Showing papers on "Spectral density published in 2006"

Cosmological parameters from combining the Lyman-alpha forest with CMB, galaxy clustering and SN constraints

Abstract: We combine the Ly-alpha forest power spectrum (LYA) from the Sloan Digital Sky Survey (SDSS) and high resolution spectra with cosmic microwave background (CMB) including 3-year WMAP, and supernovae (SN) and galaxy clustering constraints to derive new constraints on cosmological parameters. The existing LYA power spectrum analysis is supplemented by constraints on the mean flux decrement derived using a principle component analysis for quasar continua, which improves the LYA constraints on the linear power. We find some tension between the WMAP3 and LYA power spectrum amplitudes, at the ~2 sigma level, which is partially alleviated by the inclusion of other observations: we find \sigma_8=0.85\pm 0.02 compared to sigma_8=0.80 \pm 0.03 without LYA. For the slope we find ns=0.965\pm0.012. We find no evidence for the running of the spectral index in the combined analysis, dn/dln k=-(1.5\pm 1.2) x 10^{-2}, in agreement with inflation. The limits on the sum of neutrino masses are significantly improved: $\sum m_{ u} 1.3 (95% c.l.). Assuming a thermalized fourth neutrino we find m_s<0.26\eV at 95% c.l. and such neutrino cannot be an explanation for the LSND results. In the limits of massless neutrinos we obtain the effective number of neutrinos N_ u^{\rm eff}=5.3^{+0.4}_{-0.6}{}^{+2.1}_{-1.7}{}^{+3.8}_{-2.5} and N_ u^{\rm eff}=3.04 is allowed only at 2.4-sigma. The constraint on the dark energy equation of state is w=-1.04\pm 0.06. The constraint on curvature is Omega_k=-0.003\pm 0.006. Cosmic strings limits are G\mu <2.3 x 10^{-7} at 95% c.l. and correlated isocurvature models are also tightly constrained.

Cosmological Parameter Estimation Using 21 cm Radiation from the Epoch of Reionization

Abstract: A number of radio interferometers are currently being planned or constructed to observe 21 cm emission from reionization. Not only will such measurements provide a detailed view of that epoch, but, since the 21 cm emission also traces the distribution of matter in the universe, this signal can be used to constrain cosmological parameters. The sensitivity of an interferometer to the cosmological information in the signal may depend on how precisely the angular dependence of the 21 cm three-dimensional power spectrum can be measured. Using an analytic model for reionization, we quantify all the effects that break the spherical symmetry of the three-dimensional 21 cm power spectrum. We find that upcoming observatories will be sensitive to the 21 cm signal over a wide range of scales, from larger than 100 to as small as 1 comoving Mpc. Next, we consider three methods to measure cosmological parameters from the signal: (1) direct fitting of the density power spectrum to the signal, (2) using only the velocity field fluctuations in the signal, and (3) looking at the signal at large enough scales that all fluctuations trace the density field. With the foremost method, the first generation of 21 cm observations should moderately improve existing constraints on cosmological parameters for certain low-redshift reionization scenarios, and a 2 yr observation with the second-generation interferometer MWA5000 in combination with the CMB telescope Planck could improve constraints on Ω_w, Ω_(m)h^2, Ω_(b)h^2, Ω_ν, n_s, and α_s. If the universe is substantially ionized by z ~ 12 or if spin temperature fluctuations are important, we show that it will be difficult to place competitive constraints on cosmological parameters with any of the considered methods.

Memory of Initial Conditions in Gravitational Clustering

Abstract: We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime. We show that it can be thought as measuring the memory of density and velocity fields to their initial conditions. This provides a clean definition of the validity of linear theory, which is shown to be much more restricted than usually recognized in the literature. We calculate the nonlinear propagator in RPT and compare to measurements in numerical simulations, showing remarkable agreement well into the nonlinear regime. We also show that N-body simulations require a rather large volume to recover the correct propagator, due to the missing large-scale modes. Our results for the nonlinear propagator provide an essential element to compute the nonlinear power spectrum in RPT.

