Tension in the Void AIMS

A-Void Dark EnergyObservational constraints

Tension in the VoidarXiv:1201.2790

Miguel Zumalacarregui

Institute of Cosmos Sciences, University of Barcelona

with Juan Garcia-Bellido and Pilar Ruiz-Lapuente

AIMS (Cape Town), January 2012

Miguel Zumalacarregui Tension in the Void

Outline

1 A-Void Dark EnergyThe Standard Cosmological ModelInhomogeneous Universes

2 Observational constraintsCosmological DataMCMC analysis

3) Conclusions

The Standard Cosmological ModelInhomogeneous Universes

A-Void Dark Energy

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

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©

Some Popular (and Unpopular) Variations on the SCM

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

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

Beyond Homogeneity

ds2 = −dt2 +a(t)2 dr2

1− k+ [a(t) r]2 dΩ2

ds2 = −dt2 +A′2(r, t)

1− k(r)dr2 +A2(r, t) dΩ2

Beyond Homogeneity

ds2 = −dt2 +a(t)2 dr2

1− k+ [a(t) r]2 dΩ2

ds2 = −dt2 +A′2(r, t)

1− k(r)dr2 +A2(r, t) dΩ2

Beyond Homogeneity

ds2 = −dt2 +a(t)2 dr2

1− k+ [a(t) r]2 dΩ2

ds2 = −dt2 +A′2(r, t)

1− k(r)dr2 +A2(r, t) dΩ2

Inhomogeneous Cosmologies

LTB metric: ds2 = −dt2 + A′2(r,t)1−k(r) dr

2 +A2(r, t) dΩ2

Two expansion rates: HL = A′/A′ 6= 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:

H2T (r, t) = H2

[ΩM (r)

(A/A0(r))3 +1− ΩM (r)

(A/A0(r))2

2 +A2(r, t) dΩ2

H2T (r, t) = H2

[ΩM (r)

(A/A0(r))3 +1− ΩM (r)

(A/A0(r))2

2 +A2(r, t) dΩ2

H2T (r, t) = H2

[ΩM (r)

(A/A0(r))3 +1− ΩM (r)

(A/A0(r))2

2 +A2(r, t) dΩ2

H2T (r, t) = H2

[ΩM (r)

(A/A0(r))3 +1− ΩM (r)

(A/A0(r))2

2 +A2(r, t) dΩ2

H2T (r, t) = H2

[ΩM (r)

(A/A0(r))3 +1− ΩM (r)

(A/A0(r))2

2 +A2(r, t) dΩ2

H2T (r, t) = H2

[ΩM (r)

(A/A0(r))3 +1− ΩM (r)

(A/A0(r))2

Less Inhomogeneous Cosmologies

No pressure: H2T =

dt= H2

0 (r)[

ΩM (r)

(A/A0(r))3+ 1−ΩM (r)

(A/A0(r))2

]t(A, r) =

A′H2T (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

No pressure: H2T =

dt= H2

0 (r)[

ΩM (r)

(A/A0(r))3+ 1−ΩM (r)

(A/A0(r))2

]t(A, r) =

A′H2T (r,A′)

tBB(r) = t(A0, r) = t0

No pressure: H2T =

dt= H2

0 (r)[

ΩM (r)

(A/A0(r))3+ 1−ΩM (r)

(A/A0(r))2

]t(A, r) =

A′H2T (r,A′)

tBB(r) = t(A0, r) = t0

No pressure: H2T =

dt= H2

0 (r)[

ΩM (r)

(A/A0(r))3+ 1−ΩM (r)

(A/A0(r))2

]t(A, r) =

A′H2T (r,A′)

tBB(r) = t(A0, r) = t0

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 80.0

GBH Profile

DR =1Gpc

DR =0.5

DR =1.5

These are just parameters → physical quantities ρ,HL, HT ...

Depth of void Ωin

Baryon fraction fb

0 2 4 6 80.0

GBH Profile

DR =1Gpc

DR =0.5

DR =1.5

Depth of void Ωin

Baryon fraction fb

0 2 4 6 80.0

GBH Profile

DR =1Gpc

DR =0.5

DR =1.5

Depth of void Ωin

Baryon fraction fb0 2 4 6 8

GBH Profile

DR =1Gpc

DR =0.5

DR =1.5

Depth of void Ωin

Baryon fraction fb0 2 4 6 8 10

r @ GpcD

WM H rL

ΡH r ,t0L Ρ¥H t0LΡ H r ,t10 L Ρ ¥ H t10 L

HT H r ,t0L

HL H r ,t0L

Cosmological DataMCMC analysis

Observational constraints

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

DL(z) =

√Luminosity

4π Flux= H−1

H0 = 73.8± 2.4 Mpc/Km/s ↔ L = −0.120± 0.071 Mag

DL(z) =

√Luminosity

4π Flux= H−1

H0 = 73.8± 2.4 Mpc/Km/s ↔ L = −0.120± 0.071 Mag

Baryon acoustic oscillations - Standard Rulers

-CMB light released when H forms

-Sound waves in the baryon-photonplasma 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

