The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale...
Transcript of The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale...
![Page 1: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/1.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
The Homogeneity Scale of the Universe with Large Scale Structure Surveys
PhD student: P. NtelisPhD advisor: J.C. Hamilton
10 Nov 2016
![Page 2: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/2.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Cosmological Principle Homogeneous + Isotropic on Large Enough Scales
General Relativity FLRW ΛCDM
Fit on DATA
![Page 3: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/3.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Cosmological Principle Homogeneous + Isotropic on Large Enough Scales
General Relativity FLRW ΛCDM
Fit on DATA�T
T⇠ 10�5
![Page 4: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/4.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Cosmological Principle Homogeneous + Isotropic on Large Enough Scales
General Relativity FLRW ΛCDM
Fit on DATA
Is this assumption data-motivated ?
![Page 5: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/5.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
How to check for Homogeneity ?
SDSS-III / BOSSMain project:
APO telescope (New Mexico, USA) 2.5 m diameter
Spectroscopic Survey: 360 nm < λ < 1000 nm FoV: 10 400 :
Objectives: Galaxy Clustering Science Cosmological Parameters
How to check for Homogeneity ?
![Page 6: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/6.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
BOSS in a Nutshell
PLUGUE Al PLATE
1000 x SPECTROMETER
SPECTROSCOPY
![Page 7: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/7.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
cosmology dependence
Measure distances in the Universe
![Page 8: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/8.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
![Page 9: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/9.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Observable ?
Which range to measure?
![Page 10: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/10.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Observable ?
Which range to measure?
Account for RSD ?
Theory? ΛCDM, wCDM, sCDM, Modified Grav
![Page 11: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/11.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Count-in-Spheres
Select a galaxy as a center
Create a sphere of radius r
Compute number of galaxies
repeat for every galaxy
compute the mean N(r)
repeat for different scales
How to measure density
![Page 12: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/12.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Count-in-Spheres
Select a galaxy as a center
Create a sphere of radius r
Compute number of galaxies
repeat for every galaxy
compute the mean N(r)
repeat for different scales
How to measure density
![Page 13: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/13.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Fractal Dimension:
Inhomogeneous : @ small scales (clustering)
Homogeneous @ large scales
Transition to Homogeneity at:
Arbitrary Choice
Homogeneity Scale Estimator
N(< r) / rD2
![Page 14: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/14.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Fractal Dimension:
Inhomogeneous : @ small scales (clustering)
Homogeneous @ large scales
Transition to Homogeneity at:
Arbitrary Choice
Homogeneity Scale Estimator
D2(r) < 3
N(< r) / rD2
![Page 15: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/15.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Fractal Dimension:
Inhomogeneous : @ small scales (clustering)
Homogeneous @ large scales
Transition to Homogeneity at:
Arbitrary Choice
Homogeneity Scale Estimator
D2(r) < 3
N(< r) / rD2
D2(r) = 3
![Page 16: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/16.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Fractal Dimension:
Inhomogeneous : @ small scales (clustering)
Homogeneous @ large scales
Transition to Homogeneity at:
Arbitrary Choice
Homogeneity Scale Estimator
D2(r) < 3
N(< r) / rD2
D2(r) = 3
D2(RH) = 3 @ 1%
![Page 17: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/17.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Matter-Observable Reconstruction
Theory Dth2 (r)
Dth2 (r)
![Page 18: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/18.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Theory
Simulated galaxy distribution
Dth2 (r)
Dgal2 (r; b)
Dth2 (r)
Dgal2 (r; b)
Matter-Observable Reconstruction
![Page 19: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/19.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Theory
Simulated galaxy distribution
Convert to
Dth2 (r)
Dgal2 (r; b)
DMM2 (r; b)
Dgal2 (r; b)
Dth2 (r)
DMM2 (r; b)
Matter-Observable Conversion
![Page 20: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/20.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Theory
Simulated galaxy distribution
Convert to
3 diff Distributions
Need to account for bias
Dth2 (r)
Dgal2 (r; b)
DMM2 (r; b)
Dth2 (r)
DMM2 (r; b)
Matter-Observable Conversion
![Page 21: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/21.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
RSD Analysis
Determination: bias, peculiar velocities
Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h
![Page 22: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/22.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Determination: bias, peculiar velocities
Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h Fitting choices according to QPM
RSD Analysis
![Page 23: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/23.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
RSD Analysis
r < 40h�1Mpc
Determination: bias, peculiar velocities
Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h Fitting choices according to QPM
Theoretical Model CLASS soft (+Halofit)
⇠(r; b,�p) = FRSD(r; b,�p)⌦ ⇠M (r)
![Page 24: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/24.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
RSD Analysis
Determination: bias, peculiar velocities
Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h Fitting choices according to QPM
Theoretical Model CLASS soft (+Halofit)
r < 40h�1Mpc
⇠(r; b,�p) = FRSD(r; b,�p)⌦ ⇠M (r)
![Page 25: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/25.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
RSD Analysis
Determination: bias, peculiar velocities
Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h Fitting choices according to QPM
Theoretical Model CLASS soft (+Halofit)
⇠(r; b,�p) = FRSD(r; b,�p)⌦ ⇠M (r)
⇢⇠ij
![Page 26: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/26.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Results
r > 40h�1Mpc
Well Distinct Fitting Space increases with scaleD2
![Page 27: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/27.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Well Distinct Fitting Space increases with scale Cosmological Principle confirmed:
DR12 DATA
Results
![Page 28: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/28.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Well Distinct Fitting Space increases with scale Cosmological Principle confirmed:
DR12 DATA 1000 QPM-ΛCDM
D2
Results
![Page 29: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/29.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Well Distinct Fitting Space increases with scale Cosmological Principle confirmed:
DR12 DATA 1000 QPM-ΛCDM ΛCDM PLANCK 2015
D2
Results
![Page 30: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/30.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Redshift Evolution of
Confirmation of ΛCDM model
HomoScale is with time
RH
Results
![Page 31: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/31.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Conclusion
Main Features: Largest Volume ever studied at z~0.5 Precision of measurement ~1% ( Wz ~5% ) Easy application on different surveys High Robustness Through Mocks Tests
General limitations of these studies: Insensitive to radial density dependence Distance calculation assumes ΛCDM RSD Analysis assumes ΛCDM
Consistency test of ΛCDM at %-level Validation of Cosmological Principle
![Page 32: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/32.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Outlook
Predictions for future projects (EUCLID, LSST)
Use as Cosmological Standard Ruler Cosmological Parameters Nature of Dark EnergyAcceleration of the Universe
![Page 33: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/33.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Thank you for your attention !
