Can an Inhomogeneous Universe mimic Dark Energy?

Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Can an Inhomogeneous Universe mimic
Dark Energy?
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
Alessio Notari 1
BAO
Large-Scale
structure(LRG)
Gpc Void
CERN
Other observations
The Cold Spot
Redshift (low-ℓ)
June 2009, Heidelberg
Lensing (high-ℓ)
Conclusions
1
In collaboration with:
Tirthabir Biswas , Stephon Alexander, Deepak Vaid, Reza Mansouri, Wessel Valkenburg, Isabella Masina.
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
The need for Dark Energy
Void vs Dark
Energy
In Standard Cosmology we use the FLRW model.
Motivations
LTB metrics
We compute DL (or DA ) and z
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
We use this to interpret several observations (SNIa,
Hubble constant, CMB, Baryon Acoustic Oscillations,
Matter Power Spectrum...)
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
To fit the observations we need a p < 0 term
(“Dark Energy”).
The need for Dark Energy
Void vs Dark
Energy
In Standard Cosmology we use the FLRW model.
Motivations
LTB metrics
We compute DL (or DA ) and z
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
We use this to interpret several observations (SNIa,
Hubble constant, CMB, Baryon Acoustic Oscillations,
Matter Power Spectrum...)
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
To fit the observations we need a p < 0 term
(“Dark Energy”).
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Problem: We do not understand
the amount (why of the same amount as Matter today)?
its nature (is it vacuum energy?)
Main pieces of evidence
Void vs Dark
Energy
SNIa is incompatible with deceleration (independently
on other observations)
Assuming them as standard candles.
Assuming them not exactly as standard candles
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
2
Blanchard et al. ’03, Sarkar and Hunt ’04, ’07
Main pieces of evidence
Void vs Dark
Energy
SNIa is incompatible with deceleration (independently
on other observations)
Assuming them as standard candles.
Assuming them not exactly as standard candles
Motivations
LTB metrics
Building the model
CMB: best-fit with power-law (k ns ) primordial spectrum
has ΩΛ ∼ 0.7.
But good fit2 also with ΩM = 1:
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
low-h (0.45)
non-standard primordial spectrum
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
2
Blanchard et al. ’03, Sarkar and Hunt ’04, ’07
Main pieces of evidence
Void vs Dark
Energy
SNIa is incompatible with deceleration (independently
on other observations)
Assuming them as standard candles.
Assuming them not exactly as standard candles
Motivations
LTB metrics
Building the model
CMB: best-fit with power-law (k ns ) primordial spectrum
has ΩΛ ∼ 0.7.
But good fit2 also with ΩM = 1:
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
low-h (0.45)
non-standard primordial spectrum
BAO
Large-Scale
structure(LRG)
Gpc Void
The two dataset,
Other observations
The Cold Spot
SNIa
CMB together with measured h: 0.55 . h . 0.8
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
are strong evidence for ΩΛ ∼ 0.7.
2
Blanchard et al. ’03, Sarkar and Hunt ’04, ’07
Main pieces of evidence
Void vs Dark
Energy
SNIa is incompatible with deceleration (independently
on other observations)
Assuming them as standard candles.
Assuming them not exactly as standard candles
Motivations
LTB metrics
Building the model
CMB: best-fit with power-law (k ns ) primordial spectrum
has ΩΛ ∼ 0.7.
But good fit2 also with ΩM = 1:
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
low-h (0.45)
non-standard primordial spectrum
BAO
Large-Scale
structure(LRG)
Gpc Void
The two dataset,
Other observations
The Cold Spot
SNIa
CMB together with measured h: 0.55 . h . 0.8
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
are strong evidence for ΩΛ ∼ 0.7.
Other observations (BAO and LSS...) fit consistently
2
Blanchard et al. ’03, Sarkar and Hunt ’04, ’07
Is there any alternative?
Void vs Dark
Energy
Motivations
Look for other logical possibilities, in usual GR.
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Especially: can we rule out any other explanation, even
if radical, based on observations?
Is there any alternative?
Void vs Dark
Energy
Motivations
Look for other logical possibilities, in usual GR.
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
Especially: can we rule out any other explanation, even
if radical, based on observations?
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
What happens to observations when we have
departure from a homogeneous model?
Is there any alternative?
Void vs Dark
Energy
Motivations
Look for other logical possibilities, in usual GR.
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
Especially: can we rule out any other explanation, even
if radical, based on observations?
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
What happens to observations when we have
departure from a homogeneous model?
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
An opportunity to observationally test the Copernican
principle
Homogenous Universe: a good approximation?
Void vs Dark
Energy
Motivations
At z ≫ 1 (CMB epoch, for example) tiny density
fluctuations on all observed scales.
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
It is a good approximation
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
..at late times δ ≡ δρ
ρ > 1 for all scales
L . O(10)/h Mpc (1% of Hubble radius)
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Superclusters upto few hundreds of Mpc (10% of
Hubble radius), nonlinear objects ("cosmic web")
SDSS data ("The cosmic web")
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
SDSS data
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
SDSS data
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Scale of Homogenity
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Scale of convergence in SDSS data?
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
70Mpc/h:
P.Sarkar et al 2009; J.Yadav et al. 2005; Hogg et al. 2005
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
No convergence:
Sylos Labini et al. 2007 & 2009
Three physical effects of inhomogeneities
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
In general:
Backreaction
perturbations affect the background
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
Light propagation
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Light travels through voids and structures. Do they
compensate?
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Large local fluctuation
What if we live in a local void?
A local fluctuation?
Void vs Dark
Energy
Suppose that we live in a peculiar local region
Motivations
LTB metrics
Building the model
⇒ low z observations may be very different from
average.
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Acceleration is inferred comparing low z with high z...
Large-Scale
structure(LRG)
Gpc Void
Other observations
Can this mimic acceleration 3 ?
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
3
Tomita ’98, Tomita ’00, Celerier ’01, Wiltshire ’05, Moffat ’05, Alnes et
al. ’05, Mansouri et al. ’06, Biswas & A.N.’07, Garcia-Bellido and
Haugboelle ’08, Zibin et al. ’08 ...
