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Home , Homogeneity (physics)

Homogeneity Scale of the

Pierros Ntelis PhD advisor: J.C. Hamilton APC

24 March 2016 OUTLINE

Theoretical Framework BOSS Survey Method of Measurement Results with DR12 Conclusion & Outlook

P.Ntelis, March 2016 Homogeneity Scale of the Universe Theoretical Framework

General Relativity Homogeneity + Isotropy! in large scale structures

Friedman Equations Dynamics of the Universe Consolidation Main Pillars of ! modern

ΛCDM - model T 5 best fit on data 10 T ⇠

P.Ntelis, March 2016 Homogeneity Scale of the Universe How to check for Homogeneity ?

SDSS-III / BOSS ! Main 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

P.Ntelis, March 2016 Homogeneity Scale of the Universe BOSS in a Nutshell

PLUGUE Al PLATE

SPECTROSCOPY SPECTRO 1000 x METER

P.Ntelis, March 2016 Homogeneity Scale of the Universe Uniform Galaxy Sample

NGC Intrinsically Uniform Sample ! z-Cut ~ dperp-cut 0.43 < z <0.7 i mag-Cut faint-bright limits

passively evolving gals [S.Alam et al. 1501.00963] constant-stellar mass DR12 SGC ! ! BOSS DR12 CMASS Sample

P.Ntelis, March 2016 Homogeneity Scale of the Universe Observable ?

Which range to measure?

Account for RSD ?

Theory? ΛCDM, wCDM, sCDM, Modified Grav

P.Ntelis, March 2016 Homogeneity Scale of the Universe Comparison Statistics

DR12 BOSS # Objects: 786950 Large Volume 3 3 ! Veff =(5.1+2.3)h Gpc Precision 1%

WiggleZ Collaboration # Objects: 225297 Small Volume 3 3 ! Veff 1h Gpc Precision' 5%

P.Ntelis, March 2016 Homogeneity Scale of the Universe How to measure density

Count-in-Spheres Select a galaxy as a center ! Create a sphere of radius r! ! Compute number of ! repeat for every galaxy ! compute the mean N(r)! ! repeat for different scales

P.Ntelis, March 2016 Homogeneity Scale of the Universe Homogeneity Scale Estimator

Homogeneous: ! N(

P.Ntelis, March 2016 Homogeneity Scale of the Universe Matter-Observable Conversion

th Theory D2 (r)

th D2 (r)

P.Ntelis, March 2016 Homogeneity Scale of the Universe Matter-Observable Conversion

th Theory D2 (r)

th D2 (r) Simulated galaxy gal D (r; b) distribution 2

!

gal D2 (r; b)

P.Ntelis, March 2016 Homogeneity Scale of the Universe Matter-Observable Conversion

th Theory D2 (r)

th D2 (r) Simulated galaxy gal D (r; b) distribution 2

MM Convert to D2 (r; b) MM D2 (r; b)

gal ! D2 (r; b)

P.Ntelis, March 2016 Homogeneity Scale of the Universe Matter-Observable Conversion

th Theory D2 (r)

th D2 (r) Simulated galaxy gal D (r; b) distribution 2

MM Convert to D2 (r; b) MM D2 (r; b) 3 diff Distributions

Need to account for bias

P.Ntelis, March 2016 Homogeneity Scale of the Universe RSD Analysis

Determination: bias, peculiar Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h

P.Ntelis, March 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

P.Ntelis, March 2016 Homogeneity Scale of the Universe RSD Analysis

Determination:

bias, peculiar velocities 1 r<40h Mpc Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h Fitting choices according to QPM

Theoretical Model CLASS soft (+Halofit)

⇠(r; b, )=F (r; b, ) ⇠ (r) p RSD p ⌦ M

P.Ntelis, March 2016 Homogeneity Scale of the Universe RSD Analysis

Determination:

bias, peculiar velocities 1 r<40h Mpc Kaiser @ r>10Mpc/h FoG @ r<10Mpc/h Fitting choices according to QPM

Theoretical Model CLASS soft (+Halofit)

⇠(r; b, )=F (r; b, ) ⇠ (r) p RSD p ⌦ M

P.Ntelis, March 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 ⇠ ⇢ij

Theoretical Model CLASS soft (+Halofit)

⇠(r; b, )=F (r; b, ) ⇠ (r) p RSD p ⌦ M

P.Ntelis, March 2016 Homogeneity Scale of the Universe Results

Well Distinct Fitting Space increases with scale D2

1 r>40h Mpc

P.Ntelis, March 2016 Homogeneity Scale of the Universe Results

Well Distinct Fitting Space increases with scale D2 Cosmological Principle confirmed: DR12 DATA

P.Ntelis, March 2016 Homogeneity Scale of the Universe Results

Well Distinct Fitting Space increases with scale D2 Cosmological Principle confirmed: DR12 DATA 1000 QPM-ΛCDM

