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The ISW imprint of superstructuresA problem for ΛCDM?
Seshadri Nadathur
Universitat Bielefeld
Kosmologietag3 May 2012
SN, Hotchkiss, Sarkar, arXiv:1109.4126
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Key Points
• Observations of the ISW effect of only extreme density fluctuationscan give new insight about cosmological model, complementary tousual cross-correlation method
• Particularly sensitive to primordial non-gaussianities (also perhapsmodified gravity ...)
• Observation that has already been performed is > 3σ discrepantwith standard model - large density fluctuations are more abundantthan expected
• We need better designed observational method to learn more
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Outline
The late ISW effect
The ISW signal of extreme regions
ΛCDM predictionPrevious estimatesStructuresTemperature signal
Results
Conclusions
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The late ISW effect
If CMB photons traverse decaying large-scale potential fluctuations,secondary anisotropies are introduced → the late ISW effect
∆T (n)
T0=
2
c3
∫ rL
0Φ(r , z , n)a dr
Potentials decay in presence of dark energy (ΩΛ > 0) or in an openuniverse, but not for Ωm = 1
Φ ←→ matter fluctuations δ (through Poisson equation)
δ ←→ observed source density fluctuations δg (through bias)
So CgT (θ) = 〈δg (n) ∆T (n′)T0〉 6= 0
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The late ISW effect
If CMB photons traverse decaying large-scale potential fluctuations,secondary anisotropies are introduced → the late ISW effect
∆T (n)
T0=
2
c3
∫ rL
0Φ(r , z , n)a dr
Potentials decay in presence of dark energy (ΩΛ > 0) or in an openuniverse, but not for Ωm = 1
Φ ←→ matter fluctuations δ (through Poisson equation)
δ ←→ observed source density fluctuations δg (through bias)
So CgT (θ) = 〈δg (n) ∆T (n′)T0〉 6= 0
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The late ISW effect
Detection of ISW cross-correlation is an independent test of Λ
Form of cross-correlation tests primordial distribution PΦ(k), growthof structure, bias relation between δ and δg
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Usual detection method
Sawangwit et al., MNRAS 2010
(Cai et al., MNRAS 2010)
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Usual detection method
Sawangwit et al., MNRAS 2010
(Cai et al., MNRAS 2010)
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Usual detection method
Signal is small and hard to detect
Errors are large and hard to estimate
Some groups claim 2− 3σ detections using various tracers of δ, orup to 4σ on combining datasets
Padmanabhan et al., PRD 2005; Cabre et al., MNRAS 2006; Giannantonio et al., 2008 and many others
Other groups claim no rejection of null hypothesis
Sawangwit et al., MNRAS 2010; Hernandez-Monteagudo A&A 2010; Lopez-Corredoira et al., A&A 2010 etc.
Can a different approach tell us something new?
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Usual detection method
Signal is small and hard to detect
Errors are large and hard to estimate
Some groups claim 2− 3σ detections using various tracers of δ, orup to 4σ on combining datasets
Padmanabhan et al., PRD 2005; Cabre et al., MNRAS 2006; Giannantonio et al., 2008 and many others
Other groups claim no rejection of null hypothesis
Sawangwit et al., MNRAS 2010; Hernandez-Monteagudo A&A 2010; Lopez-Corredoira et al., A&A 2010 etc.
Can a different approach tell us something new?
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ISW signal of extreme regions
We can try to isolate the contribution to the cross-correlation fromthe N most extreme density fluctuations only
• Only need to know relative values of δg - reduces errors,potentially increases signal?
• Probes extreme tails of pdf, so more sensitive to deviations fromgaussianity etc.
Such a study has already been done with SDSS DR6 LRGs - a > 4σdetection of the correlation
Granett, Neyrinck, Szapudi, ApJL 2008
But is the detected signal consistent with ΛCDM?
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ISW signal of extreme regions
We can try to isolate the contribution to the cross-correlation fromthe N most extreme density fluctuations only
• Only need to know relative values of δg - reduces errors,potentially increases signal?
• Probes extreme tails of pdf, so more sensitive to deviations fromgaussianity etc.
Such a study has already been done with SDSS DR6 LRGs - a > 4σdetection of the correlation
Granett, Neyrinck, Szapudi, ApJL 2008
But is the detected signal consistent with ΛCDM?
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The Granett et al observation
• First step - identify most extreme large-scale structures in theSDSS photometric LRG sample (0.4 < z < 0.75 with medianz = 0.52)Done using structure-finding algorithms VOBOZ (for clusters) andZOBOV (for voids)
• Now averaged CMB temperature in direction of each objectidentified, and stacked the images
• Used a compensated top-hat filter of radius 4 for the averaging toremove CMB fluctuations on larger scales
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The Granett et al observation
∆T = −11.3± 3.1 µK for voids,
∆T = 7.9± 3.0 µK for clusters, and
∆T = 9.6± 2.2 µK for both together (clusters minus voids)Granett, Neyrinck, Szapudi, ApJL 2008
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ΛCDM prediction: previous estimates
• Hunt and Sarkar 2008:Obtain ∆T ∼ 0.1 µK assuming top-hat density profile - orders ofmagnitude too small!
• Inoue, Sakai, Tomita 2010:Assume a different but similar density profile〈∆T 〉 ∼ 0.5 µK - still orders of magnitude too small!