Qualitatively
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Consider a “compensated Void” : a spherical Void plus
an external shell of matter (on average same density as
“external” FLRW)
Assumption: we live near the center
Qualitatively
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
Consider a “compensated Void” : a spherical Void plus
an external shell of matter (on average same density as
“external” FLRW)
Assumption: we live near the center
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A void expands faster than the “external” FLRW
⇒ So, nearby objects inside the void redshift more
⇒ This can mimic acceleration (as we will see...)
Qualitatively
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
Consider a “compensated Void” : a spherical Void plus
an external shell of matter (on average same density as
“external” FLRW)
Assumption: we live near the center
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A void expands faster than the “external” FLRW
⇒ So, nearby objects inside the void redshift more
⇒ This can mimic acceleration (as we will see...)
How much contrast δ and how large L is needed?
About Voids
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Before going to the quantitative analysis...
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Let us review some literature and observations on Voids
Large Voids?
Void vs Dark
Energy
Motivations
LTB metrics
: some features of the low multipole
anomalies in the CMB data could be explained by a
pair of huge Voids (L ∼ 200 Mpc/h, δ ∼ −0.3)
Inoue and Silk ’06
Building the model
Results
Local Void:
Fitting the
data
The CMB has a Cold Spot (M. Cruz et al. (’06 and ’07)): it could be
explained by another similar Large Void (Inoue and Silk ’06)
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
The Cold Spot in the CMB claimed to be correlated with
an underdense region in the LSS, Radio sources (Rudnick,
Brown and Williams ’07, but see Smith & Huterer ’08 ...)
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
It could be detected via lensing (S. Das and D. Spergel ’08, I.Masina and
) and via non-gaussian coupling Rees-Sciama
effect - lensing ( I.Masina and A.N ’09)
A.N ’08-’09
Observational Status
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Some observational evidence for a local large
underdense region (∼ 25% less dense, r ∼ 200 Mpc/h)
from number counts of galaxies (2MASS)
(Frith et al. ’03)
It would represent a 4σ fluctuation, at odds with ΛCDM.
Observational Status
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
Some observational evidence for a local large
underdense region (∼ 25% less dense, r ∼ 200 Mpc/h)
from number counts of galaxies (2MASS)
(Frith et al. ’03)
It would represent a 4σ fluctuation, at odds with ΛCDM.
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Many Large Voids identified via ISW effect in the SDSS
LRG catalog (about 100 Mpc/h radius) (Granett et al. ’08)
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Also in contradiction with ΛCDM: P < 10−8 (Sarkar & Hunt ’08)
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Figure: Granett, Neyrinck & Szapudi ’08
Large bulk motion?
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Recent measurement (Kashlinsky et al.’08): very large
coherent motion on 300Mpc/h scale, inconsistent with
ΛCDM
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Could be due to very large scale inhomogeneous
matter distribution
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Watkins, Feldman & Hudson ’08: use peculiar velocities
of various (4500) objects in a 100 Mpc/h radius.
Find 400 km/sec (expected 100 km/sec)
A “Minimal” Void ?
Void vs Dark
Energy
What is the size we need to mimic DE?
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A “Minimal” Void ?
Void vs Dark
Energy
What is the size we need to mimic DE?
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
It will turn out that a Minimal Void needs at least the
same size (for Riess ’07 SNIa and WMAP)
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
rVoid ∼ 200 − 250 Mpc/h and δ ∼ −0.4
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
On this scale the typical contrast is:
δ ∼ 0.03 − 0.05, using linear and Gaussian spectrum
A “Minimal” Void ?
Void vs Dark
Energy
What is the size we need to mimic DE?
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
It will turn out that a Minimal Void needs at least the
same size (for Riess ’07 SNIa and WMAP)
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
rVoid ∼ 200 − 250 Mpc/h and δ ∼ −0.4
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
On this scale the typical contrast is:
δ ∼ 0.03 − 0.05, using linear and Gaussian spectrum
Conclusions
A Gpc Void seems required to fit all observations
Which primordial origin?
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
Can we get huge Voids?
Percolation of Voids?
Non-gaussianity (for example of primordial spherical
shape)?
Nucleation of primordial Bubbles (first order phase
transition during inflation)
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Main tuning: why observer at centre?
LTB exact solutions
Void vs Dark
Energy
Motivations
LTB metrics
Consider Lemaître-Tolman-Bondi exact solutions of
E.E. (with p = 0) which is
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
inhomogeneous
nonlinear
WMAP
BAO
Large-Scale
structure(LRG)
Spherically symmetric
Gpc Void
Other observations
The Cold Spot
LTB sphere embedded in FLRW ("Swiss-Cheese")
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
We study null geodesic in this metric
Earlier literature
Void vs Dark
Energy
Motivations
Mustapha, Hellaby, Ellis ’97
LTB metrics
DL − z curve
Building the model
: show that LTB can reproduce any
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Celerier ’99
: showed that LTB can mimic ΛCDM
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Tomita ’01
: Compensated Void 200 − 300 Mpc/h scale
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Lemaître-Tolman-Bondi metrics
Void vs Dark
Energy
′
Motivations
LTB metrics
R 2 (r , t)
ds = −dt +
dr 2 + R 2 (r , t)(d θ 2 + sin2 θd ϕ2 )
1 + 2r 2 k(r )
2
2
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
with comoving coordinates (r , θ, ϕ) and proper time t.
Einstein equations:
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
1 Ṙ 2 (r , t)
2 R 2 (r , t)
−
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
4πρ(r , t) =
GM(r )
r 2 k(r )
=
,
R 3 (r , t)
R 2 (r , t)
M ′ (r )
,
R ′ (r , t)R 2 (r , t)
LTB metrics
Void vs Dark
Energy
′
Motivations
ds2 = −dt 2 +
R 2 (r , t)
dr 2 + R 2 (r , t)(dθ2 + sin2 θdϕ2 )
1 + 2r 2 k (r )
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
It has the solutions:
For k (r ) > 0 (k (r ) < 0),
SNIa Hubble diagram
WMAP
BAO
R
=
t − tb (r )
=
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
GM(r )
[cos h(u) − 1],
2r 2 |k (r )|
GM(r )
[sin h(u) − u].
