Rotation of the cosmic microwave background polarization from weak gravitational lensing

When a cosmic microwave background (CMB) photon travels from the surface of last scatter through spacetime metric perturbations, the polarization vector may rotate about its direction of propagation. This gravitational rotation is distinct from, and occurs in addition to, the lensing deflection of the photon trajectory. This rotation can be sourced by linear vector or tensor metric perturbations and is fully coherent with the curl deflection field. Therefore, lensing corrections to the CMB polarization power spectra as well as the temperature-polarization cross-correlations due to non-scalar perturbations are modified. The rotation does not affect lensing by linear scalar perturbations, but needs to be included when calculations go to higher orders. We present complete results for weak lensing of the full-sky CMB power spectra by general linear metric perturbations, taking into account both deflection of the photon trajectory and rotation of the polarization. For the case of lensing by gravitational waves, we show that the B modes induced by the rotation largely cancel those induced by the curl component of deflection.Comment: 5 pages, 3 figures, revised to match the version appeared in PR

Multimessenger Parameter Estimation of GW170817

We combine gravitational wave (GW) and electromagnetic (EM) data to perform a Bayesian parameter estimation of the binary neutron star (NS) merger GW170817. The EM likelihood is constructed from a fit to a large number of numerical relativity simulations which we combine with a lower bound on the mass of the remnant's accretion disk inferred from the modeling of the EM light curve. In comparison with previous works, our analysis yields a more precise determination of the tidal deformability of the binary, for which the EM data provide a lower bound, and of the mass ratio of the binary, with the EM data favoring a smaller mass asymmetry. The 90\% credible interval for the areal radius of a $1.4\ M_\odot$ NS is found to be $12.2^{+1.0}_{-0.8} \pm 0.2\ {\rm km}$ (statistical and systematic uncertainties).Comment: 7 pages, 3 figures, accepted to the EPJA Topical Issue: The first Neutron Star Merger Observation - Implications for Nuclear Physic

On the exponential convergence of the Kaczmarz algorithm

The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a way that its solution path can be interpreted as the output from a particular dynamical system. The asymptotic stability results of the corresponding dynamical system can then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds