Global solution to the Cauchy problem on a universe fireworks model

The global existence of small self-interacting scalar field propagating in the contracting universe

We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lama$\hat{i}$tre-Robertson-Walker model of the contracting universe. For the Klein-Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution.

Waves on accelerating dodecahedral universes

We investigate the wave propagation on a compact 3-manifold of constant positive curvature with a non trivial topology, the Poincaré dodecahedral space, when the scale factor is exponentially increasing. We prove the existence of a limit state as t tends to infinity and we get its analytic expression. The deep sky is described by this asymptotic profile thanks to the Sachs-Wolfe formula. We transform the Cauchy problem into a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We perform an accurate scheme of computation: we employ a variational method using a …

Topological sectors for Weyl-algebra net in the Einstein cylindrical universe

This paper is an extended and more detailed version of arXiv:0812.0533. We tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some crucial results of the algebraic framework of quantization, we address the problem of the construction of the topological cocycles. All constructed cocycles lead to unitarily equivalent representations of the fundamental group of the circle (see…

The Dirac system on the Anti-de Sitter Universe

We investigate the global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove that there exists unitary dynamics, but its uniqueness crucially depends on the ratio beween the mass $M$ of the field and the cosmological constant $Λ>0$ : it appears a critical value, $Λ/12$, which plays a role similar to the Breitenlohner-Freedman bound for the scalar fields. When $M^2\geq Λ/12$ there exists a unique unitary dynamics. In opposite, for the light fermions satisfyi…

带软势的Einstein-Boltzmann系统齐次解的未来全局存在性

Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials

该研究针对带软势的Einstein-Boltzmann系统的宇宙学柯西问题，在Bianchi I对称与正宇宙学常数假设下，通过新权函数结合Illner-Shinbrot方法，证明了哈勃初值接近临界值时空间齐次解的未来全局存在性与渐近行为。

The Klein-Gordon Equation in Anti-de Sitter Cosmology

This paper deals with the Klein-Gordon equation on the Poincaré chart of the 5-dimensional Anti-de Sitter universe. When the mass $μ$ is larger than $-{1}{4}$, the Cauchy problem is well posed despite the loss of global hyperbolicity due to the time-like horizon. We express the finite energy solutions in the form of a continuous Kaluza-Klein tower and we deduce a uniform decay as $\mid t\mid^{-{3}{2}}$. We investigate the case $μ={ν^2-1}{2}$, $ν\in\NN^*$, which encompasses the gravitational fluctuations, $ν=4$, and the electromagnetic waves, $ν=2$. The propagation of the wave front set shows t…