[2r 2 |k (r )|]3/2
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
k (r ) = 0,
R(r , t) =
9GM(r )
2
1/3
2
[t − tb (r )] 3 .
(2.1)
Choosing the functions
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
tb (r ) = 0 for our purposes, and “Gauge” choice:
M(r ) ∝ r 3
Choosing the functions
Void vs Dark
Energy
Motivations
tb (r ) = 0 for our purposes, and “Gauge” choice:
M(r ) ∝ r 3
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
k(r ) contains all the physical information about the
profile.
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
k = 0 flat FLRW, k = ±1 open/closed FLRW.
Choosing the functions
Void vs Dark
Energy
Motivations
tb (r ) = 0 for our purposes, and “Gauge” choice:
M(r ) ∝ r 3
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
k(r ) contains all the physical information about the
profile.
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
k = 0 flat FLRW, k = ±1 open/closed FLRW.
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
The idea is to describe structure formation
(start with δ(r , tI ) ≪ 1 and end up with δ(r , tnow ) ≫ 1)
Conclusions
We play with k(r ) to describe δ(r , tI ).
LTB merged to FLRW
Void vs Dark
Energy
Matching of an LTB sphere (of radius L) to FLRW:
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
k ′ (0) = k ′ (L) = 0 ,
4πΩk
k(L) =
3(1 − Ωk )
LTB merged to FLRW
Void vs Dark
Energy
Matching of an LTB sphere (of radius L) to FLRW:
Motivations
k ′ (0) = k ′ (L) = 0 ,
4πΩk
k(L) =
3(1 − Ωk )
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
We use:
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
k (r ) = kmax
4
2
r
−1
L
k (r ) = 0 (flat)
Conclusions
Two parameters, L and kmax .
(for r < L)
(for r > L)
The density
Void vs Dark
Energy
Roughly:
Motivations
LTB metrics
Building the model
ρ(r , t) ≃
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
Mp2
where hρi(t) ≡
,
6πt 2
hρi(t)
,
1 + (t/t0 )2/3 ǫ(r )
and ǫ(r ) ≡ 3k(r ) + rk ′ (r ) .
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
ǫ ≪ 1 linear growth
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
ǫ not small: δ grows rapidly (as in Zel’dovich approx)
Conclusions
We work at most with δ ∼ O(1).
The density profile
Void vs Dark
Energy
Motivations
1
LTB metrics
0.75
Building the model
0.5
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
0.25
∆Ρ
€€€€€€€€€
Ρ
0
-0.25
-0.5
Gpc Void
Other observations
-0.75
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
0
0.02
0.04
z
0.06
0.08
Redshift
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Solve for t(r ) along a ds2 = 0 trajectory
Then solve for z(r )
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
dz
(1 + z(r ))Ṙ ′ (r , t(r ))
p
=
.
dr
1 + 2r 2 k (r )
Redshift
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Solve for t(r ) along a ds2 = 0 trajectory
Then solve for z(r )
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
dz
(1 + z(r ))Ṙ ′ (r , t(r ))
p
=
.
dr
1 + 2r 2 k (r )
The result z(r ) can be found numerically
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
We also have some very good analytical
approximations
Luminosity (Angular) Distance
Void vs Dark
Energy
Always in GR, luminosity distance and angular distance:
DL = DA (1 + z)2 .
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
DA2
√
dθS dφS gθθ gφφ 2
dA
≡
=
R |S ,
dΩ
d θ̄O d φ̄O
Luminosity (Angular) Distance
Void vs Dark
Energy
Always in GR, luminosity distance and angular distance:
DL = DA (1 + z)2 .
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
DA2
√
dθS dφS gθθ gφφ 2
dA
≡
=
R |S ,
dΩ
d θ̄O d φ̄O
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
If observer in the center:
DA2 = R 2 |S .
For generic observer (but radial trajectory):
Z rS
R ′ (r , t(r ))
dr ,
DA = RS RO
2
rO (1 + 2E(r ))(1 + z(r ))R(r , t(r ))
Analytical approximation
Void vs Dark
Energy
f
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
u0
≡
√
3
2(cosh(u) − 1)
−1
2/3
3 (sinh(u) − u)2/3
= 61/3 (sinh(u) − u)1/3 .
Then, one can use this function in the following equations:
π
τ (r ) = τ0 − γ 2 M̄r [1 + f (γ 2 τ02 k (r ))] ,
9
2
4πγ 2 M̄r
τ0
2 2
exp
f (γ τ0 k (r ))
1 + z(r ) =
τ (r )
9
π 2
DL (r ) =
γ r τ (r )2 [1 + f (γ 2 τ02 k (r ))][1 + z(r )]2
3
¯ 1/3
2M
τ0 =
3H0
√ !1/3
9 2
γ =
π
(2.2)
(2.3)
(2.4)
(2.5)
(2.6)
(2.7)
(2.8)
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Observer outside: z
Void vs Dark
Energy
Net effect from one hole4 :
∆z
1+z
≈ (L/rH )3 f (δ)
Motivations
At 2nd order usual Rees-Sciama effect (L/rH )3 δ2
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
f (δ) does not compensate the suppression for δ ≫ 1
SNIa Hubble diagram
WMAP
BAO
Tight packing: Nholes × O(L/rH )3 ∼ O(L/rH )2
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Still small (for late acceleration)
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Interesting in the CMB, as a Rees-Sciama effect.
4
T. Biswas-A. N. ’06-’07
Observer outside: Distance
Void vs Dark
Energy
Net effect scales as
Motivations
∆z
1+z
≈ (L/rH )2 f (δ) 5
LTB metrics
Building the model
f (δ) does not compensate the suppression for δ ≫ 1
Results
Local Void:
Fitting the
data
Tight packing: Nholes O(L/rH )3 = O(L/rH )
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Not so small...
