(Non-)Thermal Production of WIMPs during Kination
Abstract
:1. Introduction
2. Boltzmann Equations for the Model
3. Production of WIMPs during Kination
- Thermal production with chemical equilibrium (“freeze-out”). We first focus on the case , corresponding to the negligible decay with respect to the annihilation into SM particles and approximated by the red dot-dashed and blue solid lines in Figure 2. We assume that the temperature is lower than the freeze-out temperature , which is defined as the temperature at which , orHowever, in modified cosmologies where the expansion rate is faster than during radiation (such as kination), WIMP annihilation persists even after the departure from chemical equilibrium (i.e., freeze-out) has occurred, actually ceasing when the Universe transitions to the standard radiation-dominated scenario [78]. For this reason, the WIMP number density in the kination cosmology is not fixed at and annihilation continues until the temperature drops to . We assume that the freeze-out is reached at , when . At later times, using the approximation in Equation (18) and the non-relativistic regime for the WIMPs, Equation (13) reads
- Thermal production without ever reaching chemical equilibrium (“freeze-in”). If the cross section is sufficiently low [77], WIMPs never reach thermal equilibrium and their number density freezes in at a fixed quantity. Since the number density of particles is always smaller than their value at thermal equilibrium, we neglect so Equation (13) with readsThe solution to Equation (25) reaches the asymptotic value of X at freeze-inThe solution describes, for example, the lines with positive slopes in Figure 2, for and the cross sections GeV, GeV, and GeV.
- Non-thermal production without chemical equilibrium. We now discuss the non-thermal production of DM, in the case in which the particle has never reached the chemical equilibrium. For a sufficiently large branching ratio b and for , the abundance of DM is set by the decay of the field, with an energy density at given by [53,55,58,61,63,81]Deriving the result from directly integrating Equation (13) with and neglecting the contributions from R and X in the denominator gives an extra logarithmic dependence on , as
- Non-thermal production with chemical equilibrium. If the branching ratio b is sufficiently high, the evolution of the WIMP number density attains a secular equilibrium in which the rate at which WIMPs are produced from the decay of the field equates that from WIMP annihilation. In this regime, the quantity X is fixed to the value obtained by setting to zero the right-hand side of Equation (13),The result in Equation (32), confirmed numerically in Figure 3 below, can be alternatively derived by considering the balancing between the decay rate of the field into WIMPs and the annihilation rate of WIMPs, valid at when , asThe value of remains constant until , without experiencing the additional depletion obtained in the freeze-out regime with a faster-than-radiation expansion rate [77,78]. However, when the temperature of the plasma falls below , the secular equilibrium is no longer maintained since the energy density in the field drops to zero and WIMPs are no longer produced. In this new regime, radiation evolves as and Equation (13) reads
4. Discussion and Summary
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
DM | Dark Matter |
BBN | Big Bang Nucleosynthesis |
WIMP | Weakly Interacting Massive Particle |
LRTS | Low Reheat Temperature Scenario |
KS | Kination Scenario |
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Visinelli, L. (Non-)Thermal Production of WIMPs during Kination. Symmetry 2018, 10, 546. https://doi.org/10.3390/sym10110546
Visinelli L. (Non-)Thermal Production of WIMPs during Kination. Symmetry. 2018; 10(11):546. https://doi.org/10.3390/sym10110546
Chicago/Turabian StyleVisinelli, Luca. 2018. "(Non-)Thermal Production of WIMPs during Kination" Symmetry 10, no. 11: 546. https://doi.org/10.3390/sym10110546