Title
Stability of cosmological spacetimes undergoing decelerated expansion
Abstract
In this talk I will discuss recent work on the stability problem for cosmological solutions to the Einstein equations undergoing decelerated expansion. One mechanism by which decelerated expansion occurs in general relativity is by coupling the Einstein equations to a nonlinear scalar field with an exponential potential. This system admits Friedmann Lemaitre-Robertson-Walker (FLRW) solutions with compact spatial topology and power-law scale factor a(t) = t^p. Previous stability results have been obtained for such spacetimes when the expansion is accelerated, but the slowly expanding regime remains poorly understood. I will present a new result which establishes future-stability of these FLRW solutions with expansion exponent 2/3 < p < 1, as solutions to the Einstein-nonlinear scalar field system. I will then discuss the key ideas behind the proof of this statement, as well as the long-time dynamics of the perturbed solutions.
Please note that the seminar will take place in person in room 140 of Huxley Building.