Redshift Space Distortions
Dr. Mariana Vargas Magana Instituto de Fisica, UNAM.
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Observables
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Perturbations Evolution
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Review: Linear Perturbation Theory
• Small initial deviations from homogeneous FLRW model
• Inhomogenities grew by gravitacional inestability.
� =⇢� ⇢̄
⇢̄<< 1
linearity condition
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Dynamics: Growth Factor
Evolution of perturbations in a expanding Universe is given by
which has the general solution
The growing solution D+(t) is called linear growth function and is normalized such that D+(t0) = 1.
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Dynamics: Growth FactorStructure formation at large scales
Linear Growth D(a), D(a=1)=1 Snapshots de 2 N-body simulaciones a diferentes tiempos, muestra fluctuaciones de densidad mayores en un modelo LCDM comparado con un universo dominado por materia (EdS).
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Dynamics: Growth Factor
Evolution of perturbations in a expanding Universe is given by
which has the general solution
The growing solution D+(t) is called linear growth function and is normalized such that D+(t0) = 1.
The growth factor is defined as: f(a) =d lnD
d ln a
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Growth factor
The growth factor can be right with a good approximation as:
f(a) ⇡ ⌦�m(a)
γ is named « growth index »and can be calculated for different models (Linder 2005)
CDM ) � = 0.6
⇤CDM ) � = 0.55
DGP ) � ⇡ 0.68
!CDM ) � = 0.55 + 0.05[1 + !]
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Growth Factor
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Why: Testing General Relativity
• Growth function G(a): δ(k, a) = aG(a)δi(k)
• In General Relativity G(a) is determined once H(a) is specified/measured; generically this relation is different in modified gravity models
Beth Reid INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Why: Testing General Relativity
• allowed growth in ΛCDM given 2009 CMB, SN, BAO, H0
• constrained by RSD
Beth Reid INPA Sept 23
Mor
tons
on, H
u, H
uter
er 2
010,
PR
D, 8
1, 0
6300
7
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Why: Testing General Relativity
• General Quintessence models, massive neutrinos suppress RSD signal
Beth Reid INPA Sept 23
Mor
tons
on, H
u, H
uter
er 2
010,
PR
D, 8
1, 0
6300
7
Non-flat quintessence models with early dark energy
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Redshift Space Distortions: What
Beth Reid 5
x x
real to redshift space separations
|vp| ~ d σ8/d ln a = σ8 * f
isotropic squashed along line of sight
z∇ ⋅ vp = -aHf δm
INPA Sept 23
f = d ln σ8 /d ln a
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Redshift Space Distortions (RSD)
Hamilton 1997
Unreconstructed no RSD Unreconstructed with RSD
Reconstructed no RSD Reconstructed with RSD
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Distorsiones de Corrimiento al rojo
distancia por corrimiento al rojo
Verdadera distancia velocidad peculiar
Estas distorsiones generan un incremento del agrupamiento a lo largo de la linea de visión en comparación con la dirección perpendicular.
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Real space
Distorsiones de Corrimiento al rojo
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Redshift space
Distorsiones de Corrimiento al rojo
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Real Space Correlation Function
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Redshift Space Correlation function
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Redshift Space Distortions: How
• ξ(rσ, rπ): number of pairs in excess of random as a function of pair separation OR the avg density around a galaxy
Beth Reid 6
White et al. 2011 mock catalogs
ξ(rσ, rπ)
INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Redshift Space Distortions: How
• Sidenote: Alcock-Paczynski effect is degenerate with RSD
Beth Reid 7
White et al. 2011 mock catalogs
ξ(rσ, rπ)
INPA Sept 23
α∥
α⊥
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Background: Linear RSD (Kaiser 1987)
Beth Reid 13 INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Background: Legendre Polynomial moments
Beth Reid 14
General Expansion
Linear theory prediction
INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Resultados cosmológicos de RSD con BOSS
Alam, Ho & Vargas 2014
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
CLPT(Wang 2014, Carlson 2013)
pairwise!velocity
dispersion of pairwise velocity
depends on linear power spectrum
Real space Correlation function and velocity statistics is provided by CLPT
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Gaussian streaming Model (GSM )
Mean LOS velocity
velocity dispersion
Redshift space Correlation function is provided by GSM
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Resultados cosmológicos de RSD con BOSS
Alam, Ho & Vargas 2014
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Test with simulations
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Medotodologia
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Resultados cosmológicos de RSD con BOSS
In linear theory, b and f are completely degenerate with 𝞼8, and observed clustering is only sensitive to their combination b𝞼8 and f𝞼8
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Diversidad de Modelos para RSD en BOSS
Reference MODEL SPACE Range
Samushia 2013 LPT CS 24-152
Beuther 2013 eTNS(Tayura) RegPT FS 0.01-0.2
Chuang 2013 Dew +FOG CS 32-200
Sanchez 2013 “PT” CS(W)
Alam 2014 CLPT CS 30-130
Reid 2013 LPT+HOD CS 0.8-32
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
200 220 240 260 280 300Radial Index
200
220
240
260
280
300
Ind
ex T
ran
sver
se
Preliminary
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Fingers of God(Dedos de dios)
Efecto Kaiser
escalas pequeñasgrandes escalas
BAO
Distorsiones de Corrimiento al rojo
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
RSD small scales
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Background: Fingers-of-God
Beth Reid 15
x
x
x x
x
REAL SPACE: r ~ 1 Mpc/h
REDSHIFT SPACE: r ~ 15 Mpc/hFinger-of-God features mix small and large scale power
Central galaxies
Satellite galaxies
INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Fisher Matrix forecast for BOSS
Beth Reid 16
2% theoretical uncertainty “goal” for ξ0,2
INPA Sept 23
IF we can determine σ from small-scale clustering (e.g.,
HOD), gain factor of 2 on RSD
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Outline
• What are redshift space distortions (RSD) and why are they the coolest cosmological probe in town?
• Projections for BOSS RSD constraints
• Step away from the Kaiser formula: building intuition in configuration space
• A model for the redshift space distortions of halos
Beth Reid INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Legendre Polynomial moments
Beth Reid 19
General Expansion
Linear theory prediction
INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Legendre Polynomial moments
Beth Reid 20
General Expansion
Relation to Pℓ(k)
INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Legendre Polynomial moments:scale dependence
Beth Reid 21
L0(μ) = 1
L2(μ) = 1.5μ2 - 0.5
L4(μ) = 4.375μ4 - 3.75μ2 + 0.375
INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Configuration space quantities of interest:
Beth Reid 22
rσ
rπr vz
v̅r, σ2r
v̅t=0, σ2ty rπ
INPA Sept 23
Perp ||
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Linear theory pairwise velocities (δg = bδm)
Beth Reid 23 INPA Sept 23
mean infall velocity
velocity dispersion
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Fisher 1995: the Kaiser formula in configuration space
Beth Reid 24
• δ(x), v(x’) correlated Gaussian fields
• Expand around y = rπ
• Equivalent to Kaiser formula
INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Pairwise velocity statistics in linear theory
Beth Reid 25 INPA Sept 23
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM
Small scales RSD
Mariana Vargas Magana Latest Results from BOSS and their Implications for Cosmology28 Noviembre, Instituto de Fisica, UNAM