The wave equation near flat Friedmann-Lema\^itre-Robertson-Walker and
  Kasner Big Bang singularities
  We consider the wave equation, $\square_g\psi=0$, in fixed flat
Friedmann-Lema\^itre-Robertson-Walker and Kasner spacetimes with topology
$\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for
solutions to the wave equation towards the Big Bang singularity in both
backgrounds. In particular, we characterize open sets of initial data
prescribed at a spacelike hypersurface close to the singularity, which give
rise to solutions that blow up in an open set of the Big Bang hypersurface
$\{t=0\}$. The initial data sets are characterized by the condition that the
Neumann data should dominate, in an appropriate $L^2$-sense, up to two spatial
derivatives of the Dirichlet data. For these initial configurations, the
$L^2(\mathbb{T}^3)$ norms of the solutions blow up towards the Big Bang
hypersurfaces of FLRW and Kasner with inverse polynomial and logarithmic rates
respectively. Our method is based on deriving suitably weighted energy
estimates in physical space. No symmetries of solutions are assumed.