Primordial trispectrum from inflation

Abstract: We use the $\ensuremath{\delta}N$ formalism to describe the leading order contributions to the primordial power spectrum, bispectrum, and trispectrum in multiple-field models of inflation at leading order in a perturbative expansion. In slow-roll models where the initial field fluctuations at Hubble exit are nearly Gaussian, any detectable non-Gaussianity is expected to come from super-Hubble evolution. We show that the contribution to the primordial trispectrum can be described by two nonlinearity parameters, ${\ensuremath{\tau}}_{NL}$ and ${g}_{NL}$, which are dependent upon the second and third derivatives of the local expansion with respect to the field values during inflation.

A Measurement of the Angular Power Spectrum of the CMB Temperature Anisotropy from the 2003 Flight of BOOMERANG

Abstract: We report on observations of the cosmic microwave background (CMB) obtained during the 2003 January flight of BOOMERANG. These results are derived from 195 hr of observation with four 145 GHz polarization-sensitive bolometer (PSB) pairs, identical in design to the four 143 GHz Planck High Frequency Instrument (HFI) polarized pixels. The data include 75 hr of observations distributed over 1.84% of the sky with an additional 120 hr concentrated on the central portion of the field, which represents 0.22% of the full sky. From these data we derive an estimate of the angular power spectrum of temperature fluctuations of the CMB in 24 bands over the multipole range 50 ≤ l ≤ 1500. A series of features, consistent with those expected from acoustic oscillations in the primordial photon-baryon fluid, are clearly evident in the power spectrum, as is the exponential damping of power on scales smaller than the photon mean free path at the epoch of last scattering (l ≳ 900). As a consistency check, the collaboration has performed two fully independent analyses of the time-ordered data, which are found to be in excellent agreement.

Cosmology and the Bispectrum

Abstract: The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in $50{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ spheres, and remarkably little is known about the information encoded in it about cosmological parameters beyond the power spectrum. In this work we present an attempt to bridge this gap by studying the bispectrum, paying particular attention to a joint analysis with the power spectrum and their combination with CMB data. We address the covariance properties of the power spectrum and bispectrum including the effects of beat coupling that lead to interesting cross-correlations, and discuss how baryon acoustic oscillations break degeneracies. We show that the bispectrum has significant information on cosmological parameters well beyond its power in constraining galaxy bias, and when combined with the power spectrum is more complementary than combining power spectra of different samples of galaxies, since non-Gaussianity provides a somewhat different direction in parameter space. In the framework of flat cosmological models we show that most of the improvement of adding bispectrum information corresponds to parameters related to the amplitude and effective spectral index of perturbations, which can be improved by almost a factor of 2. Moreover, we demonstrate that the expected statistical uncertainties in ${\ensuremath{\sigma}}_{8}$ of a few percent are robust to relaxing the dark energy beyond a cosmological constant.

Clustering of dark matter tracers: Renormalizing the bias parameters

Abstract: A commonly used perturbative method for computing large-scale clustering of tracers of mass density, like galaxies, is to model the tracer density field as a Taylor series in the local smoothed mass density fluctuations, possibly adding a stochastic component. I suggest a set of parameter redefinitions, eliminating problematic perturbative correction terms, that should represent a modest improvement, at least, to this method. As presented here, my method can be used to compute the power spectrum and bispectrum to 4th order in initial density perturbations, and higher order extensions should be straightforward. While the model is technically unchanged at this order, just reparametrized, the renormalized model is more elegant, and should have better convergence behavior, for three reasons: First, in the usual approach the effects of beyond-linear-order bias parameters can be seen at asymptotically large scales, while after renormalization the linear model is preserved in the large-scale limit, i.e., the effects of higher order bias parameters are restricted to relatively high k. Second, while the standard approach includes smoothing to suppress large perturbative correction terms, resulting in dependence on the arbitrary cutoff scale, no cutoff-sensitive terms appear explicitly after my redefinitions (and, relatedly, my correction terms are less sensitive to high-k,more » nonlinear, power). Third, the 3rd order bias parameter disappears entirely, so my model has one fewer free parameter than usual (this parameter was redundant at the order considered). This model predicts no significant modification of the baryonic acoustic oscillation (BAO) signal, in real space, supporting the robustness of BAO as a probe of dark energy, and providing a complete perturbative description over the relevant range of scales.« less

Searching for CPT violation with cosmic microwave background data from WMAP and BOOMERANG.