![Page 34: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/34.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
BACKUP - SLIDES
![Page 35: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/35.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Uniform Galaxy Sample
[S.Alam et al. 1501.00963]
Intrinsically Uniform Sample
z-Cut ~ dperp-cut 0.43 < z <0.7
i mag-Cut faint-bright limits
passively evolving gals constant-stellar mass
BOSS DR12 CMASS Sample
NGC
SGCDR12
![Page 36: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/36.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
GALAXIES - - - > MATTER
![Page 37: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/37.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
SDSS-IV
WiggleZ
2016, 0.2<z<3.5 7500o 1.5x106 CMASS 7.5x105 QSO2011, z<1 7500o 2.4x105 ELG
2dF-GRS2002, z<0.3 1500o 3.3x105 ELG
GALAXY SURVEYS
LSST 2019, 10000o 109 Gal
EUCLID
DESI
2022, 15000o 109 Gal
2022, 14000o 30x106 Gal z<2 Lya Forest z>2
![Page 38: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/38.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
1992 1993 2011 2013
CMB MAPSTest of Isotropy
ACT
BICEP3
![Page 39: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/39.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Optimal Homogeneity Estimators
2pt-Correlation function: Landy Szalay Estimator
Average number galaxy density
Convert to Matter-distribution estimator
Fractal Correlation dimension
⇠ls(s) =DD(s)� 2 ⇤DR(s) +RR(s)
RR(s)
N (< r) = 1 +3
r3
Z r
0⇠(s)s2ds
NM (< r) =N th
M (< r)� 1
N thb,�p
(< r)� 1[N (< r)� 1] + 1
DM2 (r) =
d ln NM (< r)
d ln r+ 3
![Page 40: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/40.jpg)
Mock Galaxies Catalogues
Basic MethodPredict evolution of mass field Identify DM halos Populate Halos with Galaxies Apply survey characteristics
Analysis UsageCompute Covariance Matrices Use in Analysis Tests
ref: 1309.5532v2, 1203.6609v2
![Page 41: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/41.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Un-Correlated
eff0.0 north 1000 qpm factor: correcting for inv cov
z2
1000 QPMs
![Page 42: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/42.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Cosmology independence
D2(r) =d ln N (< r)
d ln r! D2(↵r) =
d ln N (< ↵r)
d ln r
↵ =dmodel
(zm
)
dfiducial
(zm
)DA(z) =
c
H0
p|⌦k|
Z z
0
dz0
H(z0)
d(z) =
D2
Acz
H(z)
�1/3
![Page 43: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/43.jpg)
Analysis Null tests
measurement on mocks
Spline fitting
2 ndf
![Page 44: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/44.jpg)
Analysis Null tests
measurement on mocks
Spline fitting
CDF [�2mock
]
![Page 45: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/45.jpg)
Analysis Null tests
![Page 46: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/46.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
RSD-choices
![Page 47: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/47.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
RSD-choices
![Page 48: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/48.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
RSD-choices
![Page 49: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/49.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Correlation Matrices
⇢⇠ij
⇢Nij
⇢D2ij
![Page 50: The Homogeneity Scale of the Universe with Large Scale ... · P.Ntelis Nov 2016 Homogeneity Scale of the Universe SDSS-IV WiggleZ 2016, 0.2](https://reader033.fdocuments.net/reader033/viewer/2022042314/5f0286527e708231d404b15b/html5/thumbnails/50.jpg)
P.Ntelis Nov 2016 Homogeneity Scale of the Universe
Systematic Effects
Rarely 100%: Survey in progress Non-uniform success rate
Definition:
Importants Weights for: Closed Pairs z-failure Contamination from Stars Shot-noise, Cosmic Variance
- [Feldman, Kaiser, Peacock,1993] wtot
= (wcp
+ wzf
� 1)wsys
wfkp