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
But it should have zero angular average (unlike z)6
Lensing (high-ℓ)
Conclusions
5
6
Brouzakis-Tetradis-Tzavara ’06, Kolb-Matarrese-Riotto ’07, T. Biswas-A. N. ’07
S. Weinberg ’76, Brouzakis et al. ’06-’07
Observer outside: Beyond LTB?
Void vs Dark
Energy
Motivations
Reliable result or limited by the symmetries of the
model?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
LTB model swiss-cheese: special case
Observer outside: Beyond LTB?
Void vs Dark
Energy
Motivations
Reliable result or limited by the symmetries of the
model?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
LTB model swiss-cheese: special case
The cheese feels no backreaction by construction
Observer outside: Beyond LTB?
Void vs Dark
Energy
Motivations
Reliable result or limited by the symmetries of the
model?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
LTB model swiss-cheese: special case
The cheese feels no backreaction by construction
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
What happens without spherical symmetry?
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Szekeres swiss-cheese model with asymmetric holes
(Bolejko ’08)
Lensing (high-ℓ)
Conclusions
But still special: the cheese feels no backreaction of the
holes
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
High and low z
Void vs Dark
Energy
Motivations
LTB metrics
Evidence for acceleration comes from mismatch between:
measurements at low redshift ( 0.03 . z . 0.08 )
Building the model
Results
high-z SN (roughly 0.4 . z . 1 )
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
We choose large rVoid
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
⇒ The Local Bubble is different from the average.
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
L 2
) )
Outside just FLRW curve (plus small corrections O( r hor
Roughly
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
At high z (z & 0.1), just FLRW
Results
Local Void:
Fitting the
data
At low z "open-like" Universe with a different H
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Two Hubble parameters: h and hout
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Rapid transition near the shell-like structure
∆m for different models
Void vs Dark
Energy
Motivations
LTB metrics
Magnitude is m ≡ 5Log10D(z)
The open “empty” Universe is subtracted (ΩK = −1)
Building the model
Results
z jump =0.085 ; ∆CENTRE =-0.25
0.2
Local Void:
Fitting the
data
0.15
0.1
SNIa Hubble diagram
WMAP
0.05
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Dm
0
-0.05
-0.1
-0.15
0
0.05
0.1
0.15
z
0.2
0.25
0.3
m − z diagram: Riess data
Void vs Dark
Energy
z jump =0.085 ; ∆CENTRE =-0.48
0.75
Motivations
0.5
LTB metrics
0.25
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Dm
0
-0.25
-0.5
-0.75
-1
0
0.25
0.5
0.75
Gpc Void
1
1.25
z
Other observations
The Cold Spot
Redshift (low-ℓ)
1
Lensing (high-ℓ)
0.75
0.5
Conclusions
0.25
∆Ρ
€€€€€€€€€
Ρ
0
-0.25
-0.5
-0.75
0
0.02
0.04
z
0.06
0.08
1.5
1.75
Finding the best fit
Void vs Dark
Energy
Motivations
LTB metrics
We fix several values of L
Building the model
Results
Local Void:
Fitting the
data
What matters is just the Jump: J ≡
h
hOUT
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
This is also related to the central density contrast:
J = 2 − (1 − δ0 )1/3
We vary J and compute the χ2 .
Fitting SNIa with a Jump
Void vs Dark
Energy
Motivations
Outside ΩM = 1
Riess et al. dataset, astro-ph/0611576 (182 SNIa)
LTB metrics
240
Building the model
z jump = [0.09,0.08,0.07,0.06,0.05] (from bottom to top)
Results
230
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
220
2
Χ 210
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
200
190
180
1.05
1.1
1.15
1.2
1.25
Hin /Hout
1.3
1.35
Conclusions
Figure: Red dashed lines: 10% and 1% goodness-of-fit (182 data
points)
LTB Void fit
Void vs Dark
Energy
Motivations
LTB metrics
z jump = 0.085
200
197.5
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
195
Χ2 192.5
190
187.5
185
182.5
1.1
1.15
1.2
1.25
Hin Hout
1.3
Figure: Full LTB model. We show 1σ, 2σ, 3σ and 4σ intervals
2
(using likelihood ∝ e−χ /2 ).
χ2 : Riess data
Void vs Dark
Energy
Table: Comparison with data (full data set of Riess et al.)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Model
ΛCDM (with ΩM = 0.27, ΩΛ = 0.73)
EdS (with
p ΩM = 1, ΩΛ = 0)
Void ( hδ2 i ≈ 0.4 on L = 250/hMpc)
χ2 (181 d.o.f.)
160
274
182
χ2 : Riess data
Void vs Dark
Energy
Table: Comparison with data (full data set of Riess et al.)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
Model
ΛCDM (with ΩM = 0.27, ΩΛ = 0.73)
EdS (with
p ΩM = 1, ΩΛ = 0)
Void ( hδ2 i ≈ 0.4 on L = 250/hMpc)
χ2 (181 d.o.f.)
160
274
182
Remarks:
With instrumental error only: no smooth curve can give a
good fit
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Estimated error from intrinsic variability added in quadrature
Not as good as ΛCDM
Becomes better including curvature Ωk outside
SDSS-II will improve a lot: ∆χ2 ∼ 60
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
The WMAP data
Void vs Dark
Energy
We look at TT and TE correlations, using CosmoMC
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
In principle: we should compute propagation in EdS
from z = 1100 to z ∼ 0.1, and then in the Bubble
The WMAP data
Void vs Dark
Energy
We look at TT and TE correlations, using CosmoMC
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
In principle: we should compute propagation in EdS
from z = 1100 to z ∼ 0.1, and then in the Bubble
“Secondary” effect in the Bubble:
Small offset to DA and T0 of O(rVoid /rHor )2
Relevant only for Gpc Void
Small because of compensation
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
We ignore:
The WMAP data
Void vs Dark
Energy
We look at TT and TE correlations, using CosmoMC
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
In principle: we should compute propagation in EdS
from z = 1100 to z ∼ 0.1, and then in the Bubble
“Secondary” effect in the Bubble:
Small offset to DA and T0 of O(rVoid /rHor )2
Relevant only for Gpc Void
Small because of compensation
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
We ignore:
Off-center location: dipole
Non-sphericity (again effect on low-l)
Priors (ΛCDM)
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
The usual prior set is:
Results
Local Void:
Fitting the
data
Allow for nonzero ΩΛ .
SNIa Hubble diagram
WMAP
BAO
Power-law spectrum with index ns and running αs .
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
1
P(k) ∝ k ns (k0 )+ 2 ln(k /k0 )αs
Priors: without Λ
Void vs Dark
Energy
Motivations
LTB metrics
A different prior set, that we use:
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Not allow for ΩΛ .
Power-law spectrum with index ns and running αs ..
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
1
P(k) ∝ k ns (k0 )+ 2 ln(k /k0 )αs
Lensing (high-ℓ)
Conclusions
(we also allow for some curvature)
Fit to WMAP3
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Goodness-of-fit
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Table: Fit of WMAP
Model
Concordant ΛCDM
EdS αs 6= 0
EdS αs , Ωk 6= 0
Total
χ2eff
G.F.
3538.6 41%
3577.4 24.6%
3560.9 31.1%
Result for parameters
Void vs Dark
Energy
The EdS model, with running, has:
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
low hOUT (about ∼ 0.45)
It has to be consistent with the SNIa analysis and the
local measurements of h
low nS (about ∼ 0.73)
and large negative αs (about ∼ −0.16)
Other observations
The Cold Spot
larger value of ΩM /Ωb (around 10 instead of 6)
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
2
Ωb hout
(∼ 0.018+0.001
−0.002 ) consistent with BBN constraint
2
≤ 0.024, at 95% C.L.)
(which is 0.017 ≤ Ωb hout
Parameter likelihood
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
0.017
Results
0.018
0.019
2
Ωb hout
0.02
0.175
0.18
0.185
0.19
2
Ωm hout
0.195
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
0.65
0.7
0.75
0.8
−0.22
−0.2
−0.18
ns
−0.16
αs
−0.14
−0.12
−0.1
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
9.5
10
Ωm/Ωb
10.5
11
44
44.5
45
45.5
46
46.5
Hout
Figure: likelihoods to WMAP 3-yr for the run “EdS with αs ”
Parameter likelihood
Void vs Dark
Energy
−0.1
−0.12
−0.14
α
s
Motivations
LTB metrics
−0.16
−0.18
Building the model
−0.2
Results
−0.22
Local Void:
Fitting the
data
0.64
0.66
0.68
0.7
0.72
n
0.74
0.76
0.78
0.8
0.82
s
SNIa Hubble diagram
11
WMAP
BAO
10.5
m
Ω /Ω
b
Large-Scale
structure(LRG)
Gpc Void
10
Other observations
The Cold Spot
9.5
Redshift (low-ℓ)
44
Lensing (high-ℓ)
Conclusions
44.5
45
H
45.5
46
46.5
out
Figure: Contour likelihood plots to WMAP 3-yr for the run “EdS
with αs ”
Low H0
Void vs Dark
Energy
low hOUT (∼ 0.45)7
We get a constraint on local h (∼ 0.55)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
7
As in A. Blanchard et al.’03 and P. Hunt & S. Sarkar ’07
Low H0
Void vs Dark
Energy
Motivations
LTB metrics
low hOUT (∼ 0.45)7
We get a constraint on local h (∼ 0.55)
Compatible with local observations?
Building the model
Results
h = 0.72 ± 0.08 from HST (Freedman et al., Astrophys. J. 553, 47 (2001) )
Local Void:
Fitting the
data
h = 0.62 ± 0.01 ± 0.05 from HST with corrected Cepheids
(A. Sandage et al., Astrophys. J. 653, 843 (2006))
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
h = 0.59 ± 0.04 from Supernovae (Parodi, Saha, Sandage and Tammann,
arXiv:astro-ph/0004063. )
Gpc Void
Other observations
The Cold Spot
h = 0.54−.03
+.04 SZ effect (z ≈ 1) (Reese et al. Ap. J. 581, 53 (2002))
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
h = 0.48+.03
−.03 from lensing (0.3 . z . 0.7) (C. S. Kochanek and
P. L. Schechter, arXiv:astro-ph/0306040. )
7
As in A. Blanchard et al.’03 and P. Hunt & S. Sarkar ’07
Parameter Contours
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
0.5
Results
Local Void:
Fitting the
data
0.48
SNIa Hubble diagram
0.46
BAO
Large-Scale
structure(LRG)
h out
WMAP
0.44
Gpc Void
Other observations
0.42
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
0.4
0.5
Conclusions
0.52
0.54
0.56
0.58
0.6
h
Figure: 1-σ and 2-σ Contour plots for h vs. hout .
Summarizing the constraints
Void vs Dark
Energy
At 95% C.L. we have (for L ≈ 250/h Mpc) :
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
1.17 ≤ J ≤ 1.25 ⇒ 0.42 ≤ |δ0 | ≤ 0.58
(but note that the average
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
0.44 ≤ hout ≤ 0.47
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
0.51 ≤ h ≤ 0.59
p
hδ 2 i is smaller)
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Baryon Acoustic Oscillations
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Measurement of baryon acoustic peak in the galaxy
distribution (Eisenstein et al., 2005).
The position of the peak measures the ratio of the
sound horizon at recombination vs. angular distance at
z = 0.35
Baryon Acoustic Oscillations
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
Measurement of baryon acoustic peak in the galaxy
distribution (Eisenstein et al., 2005).
