宇宙のトポロジーを決定するための天体分 布を用いた新手法

()
Λ-CDM (e.g., Ω tot =
1.0050 +0.0060
−0.0061
, Hinshaw et al. 2009)
() ()
2 Λ-CDM
3
18 (Nowacki 1934, 1 )
1
(CMB)
(LSS) (≃ 14Gpc)
LSS 1
WMAP
(Cornish et al. 2004; Key et al. 2007; Roukema et al.
2008; Aurich 2008; Bielewicz & Banday 2011)
1 17
3 (3-torus, chimney space, slab space)
(Mota et al. 2010) 14 “”
(Fujii & Yoshii 2011a,
Fujii 2011) CMB 3
180 ◦
:
γ: (X, Y, Z) ↦−→ (−X, −Y, Z + L) (1)
1

1: 17 3 (
)
Jeffrey Weeks
1
L 2
(Fujii & Yoshii 2011a)2
⃗X 1 , ⃗X 2 γ “” ⃗X
1 ′, ⃗X
2 ′
X 2 ′ − X′ 1 = −(X 2 − X 1 ), (2)
Y 2 ′ − Y′ 1 = −(Y 2 − Y 1 ), (3)
Z 2 ′ − Z′ 1 = Z 2 − Z 1 . (4)
(X, Y, Z)
( 180 ◦ )
(x, y, z) γ
⎛
⎞ ⎛
1 0 0 0
0 -1 0 0
γ = U
U −1 +
0 0 -1 0
⎜⎝
⎟⎠ ⎜⎝
0 0 0 1
⎞
1 0 0 0
L 1 0 0 0
,
L 2 0 0 0
⎟⎠
L 3 0 0 0
2

U
(2),(3),(4) (x, y, z)
CMB
(Fujii 2011) 2 ⃗x 1 , ⃗x 2 ⃗x ′ 1 , ⃗x′ 2
3 :
(⃗x 2 − ⃗x 1 ) + (⃗x
2 ′ − ⃗x′ 1
) ( 2)
2: 4 ⃗n pec ∝ ⃗a + ⃗b
2 ⃗n pec
4 ⃗n pec ∝ ⃗a +⃗b
3
“” (X, Y, Z) 30 ◦ z
1
1
0.5
0.5
0
0
-0.5
-0.5
-1 -0.5 0 0.5 1 -1
-1 -0.5 0 0.5 1 -1
3:
3 2dF SDSS
3

4