Misaligned ALP dark matter and misaligned density fluctuations

We consider the hypothesis that dark matter is provided by an oscillating scalar field which is assumed to be a pseudo-Goldstone boson from global symmetry breaking (axion-like particle, ALP). If symmetry breaking happens after the end of inflation, the field assumes random initial values in causally disconnected regions when it starts oscillating. This leads to large isocurvature dark matter density fluctuations (i.e., misaligned with fluctuations in the other cosmic fluids). We show that this can lead to observable consequences in CMB and large-scale structure observations, which allows us to constrain the ALP parameter space.