Initial conditions for cosmological perturbations
  Penrose proposed that the big bang singularity should be constrained by
requiring that the Weyl curvature vanishes there. The idea behind this past
hypothesis is attractive because it constrains the initial conditions for the
universe in geometric terms and is not confined to a specific early universe
paradigm. However, the precise statement of Penrose's hypothesis is tied to
classical space-times and furthermore restricts only the gravitational degrees
of freedom. These are encapsulated only in the tensor modes of the commonly
used cosmological perturbation theory. Drawing inspiration from the underlying
idea, we propose a quantum generalization of Penrose's hypothesis using the
Planck regime in place of the big bang, and simultaneously incorporating tensor
as well as scalar modes. Initial conditions selected by this generalization
constrain the universe to be as homogeneous and isotropic in the Planck regime
\emph{as permitted by the Heisenberg uncertainty relations}.