Abstract: We search for signatures of Lorentz and $CPT$ violations in the cosmic microwave background (CMB) temperature and polarization anisotropies by using the Wilkinson Microwave Anisotropy Probe (WMAP) and the 2003 flight of BOOMERANG (B03) data. We note that if the Lorentz and $CPT$ symmetries are broken by a Chern-Simons term in the effective Lagrangian, which couples the dual electromagnetic field strength tensor to an external four-vector, the polarization vectors of propagating CMB photons will get rotated. Using the WMAP data alone, one could put an interesting constraint on the size of such a term. Combined with the B03 data, we found that a nonzero rotation angle of the photons is mildly favored: $\ensuremath{\Delta}\ensuremath{\alpha}=\ensuremath{-}6.0\genfrac{}{}{0}{}{+4.0}{\ensuremath{-}4.0}\genfrac{}{}{0}{}{+3.9}{\ensuremath{-}3.7}\text{ }\text{ }\mathrm{deg} (1,2\ensuremath{\sigma})$.

A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey

Abstract: We report on a measurement of the quadrupole power spectrum in the two degree field (2dF) QSO redshift (2QZ) survey. The analysis used an algorithm parallel to that for estimating the standard monopole power spectrum without first requiring computation of the correlation function or the anisotropic power spectrum. The error on the quadrupole spectrum was rather large, but the best-fit value of the bias parameter from the quadrupole spectrum is consistent with that from previous investigations of the 2dF data.

Cosmological and astrophysical parameters from the Sloan Digital Sky Survey flux power spectrum and hydrodynamical simulations of the Lyman α forest

Abstract: The flux power spectrum of the Lyman a forest in quasar [quasi-stellar object (QSO)] absorption spectra is sensitive to a wide range of cosmological and astrophysical parameters and instrumental effects. Modelling the flux power spectrum in this large parameter space to an accuracy comparable to the statistical uncertainty of large samples of QSO spectra is very challenging. We use here a coarse grid of hydrodynamical simulations run with GADGET-2 to obtain a 'best-guess' model around which we calculate a finer grid of flux power spectra using a Taylor expansion of the flux power spectrum to first order. In this way, we investigate how the interplay between astrophysical and cosmological parameters affects their measurements using the recently published flux power spectrum obtained from 3035 Sloan Digital Sky Survey (SDSS) QSOs. We find that the SDSS flux power spectrum alone is able to constrain a wide range of parameters including the amplitude of the matter power spectrum σ 8 , the matter density Ω m , the spectral index of primordial density fluctuations n, the effective optical depth τ eff and its evolution. The thermal history of the intergalactic medium (IGM) is, however, poorly constrained and the SDSS data favour either an unplausibly large temperature or an unplausibly steep temperature-density relation. By enforcing a thermal history of the IGM consistent with that inferred from high-resolution QSO spectra, we find the following values for the best-fitting model (assuming a flat universe with a cosmological constant and zero neutrino mass): Ω m = 0.28 ± 0.03, n = 0.95 ± 0.04 and σ 8 = 0.91 ± 0.07 (1σ error bars). The values for a 8 and n are consistent with those obtained by McDonald et al. with different simulations for similar assumptions. We argue, however, that the major uncertainties in this measurement are still systematic rather than statistical.

