Homogeneity Scale of the Universe Pierros Ntelis! PhD advisor: J.C. Hamilton! APC 24 March 2016 OUTLINE Theoretical Framework BOSS Galaxy Survey Method of Measurement Results with DR12 Conclusion & Outlook P.Ntelis, March 2016 Homogeneity Scale of the Universe Theoretical Framework General Relativity! Cosmological Principle! Homogeneity + Isotropy! in large scale structures Friedman Equations! Dynamics of the Universe Consolidation ! Main Pillars of ! modern Cosmology "CDM - model! δT 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? ! "CDM, ! 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 galaxies ! 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(<r) r3 @ large scales! / dlnN(<r) ! D2(r)= =3 ! dlnr ! Inhomogeneous : D 2 ( r ) < 3 @ small scales (clustering) ! ! Transition to Homogeneity at: ! ! D2(RH ) = 3 @ 1% Arbitrary Choice 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 velocities 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, σ )=F (r; b, σ ) ⇠ (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, σ )=F (r; b, σ ) ⇠ (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, σ )=F (r; b, σ ) ⇠ (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 Energy! 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 ! (<r)=1+ ⇠(s)s2ds N r3 ! Z0 Convert to Matter-distribution estimator ! th M (<r) 1 ! M (<r)= N − [ (<r) 1] + 1 N th (<r) 1 N − ! Nb,σp − Fractal Correlation dimension dln (<r) M (r)= NM +3 D2 dlnr 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[χmock] 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 (<r) dln (<↵r) (r)= N (↵r)= N D2 dlnr !D2 dlnr 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 Redshift ! 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 (<r)=1+ ⇠(s)s2ds N r3 ! Z0 ! ! dln (<r) Fractal Correlation dimension (r)= N +3 D2 dlnr P.Ntelis, March 2016 Homogeneity Scale of the Universe Results d (r) dth(r) pull(r)= 2 − 2 σd2 (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.