Constraints on light Dark Matter fermions from relic density consideration and Tsallis statistics

Abstract

The cold dark matter fermions with mass MeV scale, pair produced inside the supernova SN1987A core, can freely stream away from the supernovae and hence contributes to its energy loss rate. Similar type of DM fermions(having similar kind of coupling to the standard model photon), produced from some other sources earlier, could have contributed to the relic density of the Universe. Working in a theory with an effective dark matterphoton coupling (inversely proportional to the scale Λ) in the formalism of Tsallis statistics, we find the dark matter contribution to the relic density and obtain a upper bound on Λ using the experimental bound on the relic density for cold non-baryonic matter i.e. Ωh 2 = 0.1186 ± 0.0020. The upper bound obtained from the relic density is shown with the lower bound obtained from the Raffelt's criterion on the emissibity rate of the supernovae SN1987A energy lossε(e + e − → χχ) ≤ 10 19 erg g −1 s −1 and the optical depth criteria on the free streaming of the dark matter fermion (produced inside the supernovae core). As the deformation parameter q changes from 1.0 (undeformed scenario) to 1.1(deformed scenario), the relic density bound on Λ is found to vary from ∼ 4.9 × 10 7 TeV to 1.6 × 10 8 TeV for a fermion dark matter(χ) of mass m χ = 30 MeV, which is almost 10 times more than the lower bound obtained from the SN1987A energy loss rate and the optical depth criteria.

Model-independent astrophysical constraints on leptophilic Dark Matter in the framework of Tsallis statistics

“…(3.5) to the observed value of non-baryonic, cold DM density Ω obs CDM h 2 = 0.1186 ± 0.0020 [6], we derive the relic density constraint on the effective cut-off scale Λ as a function of the DM mass m χ in section 5. The q-dependence of the relic density constraint [89] comes from the thermal averaging, as well as due to the total effective degrees of freedom g * which depends on the temperature T and the deformation parameter q. See appendix B for a detailed discussion on g * (T ) in the q-deformed scenario.…”

Solutions of q-deformed multiple-trapping model (MTM) for charge carrier transport from time-of-flight transient (TOF) photo-current in amorphous semiconductors

“…Finally, an important point can be made about the parameter of deformation q which is the central quantity of qcalculus formalism: According to the recent works [30][31][32][33], this parameter can play a role of fitting the experimental results. To better understand this, we can mention the work of Guha and Prasanta [34]: the authors have applied the theory of q-deformed (Tsallis statistics) to describe specific heat of solid by using the Einsteins model which is well-known in the theory of physics solid state. As we know, in the ordinary physics of solid state, the Einstein model of the solid predicts the heat capacity accurately at high temperatures which is equivalent to Dulong-Petit law.…”