Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky -- namely that of systematic differences ("residuals") when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, and not caused by pixelation or masking as originally thought. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al.) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.Comment: 15 pages, 13 figure

The mass density field in simulated non-Gaussian scenarios

In this work we study the properties of the mass density field in the non-Gaussian world models simulated by Grossi et al. 2007. In particular we focus on the one-point density probability distribution function of the mass density field in non-Gausian models with quadratic non-linearities quantified by the usual parameter f_NL. We find that the imprints of primordial non-Gaussianity are well preserved in the negative tail of the probability function during the evolution of the density perturbation. The effect is already noticeable at redshifts as large as 4 and can be detected out to the present epoch. At z=0 we find that the fraction of the volume occupied by regions with underdensity delta < -0.9, typical of voids, is about 1.3 per cent in the Gaussian case and increases to ~2.2 per cent if f_NL=-1000 while decreases to ~0.5 per cent if f_NL=+1000. This result suggests that void-based statistics may provide a powerful method to detect non-Gaussianity even at low redshifts which is complementary to the measurements of the higher-order moments of the probability distribution function like the skewness or the kurtosis for which deviations from the Gaussian case are detected at the 25-50 per cent level.Comment: revised version, 9 Pages, 8 figures, MNRAS in pres

A Map of the Universe

We have produced a new conformal map of the universe illustrating recent discoveries, ranging from Kuiper belt objects in the Solar system, to the galaxies and quasars from the Sloan Digital Sky Survey. This map projection, based on the logarithm map of the complex plane, preserves shapes locally, and yet is able to display the entire range of astronomical scales from the Earth's neighborhood to the cosmic microwave background. The conformal nature of the projection, preserving shapes locally, may be of particular use for analyzing large scale structure. Prominent in the map is a Sloan Great Wall of galaxies 1.37 billion light years long, 80% longer than the Great Wall discovered by Geller and Huchra and therefore the largest observed structure in the universe.Comment: Figure 8, and additional material accessible on the web at: http://www.astro.princeton.edu/~mjuric/universe

The defect variance of random spherical harmonics

The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is obtaining the asymptotic shape of the defect variance, in the high frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern Cosmological data analysis.Comment: 19 page

Metamaterial-Inspired Quad-Band Notch Filter for LTE Band Receivers and WPT Applications

A new compact quad-band notch filter (QBNF) based on the extended composite right and left-handed transmission line (E-CRLH TL) has been presented. As known, E-CRLH TL behaves like a quad-band structure. A microstrip TL which is loaded with an open-ended ECRLH TL is presented as a QBNF. Four unwanted frequencies were used in a dual-band LTE receiver as four notch frequencies which must be eliminated (0.9 GHz, 1.3 GHz, 2.55 GHz, and 3.35 GHz). Also, this QBNF can be applied to simultaneous wireless power and data transfer (SWPDT) system to isolate the wireless power circuit from the data communication circuit. A design technique for the proposed QBNF is presented and its performance is validated using full-wave simulation results and theoretical analysis. The main advantage of this design is an overall rejection greater than 20dB at selected unwanted frequencies. Good agreements between the fullwave simulation and equivalent circuit model results have been achieved which verified the effectiveness of the proposed circuit model. The proposed QBNF is designed on an FR-4 substrate and the dimension of the proposed QBNF is 20 * 22 mm

Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies

We present an analysis of the Minkowski Functionals (MFs) describing the WMAP three-year temperature maps to place limits on possible levels of primordial non-Gaussianity. In particular, we apply perturbative formulae for the MFs to give constraints on the usual non-linear coupling constant fNL. The theoretical predictions are found to agree with the MFs of simulated CMB maps including the full effects of radiative transfer. The agreement is also very good even when the simulation maps include various observational artifacts, including the pixel window function, beam smearing, inhomogeneous noise and the survey mask. We find accordingly that these analytical formulae can be applied directly to observational measurements of fNL without relying on non-Gaussian simulations. Considering the bin-to-bin covariance of the MFs in WMAP in a chi-square analysis, we find that the primordial non-Gaussianity parameter is constrained to lie in the range -70<fNL<91 at 95% C.L. using the Q+V+W co-added maps.Comment: 9 pages, 4 figures, accpeted for publication in MNRA

