A new study has demonstrated the linear stability of Kasner spacetimes in the direction of the Big Bang. This finding is significant because Kasner spacetimes are cosmological solutions that describe the early universe, near the initial singularity, and are expected to be highly unstable. The research identifies an explicit finite-dimensional space of non-decaying self-similar solutions that define this stability, providing a complete description of the instability at a linear level without imposing symmetry assumptions.

The work addresses the expectation that quiescent (as opposed to oscillatory) vacuum Big Bang spacetimes in four dimensions, which are asymptotic to a Kasner spacetime from the perspective of a single observer at the Big Bang, should be extremely unstable due to oscillations conjectured by Belinski, Khalatnikov, and Lifshitz (BKL). The fastest growing solution identified in this study is the linearization of Taub's explicit Bianchi II solution, which describes a Kasner transition. All other non-decaying solutions are inhomogeneous analogues of this, and the linearized Kasner metric.

A key novelty of this research is the introduction of a notion of quasinormal modes on Kasner spacetimes. This idea is similar to the quasinormal modes used to describe perturbations in stationary black hole spacetimes. The application of this concept to Kasner spacetimes allows for a deeper understanding of how perturbations behave and evolve in the extreme environment of the early universe, providing a crucial analytical tool for the study of the cosmological singularity.