Usage of wavelet transform in the protection of series-compensated transmission lines

Abstract: This paper presents a new method for the boundary protection of series-compensated transmission lines, as well as fault classification. The boundary protection is based on detecting distinct frequency bands contained in the transient fault current wave. Discrete wavelet transform, using db4 as a mother wavelet, is used to capture two bands of frequencies in the transient current signal. The spectral energies of these two bands are obtained and used to determine if the fault is internal or external to the protected zone. Fault classification is done using the discrete wavelet transform. Using Haar as the mother wavelet, the coefficients of a frequency band in the range of 1 kHz-3 kHz are obtained for the three phase and ground currents. The average value of the coefficients of each current wave is then computed and used to classify the faulted phases. The basic principle of the protection scheme is described and its response to the series-compensated transmission lines is studied for a wide range of compensation levels, fault conditions, fault types, and fault locations. The stability of the algorithm under various load switching cases is also tested. Fault simulations are performed using power system computer-aided design/electromagnetic transient and direct current program and the results are then interfaced to MATLAB, where the algorithm is implemented. It is found that the proposed method gives reliable results in the boundary protection and fault classification of series-compensated lines.

Finite temperature spectral densities of momentum and R -charge correlators in N = 4 Yang-Mills theory

Abstract: We compute spectral densities of momentum and $R$-charge correlators in thermal $\mathcal{N}=4$ Yang-Mills theory at strong coupling. For $\ensuremath{\omega}\ensuremath{\sim}T$ and smaller, the spectral density differs markedly from perturbation theory; there is no kinetic theory peak. For large $\ensuremath{\omega}$, the spectral density oscillates around the zero temperature result with an exponentially decreasing amplitude. Contrast this with QCD where the spectral density of the current-current correlator approaches the zero temperature result like $(T/\ensuremath{\omega}{)}^{4}$. This difference is related to the absence of cuts in the retarded Green function in $\mathcal{N}=4$ Yang-Mills theory at strong coupling. Despite these marked differences with perturbation theory, in Euclidean space-time the correlators differ by only $\ensuremath{\sim}10%$ from the free result. The implications for lattice QCD measurements of transport are discussed.

The intracluster magnetic field power spectrum in Abell 2255

Abstract: Aims. The goal of this work is to investigate the power spectrum of the magnetic field associated with the giant radio halo in the galaxy cluster A665. Methods. For this, we present new deep Very Large Array total intensity and polarization observations at 1.4 GHz. We simulated Gaussian random three-dimensional turbulent magnetic field models to reproduce the observed radio halo emission. By comparing observed and synthetic radio halo images we constrained the strength and structure of the intracluster magnetic field. We assumed that the magnetic field power spectrum is a power law with a Kolmogorov index and we imposed a local equipartition of energy density between relativistic particles and field. Results. Under these assumptions, we find that the radio halo emission in A665 is consistent with a central magnetic field strength of about 1.3 μG. To explain the azimuthally averaged radio brightness profile, the magnetic field energy density should decrease following the thermal gas density, leading to an averaged magnetic field strength over the central 1 Mpc 3 of about 0.75 μG. From the observed brightness fluctuations of the radio halo, we infer that the outer scale of the magnetic field power spectrum is ∼450 kpc, and the corresponding magnetic field auto-correlation length is ∼100 kpc.

Acoustic oscillations in the SDSS DR4 luminous red galaxy sample power spectrum

Abstract: We calculate the redshift-space power spectrum of the Sloan Digital Sky Survey (SDSS) Data Release 4 (DR4) Luminous Red Galaxy (LRG) sample, finding evidence for a full series of acoustic features down to the scales of ~$0.2\,h\,{\rm Mpc}^{-1}$. This corresponds to the 7th peak in the CMB angular power spectrum. The acoustic scale derived, $(105.4 \pm 2.3)\,h^{-1}\,{\rm Mpc}$, agrees very well with the “concordance” model prediction and also with the one determined via the analysis of the spatial two-point correlation function by Eisenstein et al. (2005, ApJ, 633, 560). The models with baryonic features are favored by $3.3 \sigma$ over their “smoothed” counterparts without any oscillatory behavior. This is not only an independent confirmation of results by Eisenstein et al. (2005), made with different methods and software but also, to our knowledge, is the first determination of the power spectrum of the SDSS LRG sample.

