Momentum distributions of cosmic relics: Improved analysis

Abstract

We present a framework for solving a coupled set of momentum-dependent Boltzmann equations for the phase space distribution of cosmic relic particles, without resorting to approximations of assuming kinetic equilibrium or neglecting back scattering or elastic interactions. Our framework is amendable to precision numerical computations. To test it, we consider two benchmark models where the momentum-dependence of dark matter distribution function is potentially important: a real singlet scalar extension near the Higgs resonance, and a sterile neutrino dark matter model with a singlet scalar mediator. The singlet scalar example shows that even near sharp resonances the kinetic equilibrium holds well enough to justify the use of integrated momentum-independent Boltzmann equation in preliminary parameter scans. However, the integrated method may underestimate the relic density by up to 40% in extreme cases. In the sterile neutrino dark matter model we studied how the inclusion of previously ignored elastic interactions and processes with initial state sterile neutrinos could affect the non-thermal nature of their resulting distributions. Here the effects turned out to be negligible, proving the robustness of the earlier predictions.

Impact of dark matter self-scattering on its relic abundance

“…Similarly the integrations in 2 → 2 collision terms are treated in Ref. [20], which provides a detailed description of the calculation (although the authors treat the gain and loss terms differently). Also, useful expressions for a specific case f 1 + f 2 → f 3 + f χ can be found in Ref.…”

“…In Ref. [20] a similar model is considered in the context of the impact of non-thermal processes on the DM distribution function. However, it does not include the additional U (1) making the self-scattering processes absent in their case.…”

“…The impact of elastic scatterings between DM and the thermal-bath particles has been studied in recent years both at the level of tracing the evolution of DM temperature, see e.g. [5][6][7][15][16][17][18], alongside the number density in a coupled systems of Boltzmann equations (cBE) for the 0th and the 2nd moments of the distribution function, as well as at the level of numerical solution of the full momentum-dependent Boltzmann equation (fBE) [7,12,19,20]. When comparing these two approaches it was noted [7] that although cBE and fBE give in general consistent results, they can substantially differ in scenarios with strong velocity-dependent annihilations, e.g.…”

Momentum distribution of dark matter produced in inflaton decay: effect of inflaton mediated scatterings

“…For the backward term in Eq. 3.3, we can integrate the momentum p 2 using the momentum conserving delta-function and then parametrize rest of the momenta as follows [32][33][34][35]:…”

“…The Boltzmann equation is then solved using the backward difference formula in 200 bins spanning the momentum range 10 −10 GeV to 10 10 GeV. To solve the Boltzmann equation we have used a suitable differential equation solver from the SciPy library of Python [34,35]. We found that for all the cases considered in this work, the shape of the distribution freezes around T ∼ 100 GeV, and then subsequently redshifts till matter-radiation equality, implying that the scattering processes are no longer active below this bath temperature.…”