The position of the peak measures the ratio of the
sound horizon at recombination vs. angular distance at
z = 0.35
It constrains two quantities: Ωm h2 and DA (0.35)
BAO
Large-Scale
structure(LRG)
But it also depends on the spectral index ns :
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
DV = 1370±64 and Ωm h2 = 0.130 (ns /0.98)−1.2 ±0.011
Caveat:
Constraints are derived using ΛCDM
UNION data and BAO
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Table: Comparison with data (UNION+BAO scale)
Model
ΛCDM (with ΩM = 0.27, ΩΛ = 0.73)
Open Universe
Void in open Universe (L = 450/hMpc)
χ2 (308 points)
310
318
308
UNION fit with 2 Gpc
Void vs Dark
Energy
0.6
Motivations
0.4
LTB metrics
Building the model
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
0.2
µ - µOCDM
Results
Local Void:
Fitting the
data
Best fit model
Min χ2 model
Flat ΛCDM with ΩM=0.27
Open CDM with ΩM=0.3
Type Ia Supernovae
-0.0
-0.2
-0.4
-0.6
0.01
0.10
1.00
Redshift
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Figure: Taken from Garcia-Bellido & Haugboelle ’08
(similar fits also in Zibin et al. ’08)
UNION data and BAO
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
0.02 0.04 0.06 0.08 0.1
2
Ωb h
Results
0
0.2
2
Ωc h
0.4
40
60
80
100
H0
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
0.4
0.6
Ωk
0.8
15
Age/GYr
20
0
0.05
0.1
0.15
1
zB
1.2
Hlocal/H0
1.4
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
10
0.2
Ω
0.4
m
0.6
5
10
15
zre
20
Problem 1
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Combining BAO+CMB+SN
Results
Local Void:
Fitting the
data
Problematic even adding curvature:
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
BAO+CMB+HST+SN (Riess) void: 3100
BAO+CMB+HST+SN(Riess) ΛCDM: 2968
∆χ2 ∼ 140
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Galaxy power spectrum
Void vs Dark
Energy
SDSS-main sample z . 0.2
Luminous Red Galaxies 0.2 . z . 0.5
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
If the Void is small (z ∼ 0.1), at least the LRG are in the
outer region.
Problem 2: Galaxy power spectrum
Void vs Dark
Energy
Combined fit with WMAP does not fit well LRG
Motivations
CMB + LRG: void vs ΛCDM
LTB metrics
Building the model
SDSS LRG DR4
void+mν
ΛCDM+mν
Results
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
10
3
Pg [(Mpc / h) ]
Local Void:
Fitting the
data
5
Gpc Void
Other observations
The Cold Spot
4
10
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
0.01
0.1
k [h / Mpc]
WMAP prefers flat/closed universe.
LRG prefers ΩM < 1.
1
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A Larger Void?
Void vs Dark
Energy
If we consider L & 1Gpc/h
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A Larger Void?
Void vs Dark
Energy
If we consider L & 1Gpc/h
Motivations
LTB metrics
SN data fits better Alnes et al. ’07, Garcia-Bellido & Haugboelle ’07, Zibin et al.’08 ,...
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
CMB first peak fits well Alnes et al. ’07
A Larger Void?
Void vs Dark
Energy
If we consider L & 1Gpc/h
Motivations
LTB metrics
SN data fits better Alnes et al. ’07, Garcia-Bellido & Haugboelle ’07, Zibin et al.’08 ,...
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
CMB first peak fits well Alnes et al. ’07
Galaxy power spectrum could fit well (the data are
inside...and inside the matter density is lower)
Large-Scale
structure(LRG)
Gpc Void
Other observations
BAO scale also changes
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Large monopole correction
Conclusions
Work in progress... (A.N., T. Biswas, W. Valkenburg)
Radial BAO
Void vs Dark
Energy
Motivations
LTB metrics
It is possible to look (Gaztanaga et al.’08) for the BAO scale only
for the radial direction as ∆z (model-independent)
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
: it does not fit (Gpc Void) together with full
CMB (which they fit with very low h and
non-compensated Void)
Zibin, Moss & Scott ’08
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Garcia-Bellido & Haugboelle ’08: it fits as well as ΛCDM(Gpc Void),
but only first peak location and SN Union (no full CMB).
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
CMB Dipole
Void vs Dark
Energy
Motivations
How much Observer can be off-center?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Observer at Distance dO
δT
T
∼ vO ∼ ḋO
CMB Dipole
Void vs Dark
Energy
Motivations
How much Observer can be off-center?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
Observer at Distance dO
δT
T
∼ vO ∼ ḋO
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
CMB dipole ≤ 10−3 if dO ∼ 15 − 20 Mpc (Tomita et al., Alnes et
al.’06)
CMB Dipole
Void vs Dark
Energy
Motivations
How much Observer can be off-center?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
Observer at Distance dO
δT
T
∼ vO ∼ ḋO
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
CMB dipole ≤ 10−3 if dO ∼ 15 − 20 Mpc (Tomita et al., Alnes et
al.’06)
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Bulk dipole of the same size of our dipole 600km/s
(Kashlinsky et al. ’08: 600 − 1000km/s)
kSZ
Void vs Dark
Energy
Motivations
All objects inside the Void have some peculiar velocity
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
This gives rise to δT
T ∼
(kinetic SZ effect)
v
c
and spectrum distortions
kSZ
Void vs Dark
Energy
Motivations
All objects inside the Void have some peculiar velocity
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
This gives rise to δT
T ∼
(kinetic SZ effect)
v
c
and spectrum distortions
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
Goodman ’95: v/c . 0.01 (at z ∼ 0.2)
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Caldwell-Stebbins ’07-’08: rule out Voids with zb & 0.9
kSZ
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Garcia-Bellido & Haugboelle: using 9 clusters (0.2 ≤ z ≤ 0.6) with
detection of spectral distortion one finds:
v̄ = 320 km/sec and σ = 1600 km/sec
(σ expected is only about 400 km/sec!)
kSZ
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Garcia-Bellido & Haugboelle: using 9 clusters (0.2 ≤ z ≤ 0.6) with
detection of spectral distortion one finds:
v̄ = 320 km/sec and σ = 1600 km/sec
(σ expected is only about 400 km/sec!)
