Speaker
Léo Brunswic
(CRAL, ENSL, Université Lyon 1)
Description
In 2+1 Buchert's dust framework, the Gauss-Bonnet Theorem allows us to identify the Euler characteristic with a mass of topological origin, with positive or negative sign. Even though this does not extend in a straightforward manner to the 3+1 setting, a Theorem of Mess extended by Bonsante and Barbot suggest the insight extend to higher dimension. We explain how the Euler characteristic may evolve in a `sticky particle model': in dimension 2+1, a dust spacetime may be discretized to a flat spacetime with singular lines (massive point-particles); these particles may collide and we assume that at most one massive particle arises from the collision (massive particles are `sticky'). Collisions may give rise to white/black hole which change the topological type of the spacetime and, thus, the Euler characteristic of its Cauchy-surfaces. In such a scenario, Dark Energy arises through the evolution of the Euler characteristic to strongly negative values, corresponding to on average negative spatial curvature.
