By Inoue, K T
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4) 3 For locally isotropic and homogeneous background geometry, Einstein equations are divided into a decoupled set of equations each one of which consists of only one type 50 CHAPTER 4. CMB ANISOTROPY of perturbation such as scalar, vector or tensor type perturbation1 Consequently, we can argue separately for each type of components.
17: Anisotropy in Geometry Plots of a Dirichlet domain of the Weeks manifold m003(-3,1) (left) and that of m003(16,13) (right) viewed from two opposite directions in the Klein coordinates. 2). m003(16,13) has a “thin” part which is similar to the neighborhood of a cusp. The colors on the faces correspond to the identification maps. 45 46 CHAPTER 4. CMB ANISOTROPY Chapter 4 CMB Anisotropy The most incomprehensible thing about the universe is that it is comprehensible. (Albert Einstein, 1879-1955) The surprising discovery of the cosmic microwave background (CMB) by Penzias and Wilson in 1964 [69] provided firm evidence that our universe started from a hot big-bang.
3: Kolmogorov-Smirnov Test II Eigenvalues k and corresponding averaged significance levels < αD > based on 300 realizations of the base points for the test of the hypothesis IN (x) = I(x) for the Weeks and the Thurston manifolds. in the manifold5 . Thus the observed non-Gaussianity is caused by a particular choice of the base point. However, in general, the chance that we actually observe any symmetries (elements of the isometry group of the manifold or the finite sheeted cover of the manifold) is expected to be very low.