Primordial Magnetic Field Limits from Cosmic Microwave Background Bispectrum of Magnetic Passive Scalar Modes

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabatic-like scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \sim 6-9 \times 10^{-16}$, for a magnetic field of $B_0 \sim 3$ nG, assuming a nearly scale-invariant magnetic spectrum . We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \approx -1.4 \times 10^{-16}$. These values are more than $\sim 10^6$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of $B_0 \sim 2$ nG on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on $B_0$ based on the compensated mode bispectrum.Comment: 9 page

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde

Understanding complex magnetic order in disordered cobalt hydroxides through analysis of the local structure

In many ostensibly crystalline materials, unit-cell-based descriptions do not always capture the complete physics of the system due to disruption in long-range order. In the series of cobalt hydroxides studied here, Co(OH)$_{2-x}$(Cl)$_x$(H$_2$O)$_{n}$, magnetic Bragg diffraction reveals a fully compensated N\'eel state, yet the materials show significant and open magnetization loops. A detailed analysis of the local structure defines the aperiodic arrangement of cobalt coordination polyhedra. Representation of the structure as a combination of distinct polyhedral motifs explains the existence of locally uncompensated moments and provides a quantitative agreement with bulk magnetic measurements and magnetic Bragg diffraction

Scalar Field Dark Energy Perturbations and their Scale Dependence

We estimate the amplitude of perturbation in dark energy at different length scales for a quintessence model with an exponential potential. It is shown that on length scales much smaller than hubble radius, perturbation in dark energy is negligible in comparison to that in in dark matter. However, on scales comparable to the hubble radius ($\lambda_{p}>1000\mathrm{Mpc}$) the perturbation in dark energy in general cannot be neglected. As compared to the $\Lambda$CDM model, large scale matter power spectrum is suppressed in a generic quintessence dark energy model. We show that on scales $\lambda_{p} < 1000\mathrm{Mpc}$, this suppression is primarily due to different background evolution compared to $\Lambda$CDM model. However, on much larger scales perturbation in dark energy can effect matter power spectrum significantly. Hence this analysis can act as a discriminator between $\Lambda$CDM model and other generic dark energy models with $w_{de} \neq -1$.Comment: 12 pages, 13 figures, added new section, accepted for publication in Phys. Rev.

Structural and magnetic characterization of the complete delafossite solid solution (CuAlO2){1-x}(CuCrO2){x}

We have prepared the complete delafossite solid solution series between diamagnetic CuAlO2 and the t2g^3 frustrated antiferromagnet CuCrO2. The evolution with composition x in CuAl(1-x)Cr(x)O2 of the crystal structure and magnetic properties has been studied and is reported here. The room-temperature unit cell parameters follow the Vegard law and increase with x as expected. The effective moment is equal to the Cr^3+ spin-only S = 3/2 value throughout the entire solid solution. Theta is negative, indicating that the dominant interactions are antiferromagnetic, and its magnitude increases with Cr substitution. For dilute Cr compositions, J_BB was estimated by mean-field theory to be 2.0 meV. Despite the sizable Theta, long-range antiferromagnetic order does not develop until very large x, and is preceeded by glassy behavior. Data presented here, and that on dilute Al-substitution from Okuda et al., suggest that the reduction in magnetic frustration due to the presence of non-magnetic Al does not have as dominant an effect on magnetism as chemical disorder and dilution of the magnetic exchange. For all samples, the 5 K isothermal magnetization does not saturate in fields up to 5 T and minimal hysteresis is observed. The presence of antiferromagnetic interactions is clearly evident in the sub-Brillouin behavior with a reduced magnetization per Cr atom. An inspection of the scaled Curie plot reveals that significant short-range antiferromagnetic interactions occur in CuCrO2 above its Neel temperature, consistent with its magnetic frustration. Uncompensated short-range interactions are present in the Al-substituted samples and are likely a result of chemical disorder