Improved Constraints on Dark Matter Annihilations Around Primordial Black Holes

Cosmology may give rise to appreciable populations of both particle dark matter and primordial black holes (PBH) with the combined mass density providing the observationally inferred value $\Omega_{\rm DM}\approx0.26$. However, previous studies have highlighted that scenarios with both particle dark matter and PBH are strongly excluded by $\gamma$-ray limits for particle dark matter with a velocity independent thermal cross section $\langle\sigma v\rangle\sim3\times10^{-26}{\rm cm}^3/{\rm s}$, as is the case for classic WIMP dark matter. Here we extend these existing studies on $s$-wave annihilating particle dark matter to ascertain the limits from diffuse $\gamma$-rays on velocity dependent annihilations which are $p$-wave with $\langle\sigma v \rangle\propto v^2$ or $d$-wave with $\langle\sigma v \rangle\propto v^4$, which we find to be considerably less constraining. Furthermore, we highlight that even if the freeze-out process is $p$-wave it is relatively common for (loop/phase-space) suppressed $s$-wave processes to actually provide the leading contributions to the experimentally constrained $\gamma$-ray flux from the PBH halo. This work also utilyses a refined treatment of the PBH dark matter density profile and outlines an improved application of extra-galactic $\gamma$-ray bounds.Comment: 37 pages, 11 Figure

Flooded Dark Matter and S level rise

Most dark matter models set the dark matter relic density by some interaction with Standard Model particles. Such models generally assume the existence of Standard Model particles early on, with the dark matter relic density a later consequence of those interactions. Perhaps a more compelling assumption is that dark matter is not part of the Standard Model sector and a population of dark matter too is generated at the end of inflation. This democratic assumption about initial conditions does not necessarily provide a natural value for the dark matter relic density, and furthermore superficially leads to too much entropy in the dark sector relative to ordinary matter. We address the latter issue by the late decay of heavy particles produced at early times, thereby associating the dark matter relic density with the lifetime of a long-lived state. This paper investigates what it would take for this scenario to be compatible with observations in what we call Flooded Dark Matter (FDM) models and discusses several interesting consequences. One is that dark matter can be very light and furthermore, light dark matter is in some sense the most natural scenario in FDM as it is compatible with larger couplings of the decaying particle. A related consequence is that the decay of the field with the smallest coupling and hence the longest lifetime dominates the entropy and possibly the matter content of the Universe, a principle we refer to as “Maximum Baroqueness”. We also demonstrate that the dark sector should be colder than the ordinary sector, relaxing the most stringent free-streaming constraints on light dark matter candidates. We will discuss the potential implications for the core-cusp problem in a follow-up paper. The FDM framework will furthermore have interesting baryogenesis implications. One possibility is that dark matter is like the baryon asymmetry and both are simultaneously diluted by a late entropy dump. Alternatively, FDM is compatible with an elegant non-thermal leptogenesis implementation in which decays of a heavy right-handed neutrino lead to late time reheating of the Standard Model degrees of freedom and provide suitable conditions for creation of a lepton asymmetry.Physic

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page