Probing neutrino masses with CMB lensing extraction

Abstract: We evaluate the ability of future cosmic microwave background (CMB) experiments to measure the power spectrum of large scale structure using quadratic estimators of the weak lensing deflection field. We calculate the sensitivity of upcoming CMB experiments such as BICEP, QUaD, BRAIN, ClOVER and Planck to the nonzero total neutrino mass ${M}_{\ensuremath{ u}}$ indicated by current neutrino oscillation data. We find that these experiments greatly benefit from lensing extraction techniques, improving their one-sigma sensitivity to ${M}_{\ensuremath{ u}}$ by a factor of order four. The combination of data from Planck and the SAMPAN mini-satellite project would lead to $\ensuremath{\sigma}({M}_{\ensuremath{ u}})\ensuremath{\sim}0.1$ eV, while a value as small as $\ensuremath{\sigma}({M}_{\ensuremath{ u}})\ensuremath{\sim}0.035$ eV is within the reach of a space mission based on bolometers with a passively cooled 3\char21{}4 m aperture telescope, representative of the most ambitious projects currently under investigation. We show that our results are robust not only considering possible difficulties in subtracting astrophysical foregrounds from the primary CMB signal but also when the minimal cosmological model ($\ensuremath{\Lambda}$ Mixed Dark Matter) is generalized in order to include a possible scalar tilt running, a constant equation-of-state parameter for the dark energy and/or extra relativistic degrees of freedom.

On measuring the covariance matrix of the non-linear power spectrum from simulations

Abstract: We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in power spectra between different weightings. We recommend a specific set of 52 weightings containing only combinations of fundamental modes, constructed to yield a minimum variance estimate of the covariance of power. Numerical tests reveal that at non-linear scales the variance of power estimated by the weightings method substantially exceeds that estimated from a simple ensemble method. We argue that the discrepancy is caused by beat-coupling, in which products of closely spaced Fourier modes couple by non-linear gravitational growth to the beat mode between them. Beat-coupling appears whenever non-linear power is measured from Fourier modes with a finite spread of wavevector, and is therefore present in the weightings method but not in the ensemble method. Beat-coupling inevitably affects real galaxy surveys, whose Fourier modes have finite width. Surprisingly, the beat-coupling contribution dominates the covariance of power at non-linear scales, so that, counter-intuitively, it is expected that the covariance of non-linear power in galaxy surveys is dominated not by small-scale structure, but rather by beat-coupling to the largest scales of the survey.

The power spectrum of supersonic turbulence in perseus

Abstract: We test a method of estimating the power spectrum of turbulence in molecular clouds based on the comparison of power spectra of integrated intensity maps and single-velocity-channel maps, suggested by A. Lazarian and D. Pogosyan. We use synthetic 13CO data from non-LTE radiative transfer calculations based on density and velocity fields of a simulation of supersonic hydrodynamic turbulence. We find that the method yields the correct power spectrum with good accuracy. We then apply the method to the Five College Radio Astronomy Observatory 13CO map of the Perseus region, from the COMPLETE Web site. We find a power-law power spectrum with slope β = 1.81 ± 0.10. The values of β as a function of velocity resolution are also confirmed using the lower resolution map of the same region obtained with the AT&T Bell Laboratories antenna. Because of its small uncertainty, this result provides a useful constraint for numerical codes used to simulate molecular cloud turbulence.

