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. 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. A-Void Dark Energy
Observational constraints
The Standard Cosmological Model
Inhomogeneous Universes
A-Void Dark Energy
Miguel Zumalac´arregui Tension in the Void

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. A-Void Dark Energy
Observational constraints
Cosmological Data
MCMC analysis
Observational constraints
Miguel Zumalac´arregui Tension in the Void

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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