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Following the general framework of the gauge invariant perturbation theory developed in, we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive(More)
The experiments with solar, atmospheric, reactor and accelerator neutrinos have provided compelling evidences for oscillations of neutrinos caused by nonzero neutrino masses and neutrino mixing. The data imply the existence of 3-neutrino mixing in vacuum. We review the theory of neutrino oscillations, the phenomenology of neutrino mixing, the problem of the(More)
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723], some formulae for the perturbative curvatures of each order are derived. We follow the general framework of the second-order gauge invariant perturbation theory on an arbitrary background spacetime to derive these formulae. It is found(More)
Let M be an orientable closed connected 3-manifold. We introduce the notion of amalgamated Heegaard genus of M with respect to a closed separating 2-manifold F , and use it to show that the following two statements are equivalent: (i) a compact connected 3-manifold Y can be embedded in M so that the exterior of the image of Y is a union of handlebodies; and(More)