1. testing the copernican principle in the light of dark energy
Chris Clarkson
Astrophysics, Cosmology & Gravitation Centre
University of Cape Town
Thursday, 26 January 12
2. Dark Energy Evidence
• evidence of cosmological
constant from COBE + age
constraints
• independent confirmation
from SNIa
• observations consistent
with flat Lambda-CDM
‘concordance cosmology’
Thursday, 26 January 12
3. Dark Energy Evidence
• evidence of cosmological
constant from COBE + age
constraints
• independent confirmation
from SNIa
• observations consistent
with flat Lambda-CDM
‘concordance cosmology’
Thursday, 26 January 12
4. Dark Energy Evidence
• evidence of cosmological
constant from COBE + age
constraints
• independent confirmation
from SNIa flat LCDM is it!
• observations consistent
with flat Lambda-CDM
‘concordance cosmology’
Thursday, 26 January 12
5. relativity is valid up to the Planck scale, w
4
vacuum energy in terms of a mass scale as ρvac = Mvac , in te
ρ(theory) ∼ MP10−3 eV, satisf
required to explain our observations vac Mvac ∼ .
is
(obs) 4
Problems with Λ Mvac ∼ 10 Mvac . (obs) −30 (theory)
(ob
Comparing this value to the value ρvac
obtain
Nevertheless, this discrepancy of 30 orders of magnitude in ener
• Lambda doesn’t make sense as by the cosmological(obs) ∼ 10−120 ρ(theory) ,
is what is meant vacuum energy: ρvac constant problem.
vac
One may add to this problem the following puzzling obser
• Why do we live at a specialmatter densities changes as the universe expands a
vacuum and time?
ΩΛ ρΛ
= ∝ a3 .
ΩM ρM
Thus, only during a brief epoch of cosmic history is it possible
• last modes are entering the Hubble radius ... we coincide with the largest
modes whichthe transition from matter domination to Λ domination, durin
will ever exist
of the same order of magnitude. This is known as the coinciden
The issue of reliably calculating the cosmological constant,
• Perhaps Landscape arguments can answer this ... one day ...
in which that calculation leads to a result dramatically differe
• in 10500 universesproven remarkably resistant to theoretical attack. It is fair t
has anything goes..?
currently any especially promising approaches. Nevertheless, t
lines of research that are worth mentioning in this context.
The first is supersymmetry (SUSY). Supersymmetry is a sp
Thursday, 26 January 12
6. relativity is valid up to the Planck scale, w
4
vacuum energy in terms of a mass scale as ρvac = Mvac , in te
ρ(theory) ∼ MP10−3 eV, satisf
required to explain our observations vac Mvac ∼ .
is
(obs) 4
Problems with Λ Mvac ∼ 10 Mvac . (obs) −30 (theory)
(ob
Comparing this value to the value ρvac
obtain
Nevertheless, this discrepancy of 30 orders of magnitude in ener
• Lambda doesn’t make sense as by the cosmological(obs) ∼ 10−120 ρ(theory) ,
is what is meant vacuum energy: ρvac constant problem.
vac
One may add to this problem the following puzzling obser
• Why do we live at a specialmatter densities changes as the universe expands a
vacuum and time?
ΩΛ ρΛ
= ∝ a3 .
ΩM ρM
Thus, only during a brief epoch of cosmic history is it possible
• last modes are entering the Hubble radius ... we coincide with the largest
modes whichthe transition from matter domination to Λ domination, durin
will ever exist
of the same order of magnitude. This is known as the coinciden
The issue of reliably calculating the cosmological constant,
• Perhaps Landscape arguments can answer this ... one day ...
in which that calculation leads to a result dramatically differe
• in 10500 universesproven remarkably resistant to theoretical attack. It is fair t
has anything goes..?
currently any especially promising approaches. Nevertheless, t
lines of research that are worth mentioning in this context.
The first is supersymmetry (SUSY). Supersymmetry is a sp
Thursday, 26 January 12
7. relativity is valid up to the Planck scale, w
4
vacuum energy in terms of a mass scale as ρvac = Mvac , in te
ρ(theory) ∼ MP10−3 eV, satisf
required to explain our observations vac Mvac ∼ .
is
(obs) 4
Problems with Λ Mvac ∼ 10 Mvac . (obs) −30 (theory)
(ob
Comparing this value to the value ρvac
obtain
Nevertheless, this discrepancy of 30 orders of magnitude in ener
• Lambda doesn’t make sense as by the cosmological(obs) ∼ 10−120 ρ(theory) ,
is what is meant vacuum energy: ρvac constant problem.
vac
One may add to this problem the following puzzling obser
• Why do we live at a specialmatter densities changes as the universe expands a
vacuum and time?
ΩΛ ρΛ
Lambda ρM larger
ΩM
=any∝ a3 .
