Comment on "Kinetic decoupling of WIMPs: Analytic expressions"

TL;DR

This paper clarifies the discrepancy between two previous studies on dark matter kinetic decoupling temperatures during early matter-dominated eras, showing that differences arise from comparing different reference temperatures rather than conflicting results.

Contribution

The paper resolves conflicting claims about dark matter decoupling temperatures in early matter-dominated eras by clarifying the comparison methodology used in prior work.

Findings

The disparity is due to different comparison baselines for decoupling temperatures.

Decoupling during an EMDE results in colder dark matter than in radiation domination.

Correct comparison shows consistency between previous results.

Abstract

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. We show that the disparity is due to the fact that VG15 compared $T_\mathrm{kd}$ in an EMDE to the decoupling temperature in a radiation-dominated universe that would result in the same dark matter temperature at late times. Since decoupling during an EMDE leaves the dark matter colder than it would be if it decoupled during radiation domination, this temperature is much higher than $T_\mathrm{kd}$ in a standard thermal history, which is indeed lower than $T_{\mathrm{kd}}$ in an EMDE, as stated by GG08.