The cosmological principle is not in the sky

Transcription

1 The 7th KIAS Workshop on Cosmology and Structure Formation Oct. 30 Nov The cosmological principle is not in the sky Chan-Gyung Park (Division of Science Education, Chonbuk National University) in collaboration with Hyerim Noh (KASI) Hwasu Hyun, Jai-chan Hwang (KNU) 1

2 Homogeneity on large scales - Einstein s Cosmological Principle The Universe is homogeneous and isotropic on large scales. Spatial homogeneity No variation in matter density at sufficiently large scales. - Is the present Universe homogeneous on large scales? Homogeneity Mean density Correlation function & Power spectrum 2

3 Mainstream results on homogeneity test - Hogg et al. (2005) SDSS DR7 LRG (0.2 < z < 0.4) Scrimgeour et al. (2012) Ntelis (2016) Counting galaxies within a sphere, N < r Averaged N < r or D 2 r Homogeneity at r > 70 h 1 Mpc. WiggleZ Dark Energy Survey (0.1 < z < 0.9) BOSS DR12 CMASS (0.4 < z < 0.7) Homogeneity N < r r 3 D 2 r = dln N(< r ) = 3 dln r Scrimgeour+(2012) 1% deviation Transition scale of homogeneity Ntelis (2016) 3

4 Misconception about spatial homogeneity 1 L 1 L The homogeneity is achieved if the averaged amount within a volume is very close to the expectation of homogeneous distribution. fluctuations in the individual estimates 1 L 1 L averaging 1 L 4

5 Correct concept of spatial homogeneity 1 L 1 L 1 L Scatter expected in the homogeneous distribution 1 L 1 L The amount contained in a volume is the same everywhere within the scatter expected in the homogeneous distribution (due to finite data points). 5

6 SDSS DR7 LRG (Luminous Red Galaxies) sample - A good tracer of massive halos - LRG catalog provided by Kazin et al. (2010, ApJ 710, 1444) DR7-Full (0.16 < z < 0.47, N=105,831, V eff = 1.6 h 3 Gpc 3 ) z c = z c = z c = ΔR = 50h 1 Mpc Z 6

7 Generating random and mock catalogs LRG survey information 1,000 random catalogs Criterion for spatial homogeneity Lightcone halo catalogs from Horizon Run 3 N-body simulation (Kim et al. 2011) 1,296 mock catalogs Consistency of LRG statistics with current paradigm of cosmology 7

8 LRG Observed, Random, Mock data sets LRG (0.338 < z < 0.362; N=11711) Survey incompleteness map of DR7 LRG data Random 0001 (0.338 < z < 0.362; N=11854) Mock 0001 (0.338 < z < 0.362; N=11727) 8

9 Average and Standard deviation Counting galaxies within a sphere R LRG R Random points Scaled N R = Measured N R from LRG Expected N R from random distribution 1 (homogeneity) LRG Mock Random Distribution of scaled N(R) s 9

10 Counting galaxies within a truncated cone - A self-consistent test of homogeneity not relying on the radial selection function and the random data points. - Count galaxies within a truncated cone that is circumscribed about the sphere of radius R located around a galaxy within a thin slice (at z c =0.35). Observer ξ R number density within a truncated cone = number density within the whole slice of 2R thickness 2R 1 (homogeneity) 10

11 Average and Standard deviation R=100 Mpc/h z c =0.35 LRG Mock Random Distribution of ξ s R=200 Mpc/h R=300 Mpc/h Mock (min σ) Mock (max σ) 11

12 Angular distributions of ξ (z c =0.35 & R=300 Mpc/h) LRG data Random Mock [max σ] Mock [min σ] ξ 12

13 LRG versus random & mock catalogs (ξ mean & std) R=70 Mpc/h R=100 Mpc/h z c =0.35 Mock x 1296 Random x 1000 LRG R=200 Mpc/h R=300 Mpc/h 17σ 11σ 13

14 Redshift dependence of ξ mean & std The LRG deviations on large scales (300 Mpc/h) from random and mock distributions still persist at lower and higher redshifts. z c =0.25 z c =0.35 z c =0.40 Mock LRG Mock LRG Mock LRG Random Random Random 14

15 Conclusions Homogeneity not reached even at 300 h -1 Mpc. - Consistent with current paradigm of cosmology 15

16 Conclusions Homogeneity not reached even at 300 h -1 Mpc. - Consistent with current paradigm of cosmology z c =0.35 slice of Δr=600 Mpc/h 16

17 Conclusions Homogeneity not reached even at 300 h -1 Mpc. - Consistent with current paradigm of cosmology Where is the Cosmological Principle? - Not in the observed sky (in the present epoch) - CP may stay in the theoretical cosmology (in the early era) - Needs a careful study of light propagation in nonlinear clustering stage of the Universe. 17

18 Supplementary Slides 18

19 The Astrophysical Journal, 624:54 58, 2005 May 1 Transition to homogeneity at 70 Mpc/h 19

20 Scrimgeour et al. (2012, MNRAS, 425, 116) Average of N(< r) and D 2 (r) WiggleZ Dark Energy Survey (N=179, < z < 0.9. V eff 1h 3 Gpc 3 ) Homogeneity scale of the Universe, R H =70~80 Mpc/h 20

21 P. Ntelis (2016) BOSS DR12 CMASS (N=786, < z < V eff = h 3 Gpc 3 ) Homogeneity scale : R H =60~70 Mpc/h bias correction 1% deviation Transition scale of homogeneity 21

22 Average and Standard deviation LRG Mock Random Distribution of scaled N(R) s 22

23 LRG versus random & mock catalogs (ξ mean & std) z c =0.35, R=70 & 100 Mpc/h Random x 1000 LRG Random x 1000 LRG Mock x 1296 Mock x

24 LRG versus random & mock catalogs (ξ mean & std) z c =0.35, R=200 & 300 Mpc/h Random x 1000 LRG Mock x 1296 Random x 1000 Mock x 1296 LRG 24

25 Redshift dependence of ξ mean & std The LRG deviations (at 100 Mpc/h scale) from random and mock distributions still persist at lower and higher redshifts. z c =0.25 z c =0.35 z c =0.40 Mock LRG Mock LRG Mock LRG Random Random Random 25

26 Angular distributions of LRG s Shown are galaxies within the redshift slice with z c =0.35 & Δr=140 Mpc/h. 26

27 Random data points within zc=0.35 slice of Δr=600 Mpc/h 27

28 Angular distributions of LRG s LRG data Random 0001 R = 300 h 1 Mpc Mock 1216 [max σ(ξ)] Mock 1227 [min σ(ξ)] Shown are galaxies within the redshift slice with z c =0.35 & Δr=600 Mpc/h. 28

29 Counts-in-sphere using SDSS DR7 LRG data Radius (Mpc/h) Scaled N(R) mean Scaled N(R) mean (UNI) Scaled N(R) Std Scaled N(R) Std (UNI) <all galaxies used, weight average> Scaled N(R) mean Scaled N(R) mean (UNI) Scaled N(R) Std Scaled N(R) Std (UNI) <galaxies with P>0.95 used> Number of galaxies at z=0.20~0.40 Number galaxies with completeness P>

30 SDSS DR7 LRG data (for galaxies on a slice at z c = 0.35 and with Δr=50 Mpc/h) Radius (Mpc/h) Number galaxies within slice ξ mean ξ std ξ mean (UNI) ξ std (UNI) <all galaxies used, weight average> ξ mean ξ std ξ mean (UNI) <galaxies with P>0.95 used> ξ std (UNI) Number galaxies with completeness P>

31 Random catalog 0001 (for galaxies on a slice at z c = 0.35 and with Δr=50 Mpc/h) Radius (Mpc/h) Number galaxies within slice ξ mean ξ std ξ mean (UNI) ξ std (UNI) <all galaxies used, weight average> ξ mean ξ std ξ mean (UNI) <galaxies with P>0.95 used> ξ std (UNI) Number galaxies with completeness P>

32 Mock catalog 0001 (for galaxies on a slice at z c = 0.35 and with Δr=50 Mpc/h) Radius (Mpc/h) Number galaxies within slice ξ mean ξ std ξ mean (UNI) ξ std (UNI) <all galaxies used, weight average> ξ mean ξ std ξ mean (UNI) <galaxies with P>0.95 used> ξ std (UNI) Number galaxies with completeness P>

33 SDSS DR7 LRG data (for galaxies on a slice at z c = 0.35 and with Δr=50 Mpc/h) R(Mpc/h) Number of all galaxies within slice Mean of ξ STD of ξ Skewness of ξ Kurtosis of ξ Number of galaxies with P>0.95 within slice Mean of ξ STD of ξ Skewness of ξ Kurtosis of ξ

34 SDSS DR7 LRG data (for galaxies on a slice at z c = 0.25 and with Δr=50 Mpc/h) R(Mpc/h) Number of all galaxies within slice Mean of ξ STD of ξ Skewness of ξ Kurtosis of ξ Number of galaxies with P>0.95 within slice Mean of ξ STD of ξ Skewness of ξ Kurtosis of ξ SDSS DR7 LRG data (for galaxies on a slice at z c = 0.40 and with Δr=50 Mpc/h) R(Mpc/h) Number of all galaxies within slice Mean of ξ STD of ξ Skewness of ξ Kurtosis of ξ Number of galaxies with P>0.95 within slice Mean of ξ STD of ξ Skewness of ξ Kurtosis of ξ

35 SDSS DR7 LRG data (for Healpix pixels on a slice at z c = 0.35 and with Δr=50 Mpc/h) - Count the number of galaxies within the specified truncated cone with R=300 Mpc/h centered on each Healpix pixel with Nside=128 (55563/ [28%]) Catalog Number LRG Radius (Mpc/h) redshift Number galaxies within slice <all galaxies used, weight average> ξ mean ξ std <galaxies with P>0.95 used> ξ mean ξ std Random Mock