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Exclude L > 1.5Gpc, with ΩIN = 0.23.
kSZ
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Garcia-Bellido & Haugboelle: using 9 clusters (0.2 ≤ z ≤ 0.6) with
detection of spectral distortion one finds:
v̄ = 320 km/sec and σ = 1600 km/sec
(σ expected is only about 400 km/sec!)
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Exclude L > 1.5Gpc, with ΩIN = 0.23.
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
But Kashlinsky et al. measure high vc ∼ 1000km/sec
on 300 Mpc/h
(they assume kSZ, but do not see spectral distortions).
Anisotropy of H
Void vs Dark
Energy
Similarly the expansion is anisotropic if dO nonzero8 .
Motivations
LTB metrics
Two papers claim significant anisotropy in H:
Building the model
Results
D.Schwarz & Weinhorst ’07: in the SNIa dataset
(> 95%C.L.)
McClure & Dyer ’07: in the Hubble Key Project data
(9 − 20km/sec)
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
In addition this should be correlated with CMB dipole
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Also to be explored: non-sphericity of Void
Conclusions
8
Tomita (2000), Alnes et al. (’06)
Anomaly in the CMB?
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
The CMB has a Cold Region ("Cold Spot") (M. Cruz et al. (’06
◦
and ’07)), with diameter about 15
The Cold Spot
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Figure:
From Eriksen et al. ’08
The Cold Spot
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Figure:
From Eriksen et al. ’08
Possible Explanations
Void vs Dark
Energy
Motivations
A Statistical accident?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
It could be that our Universe is peculiar in such a way
that Φ has this strange feature
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
How strange is it?
Possible Explanations
Void vs Dark
Energy
Motivations
A Statistical accident?
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
It could be that our Universe is peculiar in such a way
that Φ has this strange feature
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
How strange is it?
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
About 1% chance from Gaussian Monte Carlo
simulations of the CMB map (Cruz et al.’05-’06)
Other explanation
Void vs Dark
Energy
Motivations
Exotic explanation: it could be explained by the
integrated effect along the line of sight
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
There could be a very Large Void on the line-of-sight
(160Mpc/h − 1.5Gpc/h) (Tomita’05-’06, Inoue & Silk ’06)
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Claimed to be correlated with underdense region in the
nearby galaxy distribution (Rudnick, Brown & Williams ’07). This
would mean that this "hole" is close to us.
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
But this has been challenged by (Smith & Huterer ’08 )
The Cold Spot due to a Void?
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
We assume an underdense region ("a Void"), on the
line of sight
with I.Masina; JCAP JCAP 0902:019,2009 and
arXiv:0905.1073
The Cold Spot due to a Void?
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
We assume an underdense region ("a Void"), on the
line of sight
with I.Masina; JCAP JCAP 0902:019,2009 and
arXiv:0905.1073
Two effects
SNIa Hubble diagram
WMAP
BAO
First effect (Rees-Sciama, "integrated effect"):
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A photon enters the potential of the Void
During the travel the potential evolves
The photon comes out with slightly lower energy
(redshifts)
This would give a cold region (what we see by eye)
The Lensing effect
Void vs Dark
Energy
Motivations
Second effect (Lensing)
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
If behind the Void there is a pattern, ⇒ distorted
Also the very small angular scales (high ℓ) are affected
The Lensing effect
Void vs Dark
Energy
Motivations
Second effect (Lensing)
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
If behind the Void there is a pattern, ⇒ distorted
Also the very small angular scales (high ℓ) are affected
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
This, we cannot see by eye...
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
If we see it ⇒ there is something there: detection!
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Shape of Temperature fluctuation
Void vs Dark
Energy
Motivations
∆T /T (RS) (θ, φ)
=
LTB metrics
Results
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A f (θ) if θ < θL
0
if θ ≥ θL
, tan θL ≡
A ∼ 0.5(L/rrhor )3 δ2
Building the model
Local Void:
Fitting the
data
(
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
5°
10°
15°
20°
L
D
,
Correction to the power spectrum at low-ℓ
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
Compute the aℓm for this profile ⇒ Cℓ ≡
2
2
hCℓ i ℓ(ℓ+1)
2π T0 [µK ]
Void vs Dark
Energy
P
|aℓm |2
m 2ℓ+1
1400
1200
1000
800
600
400
200
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
2
5
10
20
50
ℓ
Conclusions
The χ2 changes by O(1)
The cosmological parameters would shift by some amount
O(1%)
Bispectrum at high-ℓ
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
The presence of a Void would be highly non-gaussian
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
Consider aℓ1 m1 aℓ2 m2 aℓ3 m3 = Bℓm11ℓ2mℓ23m3
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
They are zero on average for a Gaussian field
Bispectrum at high-ℓ
Void vs Dark
Energy
More precisely we define a rotational invariant quantity:
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
B ℓ1 ℓ2 ℓ3 =
P
m1 m2 m3
ℓ1 ℓ2 ℓ3
m1 m2 m3
aℓ1 m1 aℓ2 m2 aℓ3 m3
We want to compute hBℓ1 ℓ2 ℓ3 i, in a Universe with a Void
Bispectrum at high-ℓ
Void vs Dark
Energy
More precisely we define a rotational invariant quantity:
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
B ℓ1 ℓ2 ℓ3 =
P
m1 m2 m3
ℓ1 ℓ2 ℓ3
m1 m2 m3
aℓ1 m1 aℓ2 m2 aℓ3 m3
We want to compute hBℓ1 ℓ2 ℓ3 i, in a Universe with a Void
(P)
Remember that aℓm are Gaussian:
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
(P)
(P)
haℓ1 m1 aℓ2 m2 i = δℓ1 ℓ2 δm1 m2 Cℓ
Odd numbers of aℓm ⇒ zero
Non-Gaussian correlations
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
∆T
∆T (P) ∆T (RS) ∆T (L)
+
+
,
=
T
T
T
T
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
(P)
(RS)
(L)
aℓm = aℓm + aℓm + aℓm ,
Non-Gaussian correlations
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
∆T
∆T (P) ∆T (RS) ∆T (L)
+
+
,
=
T
T
T
T
Results
(P)
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Two dominant terms:
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
(RS)
(L)
aℓm = aℓm + aℓm + aℓm ,
h(a(RS) )3 i
ha(P) a(L) a(RS) i
(a(RS) )3
Void vs Dark
Energy
Motivations
LTB metrics
(RS)
B ℓ1 ℓ2 ℓ3
=
ℓ1 ℓ2 ℓ3
0 0 0
RS RS
aRS
ℓ1 0 a ℓ2 0 a ℓ3 0 .
