Relic density and CMB constraints on dark matter annihilation with Sommerfeld enhancement

We calculate how the relic density of dark matter particles is altered when their annihilation is enhanced by the Sommerfeld mechanism due to a Yukawa interaction between the annihilating particles. Maintaining a dark matter abundance consistent with current observational bounds requires the normalization of the s-wave annihilation cross section to be decreased compared to a model without enhancement. The level of suppression depends on the specific parameters of the particle model, with the kinetic decoupling temperature having the most effect. We find that the cross section can be reduced by as much as an order of magnitude for extreme cases. We also compute the mu-type distortion of the CMB energy spectrum caused by energy injection from such Sommerfeld-enhanced annihilation. Our results indicate that in the vicinity of resonances, associated with bound states, distortions can be large enough to be excluded by the upper limit |mu|<9.0x10^(-5) found by the COBE/FIRAS experiment.Comment: 10 pages, 6 figures, accepted for publication in Physical Review D. Corrections to eqs. 9,10,14 and 16. Figures updated accordingly. No major changes to previous results. Website with online tools for Sommerfeld-related calculations can be found at http://www.mpa-garching.mpg.de/~vogelsma/sommerfeld

A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems

We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme