Constraints on Anisotropic Cosmic Expansion from Supernovae

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2 Constraints on Anisotropic Cosmic Expansion from Supernovae Based on BK, Schwarz, Seikel, Wiegand, arxiv: Benedict Kalus Bielefeld University 2 / Kosmologietag 25 th April, 2013 IBZ, Bielefeld

3 Motivation isotropy is a basic assumption of modern cosmology CMB probes symmetry at photon decoupling Hubble diagram standard procedure assumes isotropy Are SNe a fair sample of isotropically distributed standard candles? 3 / 12

4 4 / 12 Hemispherical Asymmetry Test (HAT) 1. Grid the sky 2. Consider each grid point as pole of hemisphere 3. Fit µ on each pair of hemispheres modelled as µ = 5 log 10 (d L /Mpc) luminosity-redshift-relation follows directly from cosmological principle if z < 0.2 d L (z) = cz [1 + (1 q 0 ) z ] + O (z 3) H fix q 0 = at its WMAP7 ΛCDM value

5 Application to Data apply our test to the Constitution set [Hicken et al 09], because Celestial distribution of SNe. Black SNe are in all samples, green ones not in SALT, blue ones only in MLCS2k2, and red ones only in MLCS2k2 3.1 it contains lots of nearby SNe from all the sky (except for the zone of avoidance) µ obtained by four different light-curve fitters (MLCS2k2 1.7 and 3.1, SALT and SALT II) 5 / 12

6 Maps of Hemispherical Asymmetry in H 0 MLCS2k2 1.7 (upper left), MLCS2k2 3.1 (upper right), SALT (lower left), SALT II (lower right). Maximal values: H = 3.4 km/s/mpc, i.e. H N H S = 2.59%. H N +H 6 / 12 S

7 Distance Modulus Monte Carlo 1. keep positions and redshifts of each SN 2. calculate µ, assuming WMAP7 q 0 = 0.601, H 0 = 71.0 km/s/mpc 3. MC with Gaussian errors, standard deviation equals original σ µi 4. maximise H N H S in the simulated data 5. repeat times 7 / 12

8 Distance Modulus Monte Carlo: Results 1.0 MLCS17 H MLCS31 H SALT H0 SALT2 H / 12

9 Limits on Expansion Asymmetry 1. draw random distance moduli and redshifts given their Constitution value with measurement errors 2. compute the asymmetry at the original direction of maximum asymmetry 3. after realisations, enumerate 95% quantile H 95 and 5% quantile H 5 9 / 12

10 Limits on Expansion Asymmetry fitter 5% quantile H 5 95% quantile H 95 MLCS2k2 (1.7) 0.8% 3.4% MLCS2k2 (3.1) 1.1% 3.8% SALT 0.0% 3.0% SALT II 0.7% 3.7% for a perfectly isotropic universe: H 5 < 0 at every position H 95 values provide upper limits on the anisotropy of the Hubble expansion 10 / 12

11 Limits on Expansion Asymmetry fitter 5% quantile H 5 95% quantile H 95 MLCS2k2 (1.7) 0.8% 3.4% MLCS2k2 (3.1) 1.1% 3.8% SALT 0.0% 3.0% SALT II 0.7% 3.7% for a perfectly isotropic universe: H 5 < 0 at every position H 95 values provide upper limits on the anisotropy of the Hubble expansion 10 / 12

12 SALT II green, MLCS2k2 3.1 red 11 / 12 Universität Bielefeld Faculty of Physics 90 and 95 % C.L. Contours of the Maximum Asymmetry Directions Compared with other Directions

13 12 / 12 Summary we analysed hemispherical asymmetries in H 0 in low redshift SN data inconsistent with the assumption of perfect isotropy and homogeneity directions in agreement with other directions of asymmetries and WMAP cold spot I fluctuations in the locally measured H 0 significant do not contradict global isotropy expansion asymmetry of the local Universe is 2.6% and less than 3.8% at 95% C.L.

14 Characteristics of the Samples fitter # SN with z < 0.2 mean redshift median redshift mean σ µ in mag MLCS2k2 (1.7) MLCS2k2 (3.1) SALT SALT II / 12

15 Directions of Maximum Asymmetry in H 0 fitter l b (H N H S ) max H N H S H N +H S MLCS2k2 (1.7) km/s/mpc 2.49% MLCS2k2 (3.1) km/s/mpc 2.59% SALT km/s/mpc 1.54% SALT II km/s/mpc 2.28% 14 / 12

16 Scrambled Data 1. scramble positions 2. perform a HAT 3. search for the maximum asymmetry 4. repeat times MLCS17 MLCS H H0 SALT SALT H H0 15 / 12

17 Fixing the Deceleration Parameter We fix q 0 = at its WMAP7 ΛCDM value, since q 0 poorly constrained at z < 0.2, we are only interested in H = H N H S, fixing q 0 at different values between -0.7 and 0.4, yields for SALT II H between 3.05 km/s/mpc and 2.55 km/s/mpc. 16 / 12

18 Expectations of Hemispherical Asymmetry In a perfectly homogeneous and isotropic Universe: hemispherical asymmetry only due to noise and systematics LSS is expected to give rise to a small deviation from isotropy Estimate cosmic variance of fluctuations H N H S H N +H S of the Hubble rate between the hemispheres 17 / 12

19 Cosmic Variance of Fluctuations of H 0 formalism of [Buchert 00, Li & Schwarz 08, Wiegand & Schwarz 12] relates H S/N = H S/N ( f D 0 δ 0 S/N ) with growth factor f D0 and contrast δ 0 S/N In linear regime H N H S H N +H S = 1 6 f ( ) D 0 δ0 S δ 0 N typical fluctuations between different locations: ( ) HN H σ A = σ S = 13 H N + H f D0 σhs 2 σ2 FS S ( ) where σhs 2 := σ2 δ 0 N/S and σfs 2 := σ2 ( δ 0 D ) 18 / 12

20 Predictions for Fluctuations in the Anisotropy have to account for incompleteness of the sampling use a radial window function W D to calculate σfs 2 = R P 3 0 (k) W D 2 (k) d3 k number of SN number of SN scale r in h 1 Mpc A r 2 1 B r 4 A r 2 1 B r 4 number of SN scale r in h 1 Mpc arrive at 0.7% for MLCS2k2 and SALT, scale r in h and 0.6% SALT II 1 Mpc scale r in h 1 Mpc using different forms, the values vary between 0.6% and 1.0% number of SN A r 2 1 B r 4 A r 2 1 B r / 12

21 Comparison with Cosmic Variance 1. pick random positions (l,b) 2. calculate hemispherical asymmetry at (l,b) 3. variance of H for the spheres is desired fluctuation 4. restrict random north poles (l,b) to one hemisphere, otherwise north poles could be south poles in the same sample 5. as not to miss a direction of high anisotropy do 3 runs for orthogonal directions estimated fluctuation due to CV between 0.6% and 1.0%, empirical RMS between 0.5% and 1.0% 20 / 12

22 Distance Modulus Monte Carlo: Resulting GEV ) HN H fitter µ σ ξ 1-CDF( S H N +H S MLCS2k2(1.7) % MLCS2k2(3.1) % SALT % SALT II % max 21 / 12

23 Shape Asymmetry in MLCS2k2 framework: SN light-curves parametrised by shape parameter max. asymmetry: 0.57 for MLCS2k / 12 left: MLCS2k2 1.7, right: MLCS2k2 3.1

24 Colour Asymmetry SALT and SALT II parametrise SN light-curves by colour parameter max. asymmetry: 0.64 for SALT 23 / 12 left: SALT, right: SALT II

25 Number Asymmetry hemispherical asymmetry N N N S N N +N S for the hemispheres of max. expansion anisotropies: MLCS2k2 1.7: -4.8%, MLCS2k2 3.1: -20.2%, SALT: 46.9%, SALT II: -10.6%, max. 50% 24 / 12