Quasicrystalline Inflation: From the Cosmological Dipole to Primordial Diffraction

We propose quasicrystalline inflation. Six quasiperiodic phases decompose into three phonons and three phasons. It turns out that a coherent pure-phason displacement can generate a local power dipole while the linear traceless quadrupole vanishes. From spatially varying quadratic effective field theory, we derive off-diagonal correlations whose momentum transfer is restricted to integer combinations of the six icosahedral wavevectors. These correlated off-diagonal signals provide a characteristic observational signature of primordial quasiperiodic order, primordial diffraction.