Primordial non-Gaussianity: large-scale structure signature in the perturbative bias model

I compute the effect on the power spectrum of tracers of the large-scale mass-density field (e.g., galaxies) of primordial non-Gaussianity of the form Phi=phi+fNL (phi-)+gNL phi^3+..., where Phi is proportional to the initial potential fluctuations and phi is a Gaussian field, using beyond-linear-order perturbation theory. I find that the need to eliminate large higher-order corrections necessitates the addition of a new term to the bias model, proportional to phi, i.e., delta_g=b_delta delta+b_phi fNL phi+..., with all the consequences this implies for clustering statistics, e.g., P_gg(k)=b_delta^2 P_deltadelta(k)+2 b_delta b_phi fNL P_phidelta(k)+b_phi^2 fNL^2 P_phiphi(k)+... . This result is consistent with calculations based on a model for dark matter halo clustering, showing that the form is quite general, not requiring assumptions about peaks, or the formation or existence of halos. The halo model plays the same role it does in the usual bias picture, giving a prediction for b_phi for galaxies known to sit in a certain type of halo. Previous projections for future constraints based on this effect have been very conservative -- there is enough volume at z<~2 to measure fNL to ~+-1, with much more volume at higher z. As a prelude to the bias calculation, I point out that the beyond-linear (in phi) corrections to the power spectrum of mass-density perturbations are naively infinite, so it is dangerous to assume they are negligible; however, the infinite part can be removed by a renormalization of the fluctuation amplitude, with the residual k-dependent corrections negligible for models allowed by current constraints.Comment: 11 pg, 2 fig, v2: added illustrative figure, minor improvements, v3: added references, version accepted by PR

A geometric description of the non-Gaussianity generated at the end of multi-field inflation

In this paper we mainly focus on the curvature perturbation generated at the end of multi-field inflation, such as the multi-brid inflation. Since the curvature perturbation is produced on the super-horizon scale, the bispectrum and trispectrum have a local shape. The size of bispectrum is measured by $f_{NL}$ and the trispectrum is characterized by two parameters $\tau_{NL}$ and $g_{NL}$. For simplicity, the trajectory of inflaton is assumed to be a straight line in the field space and then the entropic perturbations do not contribute to the curvature perturbation during inflation. As long as the background inflaton path is not orthogonal to the hyper-surface for inflation to end, the entropic perturbation can make a contribution to the curvature perturbation at the end of inflation and a large local-type non-Gaussiantiy is expected. An interesting thing is that the non-Gaussianity parameters are completely determined by the geometric properties of the hyper-surface of the end of inflation. For example, $f_{NL}$ is proportional to the curvature of the curve on this hyper-surface along the adiabatic direction and $g_{NL}$ is related to the change of the curvature radius per unit arc-length of this curve. Both $f_{NL}$ and $g_{NL}$ can be positive or negative respectively, but $\tau_{NL}$ must be positive and not less than $({6\over 5}f_{NL})^2$.Comment: 19 pages, 4 figures; refs added; a correction to \tau_{NL} for n-field inflation added, version accepted for publication in JCA

The Trispectrum in the Multi-brid Inflation

The trispectrum is at least as important as the bispectrum and its size can be characterized by two parameters $\tau_{NL}$ and $g_{NL}$. In this short paper, we focus on the Multi-brid inflation, in particular the two-brid inflation model in arXiv.0805.0974, and find that $\tau_{NL}$ is always positive and roughly equals to $({6\over 5}f_{NL})^2$ for the low scale inflation, but $g_{NL}$ can be negative or positive and its order of magnitude can be the same as that of $\tau_{NL}$ or even largerComment: 12 pages; minor correction, refs added; further refs added, version for publication in JCA

Gravitational Wave Background and Non-Gaussianity as a Probe of the Curvaton Scenario

We study observational implications of the stochastic gravitational wave background and a non-Gaussian feature of scalar perturbations on the curvaton mechanism of the generation of density/curvature fluctuations, and show that they can determine the properties of the curvaton in a complementary manner to each other. Therefore even if Planck could not detect any non-Gaussianity, future space-based laser interferometers such as DECIGO or BBO could practically exhaust its parameter space.Comment: 16 pages, 2 figure