Non-Gaussian phenomena and non-linear perturbations Kenji Tomita - PowerPoint PPT Presentation

Non-Gaussian phenomena and non-linear perturbations Kenji Tomita (Prof Emer of YITP , former stuff of RITP ) 冨田憲二（京大基研名誉教授、元理論研職員） 理論研 RITP , Hiroshima U (1944, Y. Mimura) United YITP , Kyoto U 基研 (1990 -) RIFP , Kyoto U (1952, Nobel prize winner H. Yukawa) 竹原 Takehara 1964 ---------------------- x --------- 2001 -----

1. Observations about anomalies in CMB and correlation with galactic distribution First year WMAP observation : Test of Gaussianity -> No non-Gaussianity (2003) Komatsu et al, ApJ Suppl 148 , 119 (2003) Detail analyses (2003 -) found later -> many non-Gaussian phenomena in CMB + correlation with galactic distribution 3 types a) Cold Spots in CMB Vielva et al (2004), Cruz et al (2005, 2006, 2007, 2008) non-Gaussianity in southern hemisphere

Cold Spot (-57 deg, 209 deg) Left: before filtering, resolved in several spots (-350 μK) Right: after filtering (4 deg) -16 μK

Kurtosis

b) Low-l anomalies in CMB remarkable deviation of quadrupole (l = 2) from the theoretical prediction octopole planarity, alignment between quadrupole and octople, alignment of low-l multipole with equinox and ecliptic plane asymmetry of tempeature fluctuation in northern and southern hemispheres (Tegmark et al 2003, de Oliveira-Costa et al 2004,  Schwarz et al 2004, Eriksen et al 2004) 

c) Super-structures (with z = 0.3 – 0.8) in SDSS and large spots in CMB correlation of SDSS Large Red Galaxies (LRGs) and WMAP supervoid → cold spot supercluster → hot spot Characteristics of non-linearity : | Δ T/T| in cold spots > Δ T/T in hot spots (Granett et al. 2008, 2009) 5 deg, 10 μK

2. Theoretical models non-linear perturbations and Integrated Sachs-Wolfe effect (ISW) observer structures CMB (clusters, voids)

For Cold Spot Theoretical models as a candidate : a 100 Mpc radius supervoid with underdensity -0.3 Observational condition depression of radio source counts (NRAO VLA Sky Survey) Rudnick et al (2007) debated : McEwen et al (2007), Smith & Huterer (2010) weak temperature decrement in 2MASS galactic survey (at z < 0.3) Francis & Peacock (2010) galaxy counts on the CMB Cold Spot (at 0.3 < z <0.9); no existence of a 100 Mpc radius supervoid with underdensity -0.3 Granett, Szapudi & Neyrinck (2010) No single supervoid as the candidate ! Texture ? (Cruz, Martinez-Gonzales, Vielva, Diego, Hobson, Turok 200 8) X Sunyaev-Zeldovich effect

For low-l anomalies Local supervoids Inoue & Silk (2006 & 2007) l ocal voids in the thin-wall approximation (first + second-orders) 2 local voids with z ∼ 0.05, δ∼ -0.3, r = 300/h Mpc s ucceeded in explaining low-l anomalies and alignment and planarity of multipoles ! Density perturbations in redshift shells from 2MASS galaxy catalog (z < 0.3) Francis & Peacock (2010) ISW effect is estimated by the ray-shooting in the reconstructed model with redshift shells. Anomalies are partly explained. Low quadrupole power, quadrupole and octopole alignment and north- south asymmetry.

Inoue-Silk (2007)

Francis -Peacock (2010)

For super-structures (with z = 0.3 – 0.8 ) in SDSS and large spots in CMB Relativistic second-order perturbations and ISW effect in Λ CDM model (Tomita & Inoue 2008) ISW effect in LTB inhomogeneous models (Sakai & Inoue 2008) Evidence of quasi-linear super-structures on the basis of the above 3 works (Inoue, Sakai & Tomita 2010) K.T.Inoue, N.Sakai and K.Tomita, ApJ 722 , 1-14(2010) Evidence of quasi-linear super-structures in the cosmic microwave background and galaxy-distribution Derivation of super-structure models reproducing representative s pots in CMB -> non-linear structures , such as inconsistent with the prediction in a concordant ΛCDM model at >3σ level.

Probability distribution function (PDF) from galaxy catalog SDSS, LRG (0.3 < z < 0.8), reconstruction of inhomogeneous models due to N-body simulation and ISW effect due to ray- shooting Papai & Szapudi 2010; Papai et al 2010 Main property of PDF such as skewness and kurtosis is same as that in the ΛCDM model compatible with WMAP data, but the tail part is so different that large cold and hot spots appear in ISW effect in the reconstructed model. The amplitude of the signal is 2σ higher than ΛCDM prediction. They had linear analysis, but non-linearity is important for accuracy.

Skewness and kurtosis are consistent with the prediction of Λ CDM model with linear bias..

Summary and discussions ● Model construction for the first “ Cold Spot ”. ● ISW signals for photoelectric-z 2MASS data are several times larger than the ΛCDM prediction (Francis & Peacock). Consistency with Inoue and Silk's analysis. ● ISW signal from SDSS–WMAP images is inconsistent with the prediction in a concordant ΛCDM model at >3σ level (Inoue et al) . Consistency with Papai et al's analysis. ● Non-linear effects (hot-ring around cold spot&dip at the center of hot spot) seem to be present in the SDSS data. ● Non-spherical void or complex of several voids ? ● Origin of non-Gaussianity ? Problem in the inflation model or the breakdown of ΛCDM model ?

Studies from now : YITP seminar ” Non-linear cosmological perturbations and non-Gaussianity ” (2009, 2010, 2011, ...) organized by T. Tanaka, M. Sasaki et al

5 0 ∆ T [ µ K] -5 -10 -15 0 2 4 6 8 10 α [deg.] (Granett et al. 2008)

10 ∆ T [ µ K] 5 0 0 2 4 6 8 10 α [deg.] (Granett et al. 2008)

Appendix 1 Cosmological acceleration Magnitude-redshift relation of SNIa Riess et al (1998), Perlmutter et al (1999) Models with acceleration a) Λ-dominated standard model cosmological constant or dark energy : 74 % of the total. consistent with most observations, but remained problems on non-G aussianity ? b) Inhomogeneous models with a local void Tomita (1999, 2000), .... , Nakao, Yoo, Clifton, ... 300Mpc -> Gpc void ? (K. Tomita, astro-ph/0906.1325) c) Modified gravity

Appendix 2 Wave geometry, studies for quantum gravity in RITP and from now Kaluza-Klein 5-dim unified theory (1921-6) Wave geometry (wave eq., but no Lagrangian) Y. Mimura (1935), founder of RITP, hibakusha Severe opinion on the use of nuclear energy General gauge theory R. Utiyama (1955) Gravitational quantum anomaly T. Kimura Quantum field theory in an expanding universe H. Nariai and T. Kimura (1960) Super-string theory High-dim world + 4-dim universe Inflation or collision in the early universe ? Cosmological constant, dark energy ? Gravtational background radiation ? Quantitative analysis of matter and antimatter ? seminar series on super-string cosmology ( 2008 - )

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1963 京都科学者会議 （竹原で開催）

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