It should be visible (S/N > 1) already in WMAP bispectrum
at ℓ . 40
Building the model
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
(RS) ℓ2 (ℓ+1)2
(2π)2
WMAP
bℓℓℓ
SNIa Hubble diagram
× 1016
Results
Local Void:
Fitting the
data
0
σ = 10◦
-10
↑
-20 primordial3
(fNL = 10 )
-30
-40
σ = 18◦
-50
-60
5
10
20
50
ℓ
Outline
Void vs Dark
Energy
1
Motivations
2
LTB metrics
Building the model
Results
3
Local Void: Fitting the data
SNIa Hubble diagram
WMAP
BAO
Large-Scale structure(LRG)
Gpc Void
Other observations
4
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Lensing Effect
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Such Void lenses primordial fluctuations
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
This is present only if there is something in the
line-of-sight (unique signature) (Das & Spergel ’08)
Signal-to-Noise
Void vs Dark
Energy
Lensing introduces fluctuations because
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
∆T ′
(n̂ ) ∼
T
+
∆T (P)
∆T (P)
(n̂) + ∂i
(n̂)∂ i Θ(n̂) +
T
T
∆T (P)
∂i ∂j
(n̂)∂ j Θ(n̂)∂ i Θ(n̂) + ... .
T
Signal-to-Noise
Void vs Dark
Energy
Lensing introduces fluctuations because
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
∆T ′
(n̂ ) ∼
T
+
SNIa Hubble diagram
∆T (P)
∆T (P)
(n̂) + ∂i
(n̂)∂ i Θ(n̂) +
T
T
∆T (P)
∂i ∂j
(n̂)∂ j Θ(n̂)∂ i Θ(n̂) + ... .
T
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
In order to compute this, we need Θ, the so-called
Lensing potential:
Rτ
∇⊥ Φ ,
∇⊥ Θ = −2 τ O d τ τOτ−τ
O
LSS
Signal-to-Noise
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Given Θ ⇒ bℓm
Signal-to-Noise
Void vs Dark
Energy
Motivations
LTB metrics
Given Θ ⇒ bℓm
Building the model
Results
Local Void:
Fitting the
data
(L) (1)
aℓm
lensing, given by:
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
(L) (1)
aℓm
=
P
ℓ′ ,ℓ′′
′
′
ℓ (ℓ +1)−ℓ(ℓ+1)+ℓ
G−mm0
ℓ ℓ′ ℓ′′
2
(LL)
We compute hCℓ
i≡
Pℓ
m=−ℓ
′′
(ℓ′′ +1) (P)∗
aℓ′ −m bℓ′′ 0
(L)(1) (L)(1) ∗
aℓm
i
haℓm
2ℓ+1
,
.
Signal-to-Noise
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
Radius L large ⇒ signal large
Visible in the power spectrum by the Planck satellite
(ℓ ∼ 2000) if L & 800 Mpc/h
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
10
0.00015
∆Cℓ 0.00010
(P) 0.00005
hCℓ i0.00000
(S/N)LL
-0.00005
Redshift (low-ℓ)
-0.00010
Lensing (high-ℓ)
-0.00015
10-2
0
Conclusions
1
10-1
1000
2000
3000
4000
5000
ℓ
10-3
0
1000
2000
3000
4000
5000
ℓ
Non-gaussian signal
Void vs Dark
Energy
ha(P) a(L) a(RS) i
Motivations
LTB metrics
Building the model
Results
Coupling between RS-Primordial-Lensing effect
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
l~1000−2000
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
l~30
l~1000−2000
Signal-to-Noise
Void vs Dark
Energy
L = 800 Mpc/h
L = 400 Mpc/h
L = 200 Mpc/h
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
10
10
10
1
1
1
10-1
10-1
10-1
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
0
500
1000
1500
2000
0
500
1000
1500
2000
0
500
1000
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Non-ambiguous signal, visible by high-resolution
experiments (Planck and higher)
1500
2000
ℓ
Assessment
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A Void of at least L ∼ 300 Mpc/h scale consistent with
WMAP and SNIa (Riess data), and local h
More data will discriminate (especially SDSS-II for
Supernovae)
Assessment
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
A Void of at least L ∼ 300 Mpc/h scale consistent with
WMAP and SNIa (Riess data), and local h
More data will discriminate (especially SDSS-II for
Supernovae)
But in trouble when combining other observations
(BAO, LRG)
Even adding curvature
Assessment
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
A Void of at least L ∼ 300 Mpc/h scale consistent with
WMAP and SNIa (Riess data), and local h
More data will discriminate (especially SDSS-II for
Supernovae)
But in trouble when combining other observations
(BAO, LRG)
Even adding curvature
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
Need for larger Void (L & Gpc/h)
Combined analyses and better data (kSZ, BAO) can
rule it out
Assessment
Void vs Dark
Energy
Motivations
LTB metrics
Building the model
Results
Local Void:
Fitting the
data
SNIa Hubble diagram
WMAP
BAO
Large-Scale
structure(LRG)
Gpc Void
Other observations
The Cold Spot
Redshift (low-ℓ)
Lensing (high-ℓ)
Conclusions
The Cold Spot - Void hypothesis can be ruled out by
Planck and high-resolution experiments (ℓmax & 2000)