• Papai, Granett, Szapudi 2010:Use a radial profile motivated by Gaussian statistics
Claim only 2σ discrepancy with ΛCDM ...
... but interpretation relies on template used outside range ofvalidity
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ΛCDM prediction
Model to be tested is ΛCDM + Gaussian primordial perturbations• Assume linear growth (large scales) + Poisson equation:
Φ(k, t) =3
2
(H0
k
)2 H(z)
aΩm (1− β(z))D(z)δ(k, z = 0)
• Assume gaussian distribution → predict abundance of extremesof δ
• Gaussian statistics → also predict profiles of δ about extremalpoints
Need only matter power spectrum for given cosmology
Bond, Bardeen, Kaiser, Szalay 1986 (BBKS)
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ΛCDM prediction: structures
Example profiles:
0 20 40 60 80 100 120 140 160−0.5
−0.4
−0.3
−0.2
−0.1
0
r (h−1Mpc)
δ(r)
δ(r)
δrandom(r)
0 20 40 60 80 100 120 140 160−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
r (h−1Mpc)
δ(r)
δ(r), δ0 = −0.2, Rf = 20 h−1Mpc
δg(r), δ0 = −0.2, Rf = 20 h−1Mpc
δ(r), δ0 = −0.3, Rf = 20 h−1Mpc
δ(r), δ0 = −0.2, Rf = 30 h−1Mpc
Profiles slightly, but not significantly, different to those used by Papai,
Granett, Szapudi 2010
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ΛCDM prediction: temperature signal
Assume the following:
• Linear treatment of ISW (ok on relevant scales ∼ 100 h−1Mpc)
• Structures centred at z = 0.52 (SDSS median redshift)
• LRGs trace matter density with simple linear bias, δg = bδ,b ≈ 2.25 for SDSS LRGs
• Number of structures N 1 so can use the mean profile tocalculate expectation values
• Sample of structures matches that seen by structure-findingalgorithms (condition on δ0)
• Ignore overdensities (sample biased towards non-linear collapsedstructures)
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ΛCDM prediction: temperature signal
〈∆T 〉 = expectation value of signal= weighted average value of ∆T for voids passing cut
So
〈∆T 〉 =
∫ δc0−1
∫ θout0 W (θ)∆T (θ)Nminσ
−10 d2θdδ0
πθ2c
∫Nminσ
−10 dδ0
where
• Nminσ−10 is weighting factor,
• δc0 is cutoff imposed by significance selection,
• W (θ) is a compensating top-hat filter, θc = 4 to matchobservation
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ΛCDM prediction: temperature signal
〈∆T 〉 clearly depends on smoothing scale Rf
Mean void size and distribution of void sizes also depends on Rf
Bias towards large voids:• Larger voids have larger ∆T• Maybe only voids with radius Rv > Rmin
v are found by ZOBOV
Bias towards deep voids:
• Deeper voids have larger ∆T• Maybe only voids with δ0 < δmin
0 are found by ZOBOV
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Results
Model bias towards larger voids by increasing Rf (increasing Rminv )
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Results
Model bias towards larger voids by increasing Rf (increasing Rminv )
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Results
Model bias towards deeper voids by decreasing δmin0 (at different Rmin
v )
green: Rminv = 70 h−1Mpc, blue: Rmin
v = 100 h−1Mpc
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Results
Model bias towards deeper voids by decreasing δmin0 (at different Rmin
v )
green: Rminv = 70 h−1Mpc, blue: Rmin
v = 100 h−1Mpc
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Theoretical simplifications
Non-linear effects of gravity:• evolution leads to colder centre, hotter edges
• overall unclear, but linear treatment might even overestimate thesignal
• in any case non-linear effects small at low z (. 10%) Cai, Cole, Jenkins,
Frenk, MNRAS 2010
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Theoretical simplifications
Varying cosmological parameters:
• σ8 alters profile about extremes and number of extremes ...... but effects on 〈∆T 〉 are tiny within σ8 ∈ (WMAP + SDSSallowed range)
• Ωm affects photon geodesics and pre-factor in ISW integral ...... but for Ωm ∈ (0.25, 0.32) effects are negligible
Varying parameters of ΛCDM model does not resolve discrepancy
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Conclusions
Observed late ISW signal discrepant with linear theory predictionsfor Gaussian perturbations in ΛCDM
Discrepancy > 3σ even with conservative assumptions
Large, deep voids in matter density more numerous than expected
Perhaps initial perturbations to the density field are not completelyGaussian?
massive structures more abundant in f (R) theories?
growth rate of perturbations different in scalar-tensor gravity?
large inhomogeneites themselves alter growth rate of structure?
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Conclusions
Observed late ISW signal discrepant with linear theory predictionsfor Gaussian perturbations in ΛCDM
Discrepancy > 3σ even with conservative assumptions
Large, deep voids in matter density more numerous than expected
Perhaps initial perturbations to the density field are not completelyGaussian?
massive structures more abundant in f (R) theories?
growth rate of perturbations different in scalar-tensor gravity?
large inhomogeneites themselves alter growth rate of structure?
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Work in progress
Study most appropriate method of observation with future surveys(2D projected fields)
Detailed predictions about expected size and form of signal instandard cosmology
Effects of adding primordial non-gaussianity
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