P.Ntelis, March 2016 Homogeneity Scale of the Universe Results

Well Distinct Fitting Space increases with scale D2 Cosmological Principle confirmed: DR12 DATA 1000 QPM-ΛCDM ΛCDM PLANCK 2015

P.Ntelis, March 2016 Homogeneity Scale of the Universe Results

Redshift Evolution of H ! R Confirmation of ΛCDM model ! HomoScale is with time

P.Ntelis, March 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

P.Ntelis, March 2016 Homogeneity Scale of the Universe Outlook

! Study alternative estimators ! Predictions for future projects (EUCLID, LSST) ! Use as Cosmological Standard Ruler Cosmological Parameters Nature of Dark ! Acceleration of the Universe

P.Ntelis, March 2016 Homogeneity Scale of the Universe Thank You Very Much !

P.Ntelis, March 2016 Homogeneity Scale of the Universe Mock Galaxies Catalogues

Basic Method! Predict evolution of mass field Identify DM halos Populate Halos with Galaxies Apply survey characteristics ! Analysis Usage! Compute Covariance Matrices Use in Analysis Tests ! ref: 1309.5532v2, 1203.6609v2

P.Ntelis, March 2016 Homogeneity Scale of the Universe Optimal Homogeneity Estimators

2pt-Correlation function: Landy Szalay Estimator ! DD(s) 2 DR(s)+RR(s) ! ⇠ (s)= ⇤ ls RR(s) ! Average number galaxy density ! 3 r ! (

P.Ntelis, March 2016 Homogeneity Scale of the Universe Analysis Null tests

2 ndf

measurement on mocks ! ! Spline fitting ! !

P.Ntelis, March 2016 Homogeneity Scale of the Universe Analysis Null tests

measurement on mocks ! ! Spline fitting ! ! 2 CDF[mock]

P.Ntelis, March 2016 Homogeneity Scale of the Universe Analysis Null tests

P.Ntelis, March 2016 Homogeneity Scale of the Universe Un-Correlated

z2

1000 QPMs

eff0.0 north 1000 qpm factor: correcting for inv cov

P.Ntelis, March 2016 Homogeneity Scale of the Universe Correlation Matrices

2 ⇢ijD

⇠ ⇢ij

⇢ijN

P.Ntelis, March 2016 Homogeneity Scale of the Universe Correlation Matrices

2 ⇢ijD

⇠ ⇢ij

⇢ijN

P.Ntelis, March 2016 Homogeneity Scale of the Universe Cosmology independence

dln (

1/3 2 cz d(z)= DA dmodel(zm) H(z) ↵ =  z dfiducial(zm) c dz0 DA(z)= H ⌦ 0 H(z0) 0 | k| Z p

P.Ntelis, March 2016 Homogeneity Scale of the Universe RSD-choices

P.Ntelis, March 2016 Homogeneity Scale of the Universe RSD-choices

P.Ntelis, March 2016 Homogeneity Scale of the Universe RSD-choices

P.Ntelis, March 2016 Homogeneity Scale of the Universe Uniform Galaxy Data Sample

christy tremonti 2009 Uniform Sample in !

P.Ntelis, March 2016 Homogeneity Scale of the Universe Uniform Galaxy Data Sample

christy tremonti 2009 Uniform Sample in Redshift ! z-Cut ~ dperp-cut 0.43 < z <0.7

z-high z-low

P.Ntelis, March 2016 Homogeneity Scale of the Universe Uniform Galaxy Data Sample

christy tremonti 2009 Uniform Sample in Redshift ! z-Cut ~ dperp-cut 0.43 < z <0.7 i mag-Cut faint-bright limits

P.Ntelis, March 2016 Homogeneity Scale of the Universe Uniform Galaxy Data Sample

christy tremonti 2009 Uniform Sample in Redshift ! z-Cut ~ dperp-cut 0.43 < z <0.7 i mag-Cut faint-bright limits passively evolving gals constant-stellar mass ! !Best BOSS CMASS Sample

P.Ntelis, March 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] w =(w + w 1)w w tot cp zf sys fkp

P.Ntelis, March 2016 Homogeneity Scale of the Universe Optimal Homogeneity Estimator

! DD(s) 2 DR(s)+RR(s) Landy Szalay Estimator ⇠ls(s)= ⇤ ! RR(s) ! ! 3 r Average number galaxy density (

P.Ntelis, March 2016 Homogeneity Scale of the Universe Results

d (r) dth(r) pull(r)= 2 2 d2 (r)

REMOVE IF NOT BETTER WITH ALL POINTS

P.Ntelis, March 2016 Homogeneity Scale of the Universe COMPARE RESULTS

Redshift Evolution of H ! R Confirmation of ΛCDM model ! HomoScale is with time

P.Ntelis, March 2016 Homogeneity Scale of the Universe P.Ntelis, March 2016 Homogeneity Scale of the Universe