Cosmology with high-redshift galaxy survey: Neutrino mass and inflation

Abstract: High-$z$ galaxy redshift surveys open up exciting possibilities for precision determinations of neutrino masses and inflationary models. The high-$z$ surveys are more useful for cosmology than low-$z$ ones owing to much weaker nonlinearities in matter clustering, redshift-space distortion, and galaxy bias, which allows us to use the galaxy power spectrum down to the smaller spatial scales that are inaccessible by low-$z$ surveys. We can then utilize the two-dimensional information of the linear power spectrum in angular and redshift space to measure the scale-dependent suppression of matter clustering due to neutrino free-streaming as well as the shape of the primordial power spectrum. To illustrate capabilities of high-$z$ surveys for constraining neutrino masses and the primordial power spectrum, we compare three future redshift surveys covering 300 square degrees at $0.5lzl2$, $2lzl4$, and $3.5lzl6.5$. We find that, combined with the cosmic microwave background data expected from the Planck satellite, these surveys allow precision determination of the total neutrino mass with the projected errors of $\ensuremath{\sigma}({m}_{\ensuremath{ u},\mathrm{tot}})=0.059$, 0.043, and 0.025 eV, respectively, thus yielding a positive detection of the neutrino mass rather than an upper limit, as $\ensuremath{\sigma}({m}_{\ensuremath{ u},\mathrm{tot}})$ is smaller than the lower limits to the neutrino masses implied from the neutrino oscillation experiments, by up to a factor of 4 for the highest redshift survey. The accuracies of constraining the tilt and running index of the primordial power spectrum, $\ensuremath{\sigma}({n}_{s})=(3.8,3.7,3.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\ensuremath{\sigma}({\ensuremath{\alpha}}_{s})=(5.9,5.7,2.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at ${k}_{0}=0.05\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, respectively, are smaller than the current uncertainties by more than an order of magnitude, which will allow us to discriminate between candidate inflationary models. In particular, the error on ${\ensuremath{\alpha}}_{s}$ from the future highest redshift survey is not very far away from the prediction of a class of simple inflationary models driven by a massive scalar field with self-coupling, ${\ensuremath{\alpha}}_{s}=\ensuremath{-}(0.8\char21{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

Prospects for direct detection of primordial gravitational waves

Abstract: We study the primordial gravitational wave background produced in models of single-field inflation. Using the inflationary flow approach, we investigate the amplitude of gravitational wave spectrum, {omega}{sub gw}, in the frequency range 1 mHz-1 Hz pertinent to future space-based laser interferometers. For models that satisfy the current observational constraint on the tensor-to-scalar ratio, r < or approx. 0.36, we derive a strict upper bound of {omega}{sub gw} < or approx. 1.6x10{sup -15} independent of the form of the inflationary potential. Applying, in addition, the observational constraints on the spectral index n{sub s} and its running, {omega}{sub gw} is expected to be considerably lower than this bound unless the shape of the potential is finely tuned. We contrast our numerical results with those based on simple power-law extrapolation of the tensor power spectrum from cosmic microwave background (CMB) scales. In addition to single-field inflation, we summarize a number of other possible cosmological sources of primordial gravitational waves and assess what might be learned from direct detection experiments such as LISA, Big Bang Observer and beyond.

Characterizing the galactic gravitational wave background with LISA

Abstract: We present a Monte Carlo simulation for the response of the Laser Interferometer Space Antenna (LISA) to the galactic gravitational wave background. The simulated data streams are used to estimate the number and type of binary systems that will be individually resolved in a 1-year power spectrum. We find that the background is highly non-Gaussian due to the presence of individual bright sources but, once these sources are identified and removed, the remaining signal is Gaussian. We also present a new estimate of the confusion noise caused by unresolved sources that improves on earlier estimates.

Black hole mass of the ultraluminous X-ray source M82 X-1

Abstract: We report the first clear evidence for the simultaneous presence of a low-frequency break and a QPO in the fluctuation power spectrum of a well-known ultraluminous X-ray source (ULX) in M82 using long XMM-Newton observations. The break occurs at a frequency of 34.2 mHz. The QPO has a centroid at νQPO = 114.3 ± 1.5 mHz, a coherence Q ≡ νQPO/ΔνFWHM 3.5, and an amplitude (rms) of 19% in the 2-10 keV band. The power spectrum is approximately flat below the break frequency and then falls off above the break frequency as a power law with the QPO superposed. This form of the power spectrum is characteristic of the Galactic X-ray binaries (XRBs) in their high or intermediate states. M82 X-1 was likely in an intermediate state during the observation. The EPIC pn spectrum is well described by a model comprising an absorbed power law (Γ ~ 2) and an iron line at ~6.6 keV with a width σ ~ 0.2 keV and an equivalent width of ~180 eV. Using the well-established correlations between the power and energy spectral parameters for XRBs, we estimate a black hole mass for M82 X-1 in the range of ~25-520 M☉, including systematic errors that arise due to the uncertainty in the calibration of the photon spectral index versus QPO frequency relation.

