A stability phase transition for cosmological fluids

26.06.2024, 11:00  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

David Fajman (Universität Wien)

Abstract:

Fluids are generally known to form shocks in finite time from small inhomogeneities. When the fluid evolves in an expanding spacetime, as in standard cosmology,

the expansion of spacetime induces a friction-like term in the fluid equation, which can prevent the formation of shocks. This yields future global solutions for small initial data

We refer to this phenomenon as fluid stabilization. While this problem is well understood in the regime of accelerated expansion, less is known in slowly expanding spacetimes. 

In fact, below accelerated expansion, whether a fluid stabilizes depends on the speed of sound of the fluid. We present a recent result, which gives a precise characterisation of 

this dependence in form of a critical curve, which constitutes the boundary of the stable regime. We establish stability on one side of the curve, which constitutes the first stabilization 

result in the decelerated regime. Complementary, we present strong numerical evidence for the sharpness of this result, implying that stabilization fails for any slower expanding spacetime.

This talk is based on joint work with M. Maliborski, M. Ofner, T. Oliynyk and Z. Wyatt.