Constraining FIMP from the structure formation of the Universe: analytic mapping from m(WDM)

A feebly interacting massive particle (FIMP), contrasting with a weakly interacting massive particle (WIMP), is an intriguing dark matter (DM) candidate. Light (keV-scale) FIMP DM is of particular interest: its radiative decay leaves a line signal in x-ray spectra; and it is warm dark matter (WDM) and alters the galactic-scale structure formation of the Universe from that with WIMP DM. Once a possible x-ray line is reported (e.g., 3.5 keV line infers 7 keV FIMP DM), one has to check whether or not this FIMP DM is compatible with the structure formation. Here is an issue: the structure formation constraint on WDM is often reported in terms of the so-called thermal WDM mass mWDM, which cannot be directly applied to FIMP parameters. In this paper, we introduce a benchmark FIMP model that represents well a broad class of FIMP models. A big advantage of this benchmark is that we can derive the analytic formula of the non-thermal phase space distribution of FIMPs produced from freeze-in processes. By further deriving a certain "warmness" quantity, we can analytically map mWDM to FIMP parameters. Our analytic map indicates that 7 keV FIMP DM, without entropy production or a degenerate spectrum, is in tension with the latest Lyman-alpha forest data. Our analytic map will be very useful for future updates of observational constraints and reports of x-ray lines. It is also very easy to incorporate our analytic formula into a Boltzmann solver so that a linear matter power spectrum is readily accessible. Our benchmark model will facilitate FIMP searches and particle physics model-building. c. 2019 IOP Publishing Ltd and Sissa Medialab11Nsciescopu