Thus,and during a brief epoch of cosmic history is it possible
only we couldn’t exist
• last modes are entering the Hubble radius ... we coincide with the largest
modes whichthe transition from matter domination to Λ domination, durin
will ever exist
of the same order of magnitude. This is known as the coinciden
The issue of reliably calculating the cosmological constant,
• Perhaps Landscape arguments can answer this ... one day ...
in which that calculation leads to a result dramatically differe
• in 10500 universesproven remarkably resistant to theoretical attack. It is fair t
has anything goes..?
currently any especially promising approaches. Nevertheless, t
lines of research that are worth mentioning in this context.
The first is supersymmetry (SUSY). Supersymmetry is a sp
Thursday, 26 January 12
8. LCDM Denial
• if acceleration isn’t cosmological constant:
}
• ‘real’ dark energy - quintessence, k-essence ...
make things worse,
but help test LCDM
• modified gravity - gr wrong on Hubble scales
• inhomogeneous universe - backreaction?
• do we live at the centre of vast void? - copernican assumption wrong
• LCDM requires 2 phases of accelerated expansion - phenomenological
Thursday, 26 January 12
9. priors critical
• assumes FLRW background spacetime - spatial homogeneity
• can we demonstrate this observationally?
• or have we already? at what confidence level?
• what do we know if we don’t assume this?
• does dark energy necessarily exist?
Thursday, 26 January 12
18. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
19. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
20. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
21. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Alnes, Amarzguioui, and Gron astro-ph/0512006
Thursday, 26 January 12
22. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Biswas, Monsouri and Notari, astro-ph/0606703
Thursday, 26 January 12
23. z jump =0.085 ; ∆CENTRE =-0.48
Spherical Symmetry → void models
0.75
0.5
0.25
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
0
m
-0.25
• can fit distance-redshift data to any FLRW DE model
-0.5
-0.75 Mustapha, Hellaby, & Ellis
-1
0 0.25 0.5 0.75 1 1.25 1.5 1.75
z
1
0.75
0.5
0.25
∆Ρ
0
Ρ
-0.25
-0.5
-0.75
Biswas, Monsouri and Notari, astro-ph/0606703
0 0.02 0.04 0.06 0.08
z
FIG. 3: In the upper plot we show a fit of the Supernovae data (Riess et al. [28]) with an LTB model which has χ2 =
d.o.f. are 181). The inhomogeneous patch extends up to z 0.085 and the underdensity in the center is δCENTRE
Thursday, 26 January 12 We have shown ∆m ≡ m − mempty : the magnitude (m ≡ 5Log10 DL ) minus the magnitude of an empty open FLRW
24. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Biswas, Monsouri and Notari, astro-ph/0606703
Thursday, 26 January 12
25. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
26. void profile today
Hubble scales ~ 5-10 Gpc
density inhomogeneity accompanied by curvature
gradients and anisotropic expansion
Thursday, 26 January 12
30. Fine tuned
Supernovae as seen by off-center observers in a local void 15
Figure 4. Magnitude dipole induced by moving the observer away from the void
center in the best fit on-center models. The curves show the difference in magnitude
for two SNe Ia with the same redshift but in opposite directions in the sky. Left panel:
A void with scale radius rs = 0.7 Gpc (z ≈ 0.18), preferred by the SDSS-II data
set. Right panel: A void with scale radius rs = 3.5 Gpc (z ≈ 1.02), preferred by the
Constitution data set.
6. Constraining the observer position with SNe Ia
Off-center observers will see an anisotropic relation between the luminosity distance
and the redshift for the SNe Ia. This means that a standard candle with the same
redshift but in different directions in the sky will have different observed magnitudes.
The isotropy of the data can be used to establish constraints on the observer position
Figure 6. The void. In this section, we will investigate how farIa as a functionin the local
inside the changes in the as values for theoff-center observers of a
Supernovae χ2 seen by fit to the SNe from the center the observer
observer’sbe located.
can position. The stars show the values when the static observer is displaced in
void
Sep 2009
the direction of the CMB dipole in the best fit on-center LTB model. The diamonds
show the values when anisotropy also has a peculiar velocity directed 2to accommodate
6.1. Maximum the observer
Michael Blomqvist1 and Edvard M¨rtsell o
the observed CMB dipole. The arrows indicate the direction of motion, either away
To get a sense for 1 The Oskarthe effect of being situated off-center has of Astronomy, Ia
how big Klein Centre for Cosmoparticle Physics, Department on the SN
from the void center or towards it. The vertical dotted line Center the position where
Stockholm University, AlbaNova University
shows
Thursday, 26 January 12 observations, we can calculate the maximum anisotropy in the form of the magnitude
the peculiar velocity is zero. The scale radius of the void is r = 5.0 Gpc for the
34. “Never let anyone tell
you you’re crazy”
Prof. Bob Nichol
Thursday, 26 January 12
35. Are void models ridiculous?
• being ‘at the centre of the
universe’ is crazy, but actually
only a coincidence of
1 in 10~9 in our Hubble volume
• possible selection effects?
