Testing Gravity using Large-Scale Redshift-Space DistortionA. Raccanelli
Caltech
In collaboration with Olivier Doré &
D. Bertacca, D. Pietrobon, L. Samushia, F. Schmidt, N. Bartolo, C. Clarkson, R. Maartens, S. Matarrese, W. Percival
Testing Gravity with
& California Institute of Technology
• Redshift-Space Distortions • Wide Angle RSD • Testing Cosmologies with SDSS • GR Corrections
Alvise Raccanelli
01 August 2012
Large Scale Small Scale
δs = Sδr
Alvise Raccanelli
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Ns(s)d3s = Nr(r)d3r
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f = γ m(z)
RSD test models of gravity
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γGR ≈ 0.55
Alvise Raccanelli
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Tripolar Spherical Harmonics expansion Szalay et al. (1998), Szapudi (2004), Papai & Szapudi (2008)
Sl1l2l(x1, x2, x) =
Cl1m1(x1)Cl2m2(x2)Clm(x)
3-j Wigner symbols
normalised spherical harmonics
ξs(r1, r2, r) =
Alvise Raccanelli
selection function, ...)
Application to real data: We need a good theoretical model
Q with NL and WA corrections
Alvise Raccanelli
Q(r) = ξ2(r)
Normalised quadrupole Q
Our formula (solid line)
Neglecting large-scale corrections leads to a wrong estimate of γ
(also Durrer’s talk)
ξ0(ϑ=0.05) Δ γ ≈ 2%ξ0(ϑ=0.10) Δ γ ≈ 5%ξ0(ϑ=0.15) Δ γ ≈ 9%
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Testing Cosmological Models
Cosmological models with a different growth history can be tested against data
Alvise Raccanelli 01 August 2012
Alvise Raccanelli
arXiv:1207.0500 We measured ξ0 and ξ2 of SDSS-II LRGs,
and compared them to predictions from UDM and nDGP as a function of their parameters. Robust methodology including corrections
from BAO nl, wide-angle, pair orientation and geometry
allowed us to extend the range of scales used 01 August 2012
Alvise Raccanelli
Unified Dark Matter ξ0
SDSS DR7 c! = 0.0020 c! = 0.0015 c! = 0.0010 c! = 0.0003 "CDM
# 0
10$4
10$3
10$2
10$1
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Unified Dark Matter ξ2
SDSS DR7 c! = 0.0020 c! = 0.0015 c! = 0.0010 c! = 0.0003 "CDM
# 2
0.001
0.01
0.1
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Alvise Raccanelli
nDGP ξ0 SDSS DR7 !CDM nDGP, rc = 4000 nDGP, rc = 1500 nDGP, rc = 200
" 0
0.001
0.01
0.1
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Alvise Raccanelli
nDGP ξ2 SDSS DR7 !CDM nDGP, rc = 4000 nDGP, rc = 1500 nDGP, rc = 200
" 2
0.001
0.01
0.1
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L U D
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L n D
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first constraints
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Galileon, f(R), ... or ΛCDM with different parameters
And new data (e.g. BOSS, BigBOSS, PFS, Euclid, SKA)
Future Tests
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Newtonian description is not anymore accurate.
We need to include General Relativistic corrections
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Gauge-invariant overdensity
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s = b

γ is a purely GR term that vanishes in the Newtonian limit
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Alvise Raccanelli
ξss = b(z1)b(z2)
1,2,L,n
×ξnL(χ12; z1, z2)
B000 ss 0 =
Mixed terms including mode coupling and GR Pure GR term
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" G R
Along the line of sight
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!12 " (z1, z1, # = 0.3, µ = 0)
" G R
z1 = z2 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Across the line of sight
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Sample variance is a problem
Wide-angle redshift distortions in general relativity
Alvise Raccanelli
BUT future surveys and new ideas (e.g. Seljak et al. multi-tracer) might help, so we need to have
a precise theoretical model 01 August 2012
Conclusion Large-scale RSD can be used to test
cosmological models
If we want to measure the growth with high precision (see White and Guzzo’s talks), we need precise modeling and to drop
simplifying assumptions
Thank You