Cmb multipole measurements in the presence of foregrounds

Abstract: Most analysis of cosmic microwave background spherical harmonic coefficients ${a}_{\ensuremath{\ell}m}$ has focused on estimating the power spectrum ${C}_{\ensuremath{\ell}}=⟨|{a}_{\ensuremath{\ell}m}{|}^{2}⟩$ rather than the coefficients themselves. We present a minimum-variance method for measuring ${a}_{\ensuremath{\ell}m}$ given anisotropic noise, incomplete sky coverage and foreground contamination, and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) data. Our method is shown to constitute lossless data compression in the sense that the widely used quadratic estimators of the power spectrum ${C}_{\ensuremath{\ell}}$ can be computed directly from our ${a}_{\ensuremath{\ell}m}$-estimators. As the Galactic cut is increased, the error bars $\ensuremath{\Delta}{a}_{\ensuremath{\ell}m}$ on low multipoles go from being dominated by foregrounds to being dominated by leakage from other multipoles, with the intervening minimum defining the optimal cut. Applying our method to the WMAP quadrupole and octopole as an illustration, we investigate the robustness of the previously reported ``axis of evil'' alignment to Galactic cut and foreground contamination.

Constraints on Supersymmetric Models of Hybrid Inflation

Abstract: We point out that the inclusion of a string component contributing around 5% to the CMB power spectrum amplitude on large scales can increase the preferred value of the spectral index n_s of density fluctuations measured by CMB experiments. While this finding applies to any cosmological scenario involving strings, we consider in particular models of supersymmetric hybrid inflation, which predict n_s >= 0.98, in tension with the CMB data when strings are not included. Using MCMC analysis we constrain the parameter space allowed for F- and D-term inflation. For the F-term model, using minimal supergravity corrections, we find that \log\kappa= -2.34\pm 0.38 and M= (0.518\pm 0.059) * 10^16 GeV. The inclusion of non-minimal supergravity corrections can modify these values somewhat. In the corresponding analysis for D-term inflation, we find \log\kappa= -4.24\pm 0.19 and m_FI= (0.245\pm 0.031) * 10^16 GeV. Under the assumption that these models are correct, these results represent precision measurements of important parameters of a Grand Unified Theory. We consider the possible uncertainties in our measurements and additional constraints on the scenario from the stochastic background of gravitational waves produced by the strings. The best-fitting model predicts a B-mode polarization signal \approx 0.3 \mu K rms peaking at l \approx 1000. This is of comparable amplitude to the expected signal due to gravitational lensing of the adiabatic E-mode signal on these scales.

Theory of parabolic arcs in interstellar scintillation spectra

Abstract: Interstellar scintillation (ISS), observed as time variation in the intensity of a compact radio source, is caused by small-scale structure in the electron density of the interstellar plasma. Dynamic spectra of ISS show modulation in radio frequency and time. Here we relate the (two-dimensional) power spectrum of the dynamic spectrum—the secondary spectrum—to the scattered image of the source. Recent work has identified remarkable parabolic arcs in secondary spectra. Each point in a secondary spectrum corresponds to interference between points in the scattered image with a certain Doppler shift and a certain delay. The parabolic arc corresponds to the quadratic relation between differential Doppler shift and delay through their common dependence on scattering angle. We show that arcs will occur in all media that scatter significant power at angles larger than the rms angle. Thus, effects such as source diameter, steep spectra, and dissipation scales, which truncate high angle scattering, also truncate arcs. Arcs are equally visible in simulations of nondispersive scattering. They are enhanced by anisotropic scattering when the spatial structure is elongated perpendicular to the velocity. In weak scattering the secondary spectrum is directly mapped from the scattered image, and this mapping can be inverted. We discuss additional observed phenomena including multiple arcs and reverse arclets oriented oppositely to the main arc. These phenomena persist for many refractive scattering times, suggesting that they are due to large-scale density structures, rather than low-frequency components of Kolmogorov turbulence.