• could high dark matter
density inhibit solar system
formation?
must be stable for ~5Gyr
• so, maybe not anti-
Copernican ?
Thursday, 26 January 12
37. Isn’t this a bit silly?
• Yes
Thursday, 26 January 12
38. Isn’t this a bit silly?
• Yes
• But:
• we should be able to rule all void models out observationally - tests CP
• helps make data ‘cosmology independent’ (eg, compare SNIa vs BAO)
• provides alternative probe of coincidence problem which can be tested
• unusual DE interpretation without LCDM as fixed point - only DE model
with known physics at late times
• can we construct a void which fits all observations? [v fine-tuned?]
Thursday, 26 January 12
39. Small scale CMB
Baumann, TASI lectures
Thursday, 26 January 12
40. Small scale CMB
• high-l CMB fixes only:
baryon-photon ratio
baryon fraction
distance to last
scattering
CC & Marco Regis
Thursday, 26 January 12
41. Small scale CMB
indistinguishable
from LCDM
Thursday, 26 January 12
43. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
44. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
45. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
46. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
47. CMB gives
expansion
rate here
Li determines
expansion rate here
Thursday, 26 January 12
50. infer expansion
rate here
CMB gives
sound horizon
rate here
assume sound
horizon here
Thursday, 26 January 12
51. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
52. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
53. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
54. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
55. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
56. measure CMB dipole
observed here
assume decoupling
temperature here
Thursday, 26 January 12
57. so...
• voids fit key background observations [just!]: SN+H0+CMB
• but simplest ‘adiabatic’ voids ruled out - probably not solution to DE!
• they assume everything homogeneous except matter density
• does that make sense?
• if we don’t have a theory to make a void, we can only make a map of it
• everything could be inhomogeneous ... what measures what?
Thursday, 26 January 12
58. kSZ measures early (in)homogeneity
measure CMB dipole
observed here
assume decoupling
temperature here
Thursday, 26 January 12
59. kSZ measures early (in)homogeneity
measure CMB dipole
observed here
assume decoupling
temperature here
Thursday, 26 January 12
60. kSZ measures early (in)homogeneity
measure CMB dipole
observed here
Bull, Clifton, assume decoupling
Ferriera 1108.2222
temperature here
Thursday, 26 January 12
61. BAO measures baryon fraction (r)
infer expansion
rate here
CMB gives
sound horizon
rate here
assume sound
horizon here
Thursday, 26 January 12
62. large-scale CMB, BAO, structure formation...
• ... all require perturbation theory
• unsolved!
• k-modes not independent - important for BAO.
Thursday, 26 January 12
63. large-scale CMB, BAO, structure formation...
• ... all require perturbation theory
• unsolved!
• k-modes not independent - important for BAO.
Thursday, 26 January 12
64. large-scale CMB, BAO, structure formation...
• ... all require perturbation theory
• unsolved!
• k-modes not independent - important for BAO.
Thursday, 26 January 12
65. could specify model as a Cauchy problem
re
he
ta
in
da
te
ify
gr
a
ec
te
sp
in
to
pa
s t
hard to ‘rule out’!
Thursday, 26 January 12
66. testing the Copernican/cosmological principles
• we only view the universe
from one event
• fixed in space & time
• what observations take us
form CP -> homogeneity?
• how to we test CP
generically?
• independently of theory of
gravity or dark energy
Thursday, 26 January 12
67. when does CP imply homogeneity ?
• if everyone sees an isotropic CMB => homo [Ehlers, Geren, Sachs, 1968]
• if everyone sees isotropic distances => homo [Hasse, Perlick, 199..]
• etc
• can we see the universe from anywhere else?
• do we need to?
Thursday, 26 January 12
68. kSZ lets us see CMB as others see it
not enough observers - need to detect double scatterings!
Thursday, 26 January 12
69. check consistency of
the standard model
infer expansion
rate here from BAO
} estimate age along
here
Heavens, Jimenez, Maartens 1107.5910
Thursday, 26 January 12
70. ‘on lightcone’ test
• in FLRW we can combine Hubble rate and distance data to find curvature
2
[H(z)D (z)] 1
k =
[H0 D(z)]2
⇥
dL = (1 + z)D = (1 + z) dA
2
• independent of all other cosmological parameters, including dark energy
model, and theory of gravity
• tests the Copernican principle and the basis of FLRW
⇥
C (z) = 1 + H 2
DD D 2
+ HH DD = 0
Clarkson, Basset & Lu, PRL 100 191303
Thursday, 26 January 12
71. Using age data to reconstruct H(z)
need to reconstruct D(z) and H(z)
independently of model - difficult
Shafieloo & Clarkson, PRD
Thursday, 26 January 12
72. consistency of standard model
• void models unlikely to be DE explanation
• highlights need to test homogeneity assumption
• ‘tests’ formulate CP as null hypothesis
• compare observables or observe inside lightcone
• ideally, in model-independent ways - independently of DE/GR
• how do we place confidence limits on FLRW?
Thursday, 26 January 12