Quantum Geometry In Action: Big Bang and Black Holes

Pre-big bang geometric extensions of inflationary cosmologies

Robertson-Walker spacetimes within a large class are geometrically extended to larger cosmologies that include spacetime points with zero and negative cosmological times. In the extended cosmologies, the big bang is lightlike, and though singular, it inherits some geometric structure from the original spacetime. Spacelike geodesics are continuous across the cosmological time zero submanifold which is parameterized by the radius of Fermi space slices, i.e, by the proper distances along spacelike geodesics from a comoving observer to the big bang. The continuous extension of the metric, and the …

Initial data on big bang singularities in symmetric settings

In a recent article, we propose a general geometric notion of initial data on big bang singularities. This notion is of interest in its own right. However, it also serves the purpose of giving a unified perspective on many of the results in the literature. In the present article, we give a partial justification of this statement by rephrasing the results concerning Bianchi class A orthogonal stiff solutions and solutions in the $\mathbb{T}^{3}$-Gowdy symmetric vacuum setting in terms of our general geometric notion of initial data on the big bang singularity.

Propagation of Massive Scalar Fields in Pre-Big Bang Cosmologies

We investigate the linear and semilinear massive Klein-Gordon equations in geometrical frameworks of type "Conformal Cyclic Cosmology" of R. Penrose, or "Singular Bouncing Scenario" as well. We give sufficient conditions on the decay of the mass to the fields be able to propagate across the Big-Bang.

大爆炸静止奇点形成中的完整渐近行为

Complete asymptotics in the formation of quiescent big bang singularities

本文通过证明Oude Groeniger等人结果中的解诱导奇点数据，将大爆炸奇点形成的不同数学结果统一起来，扩展了稳定大爆炸形成的结论。

The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well behaved

We show that the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.

Solutions of the wave equation bounded at the Big Bang

By solving a singular initial value problem, we prove the existence of solutions of the wave equation $\Box_gϕ=0$ which are bounded at the Big Bang in the Friedmann-Lemaitre-Robertson-Walker cosmological models. More precisely, we show that given any function $A \in H^3(Σ)$ (where $Σ=\mathbb{R}^n, \mathbb{S}^n$ or $\mathbb{H}^n$ models the spatial hypersurfaces) there exists a unique solution $ϕ$ of the wave equation converging to $A$ in $H^1(Σ)$ at the Big Bang, and whose time derivative is suitably controlled in $L^2(Σ)$.