  We consider the possibility that the primordial fluctuations (scalar and
tensor) might have been standing waves at their moment of creation, whether or
not they had a quantum origin. We lay down the general conditions for spatial
translational invariance, and isolate the pieces of the most general such
theory that comply with, or break translational symmetry. We find that, in
order to characterize statistically translationally invariant standing waves,
it is essential to consider the correlator $\langle c_0({\mathbf k})
c_0({\mathbf k}')\rangle$ in addition to the better known $\langle c_0({\mathbf
k}) c_0^\dagger({\mathbf k}')\rangle$ (where $c_0({\mathbf k})$ are the complex
amplitudes of travelling waves). We then examine how the standard process of
"squeezing" (responsible for converting travelling waves into standing waves
while the fluctuations are outside the horizon) reacts to being fed primordial
standing waves. For translationally invariant systems only one type of standing
wave, with the correct temporal phase (the "sine wave"), survives squeezing.
Primordial standing waves might therefore be invisible at late times -- or not
-- depending on their phase. Theories with modified dispersion relations behave
differently in this respect, since only standing waves with the opposite
temporal phase survive at late times.
