The ISW imprint of superstructures - uni-bielefeld.de › fileadmin › _temp_ › Sesh2012.… ·...

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The ISW imprint of superstructures A problem for ΛCDM? Seshadri Nadathur Universit¨ at Bielefeld Kosmologietag 3 May 2012 SN, Hotchkiss, Sarkar, arXiv:1109.4126

Transcript of The ISW imprint of superstructures - uni-bielefeld.de › fileadmin › _temp_ › Sesh2012.… ·...

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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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