distance+rescaling complementary probes Strongly ruled out Model χ2 − log E FRW-ΛCDM 536.6 282.2 flat-CGBH +19.8 +10 open-CGBH +9.4 +6 Miguel Zumalac´arregui Tension in the Void
  63. 63. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy Miguel Zumalac´arregui Tension in the Void
  64. 64. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy BAO and SNe alone strongly rule out the GBH model with homogeneous Big Bang and baryon fraction Miguel Zumalac´arregui Tension in the Void
  65. 65. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy BAO and SNe alone strongly rule out the GBH model with homogeneous Big Bang and baryon fraction Purely geometrical result, whatever Luminosity & BAO scale Miguel Zumalac´arregui Tension in the Void
  66. 66. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy BAO and SNe alone strongly rule out the GBH model with homogeneous Big Bang and baryon fraction Purely geometrical result, whatever Luminosity & BAO scale Possible ways to save large void models: Change the profile ΩM (r) Miguel Zumalac´arregui Tension in the Void
  67. 67. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy BAO and SNe alone strongly rule out the GBH model with homogeneous Big Bang and baryon fraction Purely geometrical result, whatever Luminosity & BAO scale Possible ways to save large void models: Change the profile ΩM (r) Inhomogeneous Big Bang ↔ free H0 Miguel Zumalac´arregui Tension in the Void
  68. 68. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy BAO and SNe alone strongly rule out the GBH model with homogeneous Big Bang and baryon fraction Purely geometrical result, whatever Luminosity & BAO scale Possible ways to save large void models: Change the profile ΩM (r) Inhomogeneous Big Bang ↔ free H0 Large scale isocurvature ρb = fb(r) ρm Miguel Zumalac´arregui Tension in the Void
  69. 69. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy BAO and SNe alone strongly rule out the GBH model with homogeneous Big Bang and baryon fraction Purely geometrical result, whatever Luminosity & BAO scale Possible ways to save large void models: Change the profile ΩM (r) Inhomogeneous Big Bang ↔ free H0 Large scale isocurvature ρb = fb(r) ρm BAO are a powerful test for large voids models of acceleration Miguel Zumalac´arregui Tension in the Void
  70. 70. A-Void Dark Energy Observational constraints Cosmological Data MCMC analysis Conclusions Large voids as alternative to dark energy BAO and SNe alone strongly rule out the GBH model with homogeneous Big Bang and baryon fraction Purely geometrical result, whatever Luminosity & BAO scale Possible ways to save large void models: Change the profile ΩM (r) Inhomogeneous Big Bang ↔ free H0 Large scale isocurvature ρb = fb(r) ρm BAO are a powerful test for large voids models of acceleration If large voids ruled out ⇒ need small Λ or “new” physics Miguel Zumalac´arregui Tension in the Void

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