Impact of adiabatic temperature fluctuations on the power spectrum of axion density perturbations

Axions and axion-like particles (ALPs) have gained substantial attention as potential candidates for cold dark matter. The ALP field can exhibit fluctuations stemming from initial conditions. These initial field fluctuations hold the potential to give rise to gravitationally bound configurations known as axion miniclusters (AMC). While this proposition is widely accepted in the post-inflationary Peccei-Quinn symmetry-breaking scenario, uncertainties persist regarding the pre-inflationary scenario, where the effects of the initial field fluctuations may be suppressed by inflation. In this study, we investigate the influence of adiabatic temperature fluctuations of the primordial plasma on the evolution of axion density perturbations and their power spectrum, aiming to explore the possibility of AMC formation in the pre-inflationary scenario. Our analysis reveals that the impact of adiabatic temperature fluctuations becomes significant when $f_{\rm a} / H_{\rm inf} \gtrsim 1.25 \times 10^4$ and surpasses that of quantum fluctuations by up to five orders of magnitude on large scales. This emphasizes the possibility of also forming AMC within the pre-inflationary scenario. Consequently, a detection of AMC would not reliably differentiate between the pre- and post-inflationary origin of axions.