Comment on "Kinetic decoupling of WIMPs: Analytic expressions"

Understand

Visinelli and Gondolo (2015, hereafter VG15) derived analytic expressions for the evolution of the dark matter temperature in a generic cosmological model.

• They then calculated the dark matter kinetic decoupling temperature $T_{\mathrm{kd}}$ and compared their results to the Gelmini and Gondolo (2008, hereafter GG08) calculation of $T_{\mathrm{kd}}$ in an early matter-dominated era (EMDE), which occurs when the Universe is dominated by either a decaying oscillating scalar field or a semistable massive particle before Big Bang nucleosynthesis.
• VG15 found that dark matter decouples at a lower temperature in an EMDE than it would in a radiation-dominated era, while GG08 found that dark matter decouples at a higher temperature in an EMDE than it would in a radiation-dominated era.
• VG15 attributed this discrepancy to the presence of a matching constant that ensures that the dark matter temperature is continuous during the transition from the EMDE to the subsequent radiation-dominated era and concluded that the GG08 result is incorrect.