2(1− k)+A′′

]r2 + 2

A′tr = 0

t r ⇒ Constant coordinate separation (zero order)

2(1− k)+A′′

]r2 + 2

A′tr = 0

2(1− k)+A′′

]r2 + 2

A′tr = 0

2(1− k)+A′′

]r2 + 2

A′tr = 0

Observations in LTB universes (Constrained case)

ìì-2 0 2 4 6 8 10

r @ GpcD

constant t H z =0L

t H z =1L

t H z =100 L

constant Ρ

z~1100

Homogeneous state at

early times, large r

øøWe are here

-2 0 2 4 6 8 10

r @ GpcD

constant tH z =0L

tH z =1L

tH z =100L

constant Ρ

z~1100

øøWe are here

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tH z =1L

tH z =100L

constant Ρ

z~1100

Ia SNe zd1.5

øøWe are here

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r @ GpcD

constant tH z =0L

tH z =1L

tH z =100L

constant Ρ

z~1100

Ia SNe zd1.5

BAO zd0.8

øøWe are here

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-2 0 2 4 6 8 10

r @ GpcD

constant tH z =0L

tH z =1L

tH z =100L

constant Ρ

z~1100

Ia SNe zd1.5

BAO zd0.8

Relate to early time

and asymptoticvalue

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 6= lL

FRW → only time evolution!

lL(r, t) =A′(r, t)

A(r, t)

A(r, te)learly

lL(r, t) =A′(r, t)

A(r, t)

A(r, te)learly

lL(r, t) =A′(r, t)

A(r, t)

A(r, te)learly

lL(r, t) =A′(r, t)

A(r, t)

A(r, te)learly

The observed BAO scale

Observations → galaxy correlation in angular and redshift space

Geometric mean d ≡(δθ2δz

)1/3δθ =

lT (z)

DA(z), δz = (1 + z)HL(z) lL(z)

Different result than FRW

dLTB(z) = ξ(z) dFRW(z)

ξ(z) = rescaling = (ξ2T ξL)1/3

Inhomogeneous, anisotropic0.0 0.2 0.4 0.6 0.8 1.0

Transverse

rescalingLongitudinal

rescaling

The observed BAO scale

Observations → galaxy correlation in angular and redshift space

Geometric mean d ≡(δθ2δz

)1/3δθ =

lT (z)

DA(z), δz = (1 + z)HL(z) lL(z)

Different result than FRW

dLTB(z) = ξ(z) dFRW(z)

ξ(z) = rescaling = (ξ2T ξL)1/3

Inhomogeneous, anisotropic0.0 0.2 0.4 0.6 0.8 1.0

Transverse

rescalingLongitudinal

rescaling

MCMC data and models

Observations:

WiggleZ BAO: 3× d measurements + Carnero et al.: 1× δθ4 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 thirdFixes the BAO scale

Monte Carlo Markov Chain Analysis of

FRW reference model: ΛCDM

LTB models with homogeneous BB: Ωout = 1 and Ωout ≤ 1

Observations:

MCMC: FRW-ΛCDM reference model

Using BAO scale, CMB peaks, Supernovae and H0+BAO+CMB+SNe

BAO ∼ SNe: Arbitrarylength/luminosity (beforeadding CMB/H0)

CMB constraints muchweaker than usual1− Ωk . 1%

⇒ don’t take our CMB constraints too seriously

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?

MCMC: constrained GBH, Ωout = 1

Depth of the Void:

SNe → Ωin ≈ 0.1 (< 0.18)

BAO → Ωin ≈ 0.3 (> 0.2)

New: 3σ Away!!!

SNe+H0 → hin ≈ 0.74

BAO+CMB → hin ≈ 0.62

known, worse if full CMB used

Do asymptotically open models work better?Miguel Zumalacarregui Tension in the Void

MCMC: constrained GBH, Ωout ≤ 1

Depth of the Void:

SNe → Ωin ≈ 0.1

BAO → Ωin ≈ 0.3

Still 3σ Away!!!

Ωout ≈ 0.85↔ higher Hin

t0 ∝ 1/Hin → t0 . 12Gyr

Only better H0, but Universe too young

Best fit models

Tension in the Void

Bad fit to SNe and BAO

SNe measure distanceBAO: distance+rescaling

complementary probes

Strongly ruled out

0 2 4 6 8 100.0

r @ GpcD

constrained GBH Profile, Wout=1

BAO: Win>0.18

SNe: Win<0.18

Best fit models

Tension in the Void

Bad fit to SNe and BAO

SNe measure distanceBAO: distance+rescaling

complementary probes

Strongly ruled out

Model χ2 − logE

FRW-ΛCDM 536.6 282.2

flat-CGBH +19.8 +10open-CGBH +9.4 +6

Conclusions

Large voids as alternative to dark energy

BAO and SNe alone strongly rule out the GBH model withhomogeneous 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

Conclusions

Tension in the Void AIMS

Technology

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