Multipole invariants and non-Gaussianity

We propose a framework for separating the information contained in the CMB multipoles, $a_{\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to components of the $n$-point correlation function (power spectrum, bispectrum). We find the invariants' distributions using a mixture of analytical and numerical methods. We also evaluate them for the co-added WMAP first year map

The Multipole Vectors of WMAP, and their frames and invariants

We investigate the Statistical Isotropy and Gaussianity of the CMB fluctuations, using a set of multipole vector functions capable of separating these two issues. In general a multipole is broken into a frame and $2\ell-3$ ordered invariants. The multipole frame is found to be suitably sensitive to galactic cuts. We then apply our method to real WMAP datasets; a coadded masked map, the Internal Linear Combinations map, and Wiener filtered and cleaned maps. Taken as a whole, multipoles in the range $\ell=2-10$ or $\ell=2-20$ show consistency with statistical isotropy, as proved by the Kolmogorov test applied to the frame's Euler angles. This result in {\it not} inconsistent with previous claims for a preferred direction in the sky for $\ell=2,...5$. The multipole invariants also show overall consistency with Gaussianity apart from a few anomalies of limited significance (98%), listed at the end of this paper.Comment: 9 pages. Submitted to MNRA

Template fitting and the large-angle CMB anomalies

We investigate two possible explanations for the large-angle anomalies in the Cosmic Microwave Background (CMB): an intrinsically anisotropic model and an inhomogeneous model. We take as an example of the former a Bianchi model (which leaves a spiral pattern in the sky) and of the latter a background model that already contains a non-linear long-wavelength plane wave (leaving a stripy pattern in the sky). We make use of an adaptation of the ``template'' formalism, previously designed to detect galactic foregrounds, to recognize these patterns and produce confidence levels for their detection. The ``corrected'' maps, from which these patterns have been removed, are free of anomalies, in particular their quadrupole and octupole are not planar and their intensities not low. We stress that although the ``template'' detections are not found to be statistically significant they do correct statistically significant anomalies.Comment: 8 pages. MNRAS submitte

Effects of weak self-interactions in a relativistic plasma on cosmological perturbations

The exact solutions for linear cosmological perturbations which have been obtained for collisionless relativistic matter within thermal field theory are extended to a self-interacting case. The two-loop contributions of scalar $\lambda\phi^4$ theory to the thermal graviton self-energy are evaluated, which give the $O(\lambda)$ corrections in the perturbation equations. The changes are found to be perturbative on scales comparable to or larger than the Hubble horizon, but the determination of the large-time damping behavior of subhorizon perturbations requires a resummation of thermally induced masses.Comment: 11 pages, REVTEX, 4 postscript figures included by epsf.sty - expanded version (more details on the resummation of thermal masses which is required for the late-time damping behaviour

Stochastic Inflation and Replica Field Theory

We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on the shape of the filter that separates long from short wavelength modes. While for filters with infinite support the phenomenon of dimensional reductions is found on large super-horizon scales, filters with compact support return a scale-invariant power spectrum in the infra-red. Features of the power spectrum, induced by the filter, decay within a few e-foldings. Thus the late-time power spectrum is independent of the filter details.Comment: 15 pages, 14 figure

Reconnections of Vortex Loops in the Superfluid Turbulent HeII. Rates of the Breakdown and Fusion processes

Kinetics of merging and breaking down vortex loops is the important part of the whole vortex tangle dynamics. Another part is the motion of individual lines, which obeys the Biot-Savart law in presence of friction force and of applied external velocity fields if any. In the present work we evaluate the coefficients of the reconnection rates $A(l_{1},l_{2},l)$ and $B(l,l_{1},l_{2})$. Quantity $A$ is a number (per unit of time and per unit of volume) of events, when two loops with lengths $l_{1}$and $l_{2}$ collide and form the single loop of length $l=l_{1}+l_{2}$. Quantity $$ describes the rate of events, when the single loop of the length $l$ breaks down into two the daughter loops of lengths $l_{1}$ and $l_{2}$. These quantities ave evaluated as the averaged numbers of zeroes of vector $\mathbf{S}$ connecting two points on the loops of $\xi_{2}$ and $\xi_{1}$ at moment of time $t$. Statistics of the individual loops is taken from the Gaussian model of vortex tangle. PACS-number 67.40Comment: 9 pages, 5 figures, To be submitted to JLT

Fabrication of alignment structures for a fiber resonator by use of deep-ultraviolet lithography

We present a novel method to mount and align an optical-fiber-based resonator on the flat surface of an atom chip with ultrahigh precision. The structures for mounting a pair of fibers, which constitute the fiber resonator, are produced by a spin-coated SU-8 photoresist technique by use of deep-UV lithography. The design and production of the SU-8 structures are discussed. From the measured finesses we calculate the coupling loss of the SU-8 structures acting as a kind of fiber splice to be smaller than 0.013 dB.Comment: 4 pages, 3 figure