Scattering of light from quasi-homogeneous sources by quasi-homogeneous media.

Abstract: The field generated by scattering of light from a quasi-homogeneous source on a quasi-homogeneous, random medium is investigated. It is found that, within the accuracy of the first-order Born approximation, the far field satisfies two reciprocity relations (sometimes called uncertainty relations). One of them implies that the spectral density (or spectral intensity) is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential. The other implies that the spectral degree of coherence of the far field is proportional to the convolution of the correlation coefficient of the source and the spatial Fourier transform of the strength of the scattering potential. While the case we consider might seem restrictive, it is actually quite general. For instance, the quasi-homogeneous source model can be used to describe the generation of beams with different coherence properties and different angular spreads. In addition, the quasi-homogeneous scattering model adequately describes a wide class of turbulent media, including a stratified, turbulent atmosphere and confined plasmas.

Pseudo- C ℓ estimators which do not mix E and B modes

Abstract: Pseudo-${C}_{\ensuremath{\ell}}$ quadratic estimators for CMB temperature and polarization power spectra have been used in the analysis pipelines of many CMB experiments, such as WMAP and Boomerang. In the polarization case, these estimators mix E and B modes, in the sense that the estimated B-mode power is nonzero for a noiseless CMB realization which contains only E modes. Recently, Challinor, and Chon showed that for moderately sized surveys (${f}_{\mathrm{sky}}\ensuremath{\sim}0.01$), this mixing limits the gravity wave B-mode signal which can be detected using pseudo-${C}_{\ensuremath{\ell}}$ estimators to $T/S\ensuremath{\sim}0.05$. We modify the pseudo-${C}_{\ensuremath{\ell}}$ construction, defining pure pseudo-${C}_{\ensuremath{\ell}}$ estimators, which do not mix E and B modes in this sense. We study these estimators in detail for a survey geometry similar to that which has been proposed for the QUIET experiment, for a variety of noise levels, and both homogeneous and inhomogeneous noise. For noise levels $\ensuremath{\lesssim}20\text{ }\text{ }\ensuremath{\mu}\mathrm{K}\mathrm{\text{\ensuremath{-}}}\mathrm{arc}\text{ }\mathrm{min}$, our modification significantly improves the B-mode power spectrum errors obtained using pseudo-${C}_{\ensuremath{\ell}}$ estimators. In the homogeneous case, we compute optimal power spectrum errors using a Fisher matrix approach, and show that our pure pseudo-${C}_{\ensuremath{\ell}}$ estimators are roughly 80% of optimal, across a wide range of noise levels. There is no limit, imposed by the estimators alone, to the value of $T/S$ which can be detected.

Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses

Abstract: We present ab initio quantum and classical investigations on the production and control of a single attosecond pulse by using few-cycle intense laser pulses as the driving field. The high-harmonic-generation power spectrum is calculated by accurately and efficiently solving the time-dependent Schr\"odinger equation using the time-dependent generalized pseudospectral method. The time-frequency characteristics of the attosecond xuv pulse are analyzed in detail by means of the wavelet transform of the time-dependent induced dipole. To better understand the physical processes, we also perform classical trajectory simulation of the strong-field electron dynamics and electron returning energy map. We found that the quantum and classical results provide complementary and consistent information regarding the underlying mechanisms responsible for the production of the coherent attosecond pulse. For few-cycle $(5\phantom{\rule{0.3em}{0ex}}\mathrm{fs})$ driving pulses, it is shown that the emission of the consecutive harmonics in the supercontinuum cutoff regime can be synchronized and locked in phase resulting in the production of a coherent attosecond pulse. Moreover, the time profile of the attosecond pulses can be controlled by tuning the carrier envelope phase.