The Maximum B-mode Polarization of the Cosmic Microwave Background from Inhomogeneous Reionization

We compute the B-mode polarization power spectrum of the CMB from an epoch of inhomogeneous reionization, using a simple model in which HII regions are represented by ionized spherical bubbles with a log normal distribution of sizes whose clustering properties are determined by large-scale structure. Both the global ionization fraction and the characteristic radius of HII regions are allowed to be free functions of redshift. Models that would produce substantial contamination to degree scale gravitational wave B-mode measurements have power that is dominated by the shot noise of the bubbles. Rare bubbles of >100 Mpc at z>20 can produce signals that in fact exceed the B-modes from gravitational lensing and are comparable to the maximal allowed signal of gravitational waves (~0.1uK) while still being consistent with global constraints on the total optical depth. Even bubbles down to 20 Mpc at z~15, or 40 Mpc at z~10 can be relevant (0.01uK) once the lensing signal is removed either statistically or directly. However, currently favored theoretical models that have ionization bubbles that only grow to such sizes at the very end of a fairly prompt and late reionization produce signals which are at most at these levels.Comment: 14 pages, 11 figures; published in ApJ; corrected Fig. 4 and updated reference

Notes on two-parameter quantum groups, (I)

A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An operator realization of the positive part is given.Comment: 11 page

On the Three-dimensional Lattice Model

Using the restricted star-triangle relation, it is shown that the $N$-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice proposed by Mangazeev, Sergeev and Stroganov is a particular case of the Bazhanov-Baxter model.Comment: 8 pages, latex, 4 figure

Relativistic description of magnetic moments in nuclei with doubly closed shells plus or minus one nucleon

Using the relativistic point-coupling model with density functional PC-PK1, the magnetic moments of the nuclei $^{207}$Pb, $^{209}$Pb, $^{207}$Tl and $^{209}$Bi with a $jj$ closed-shell core $^{208}$Pb are studied on the basis of relativistic mean field (RMF) theory. The corresponding time-odd fields, the one-pion exchange currents, and the first- and second-order corrections are taken into account. The present relativistic results reproduce the data well. The relative deviation between theory and experiment for these four nuclei is 6.1% for the relativistic calculations and somewhat smaller than the value of 13.2% found in earlier non-relativistic investigations. It turns out that the $\pi$ meson is important for the description of magnetic moments, first by means of one-pion exchange currents and second by the residual interaction provided by the $\pi$ exchange.Comment: 11 pages, 7 figure

Secondary CMB anisotropies in a universe reionized in patches

In a universe reionized in patches, the Doppler effect from Thomson scattering off free electrons generates secondary cosmic microwave background (CMB) anisotropies. For a simple model with small patches and late reionization, we analytically calculate the anisotropy power spectrum. Patchy reionization can, in principle, be the main source of anisotropies on arcminute scales. On larger angular scales, its contribution to the CMB power spectrum is a small fraction of the primary signal and is only barely detectable in the power spectrum with even an ideal, i.e. cosmic variance limited, experiment and an extreme model of reionization. Consequently patchy reionization is unlikely to affect cosmological parameter estimation from the acoustic peaks in the CMB. Its detection on small angles would help determine the ionization history of the universe, in particular the typical size of the ionized region and the duration of the reionization process.Comment: 7 pages, 2 figures, submitted to Ap

Notes on two-parameter quantum groups, (II)

This paper is the sequel to [HP1] to study the deformed structures and representations of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ associated to the finite dimensional simple Lie algebras \mg. An equivalence of the braided tensor categories \O^{r,s} and \O^{q} is explicitly established.Comment: 21 page

Green's function method for single-particle resonant states in relativistic mean field theory

Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a reference, the energies and widths of single-particle resonant states are extracted from the density of states without any ambiguity. As an example, the energies and widths for single-neutron resonant states in $^{120}$Sn are compared with those obtained by the scattering phase-shift method, the analytic continuation in the coupling constant approach, the real stabilization method and the complex scaling method. Excellent agreements are found for the energies and widths of single-neutron resonant states.Comment: 20 pages, 7 figure

Reionization Revisited: Secondary CMB Anisotropies and Polarization

Secondary CMB anisotropies and polarization provide a laboratory to study structure formation in the reionized epoch. We consider the kinetic Sunyaev-Zel'dovich effect from mildly nonlinear large-scale structure and show that it is a natural extension of the perturbative Vishniac effect. If the gas traces the dark matter to overdensities of order 10, as expected from simulations, this effect is at least comparable to the Vishniac effect at arcminute scales. On smaller scales, it may be used to study the thermal history-dependent clustering of the gas. Polarization is generated through Thomson scattering of primordial quadrupole anisotropies, kinetic (second order Doppler) quadrupole anisotropies and intrinsic scattering quadrupole anisotropies. Small scale polarization results from the density and ionization modulation of these sources. These effects generically produce comparable E and B-parity polarization, but of negligible amplitude (0.001-0.01 uK) in adiabatic CDM models. However, the primordial and kinetic quadrupoles are observationally comparable today so that a null detection of B-polarization would set constraints on the evolution and coherence of the velocity field. Conversely, a detection of a cosmological B-polarization even at large angles does not necessarily imply the presence of gravity waves or vorticity. For these calculations, we develop an all-sky generalization of the Limber equation that allows for an arbitrary local angular dependence of the source for both scalar and symmetric trace-free tensor fields on the sky.Comment: 14 pages, 12 figures, minor changes and typo fixes reflect published versio