Warm dark matter does not do better than cold dark matter in solving small-scale inconsistencies

Over the last decade, warm dark matter (WDM) has been repeatedly proposed as an alternative scenario to the standard cold dark matter (CDM) one, potentially resolving several disagreements between the CDM model and observations on small scales. Here, we reconsider the most important CDM small-scale discrepancies in the light of recent observational constraints on WDM. As a result, we find that a conventional thermal (or thermal-like) WDM cosmology with a particle mass in agreement with Lyman-$\alpha$ is nearly indistinguishable from CDM on the relevant scales and therefore fails to alleviate any of the small-scale problems. The reason for this failure is that the power spectrum of conventional WDM falls off too rapidly. To maintain WDM as a significantly different alternative to CDM, more evolved production mechanisms leading to multiple dark matter components or a gradually decreasing small-scale power spectrum have to be considered.
Comment: Typo corrected in Eq 1. Does not affect any results