Differential transforms of Cesàro averages in weighted spaces

In this paper we obtain convergence results for the series of differences of Cesàro averages along lacunary sequences in the setting of weighted Lp-spaces. These results give some information about how the Cesàro averages converge. The paper extends results of an earlier work by R. L. Jones and J. Rosenblatt. The operators considered are essentially convolution operators given by kernels more singular than the ones in the article by Jones and Rosenblatt

Two weighted inequalities for convolution maximal operators

[τh ϕ]R (x) are of weak type (p, p) with respect to (u, v), 1 0. In this paper we characterize the pair of weights (u, v) such that the operators Mτh ϕ f (x) = supR>0 $

The Measure of Cosmological Parameters

New, large, ground and space telescopes are contributing to an exciting and rapid period of growth in observational cosmology. The subject is now far from its earlier days of being data-starved and unconstrained, and new data are fueling a healthy interplay between observations and experiment and theory. I briefly review here the status of measurements of a number of quantities of interest in cosmology: the Hubble constant, the total mass-energy density, the matter density, the cosmological constant or dark energy component, and the total optical background light.Comment: 12 pages, 4 figures, to be published in "2001: A Spacetime Odyssey: Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics", Michael J. Duff & James T. Liu, eds., (World Scientific, Singapore), in pres

Elliptic CMB Sky

The ellipticity of the anisotropy spots of the Cosmic Microwave Background measured by the Wilkinson Microwave Anisotropy Probe (WMAP) has been studied. We find an average ellipticity of about 2, confirming with a far larger statistics similar results found first for the COBE-DMR CMB maps, and then for the BOOMERanG CMB maps. There are no preferred directions for the obliquity of the anisotropy spots. The average ellipticity is independent of temperature threshold and is present on scales both smaller and larger than the horizon at the last scattering. The measured ellipticity characteristics are consistent with being the effect of geodesics mixing occurring in an hyperbolic Universe, and can mark the emergence of CMB ellipticity as a new observable constant describing the Universe. There is no way of simulating this effect. Therefore we cannot exclude that the observed behavior of the measured ellipticity can result from a trivial topology in the popular flat $\Lambda$-CDM model, or from a non-trivial topology.Comment: 10 pages, 5 figures, the version to appear in Mod.Phys.Lett.

Multi-mode TES bolometer optimization for the LSPE-SWIPE instrument

In this paper we explore the possibility of using transition edge sensor (TES) detectors in multi-mode configuration in the focal plane of the Short Wavelength Instrument for the Polarization Explorer (SWIPE) of the balloon-borne polarimeter Large Scale Polarization Explorer (LSPE) for the Cosmic Microwave Background (CMB) polarization. This study is motivated by the fact that maximizing the sensitivity of TES bolometers, under the augmented background due to the multi-mode design, requires a non trivial choice of detector parameters. We evaluate the best parameter combination taking into account scanning strategy, noise constraints, saturation power and operating temperature of the cryostat during the flight.Comment: in Journal of Low Temperature Physics, 05 January 201

Modified Chaplygin Traversable Wormholes

The modified Chaplygin gas (MCG) is a strong candidate for the unified model of dark matter and dark energy. The equation of state of this modified model is valid from the radiation era to the $\Lambda$CDM model. In early epoch (when $\rho$ was large), dark matter had the dominant role while at later stages (when $\rho$ is small), the MCG model behaves as dark energy. In this work, we have found exact solution of static spherically symmetric Einstein equations describing a wormhole for an inhomogeneous distribution of modified Chaplygin gas. For existence of wormhole solution, there are some restrictions relating the parameters in the equation of state for MCG and the throat radius of the wormhole. Physical properties and characteristics of these modified Chaplygin wormholes are analyzed in details.Comment: 9 pages, 1 figur

Digital Deblurring of CMB Maps II: Asymmetric Point Spread Function

In this second paper in a series dedicated to developing efficient numerical techniques for the deblurring Cosmic Microwave Background (CMB) maps, we consider the case of asymmetric point spread functions (PSF). Although conceptually this problem is not different from the symmetric case, there are important differences from the computational point of view because it is no longer possible to use some of the efficient numerical techniques that work with symmetric PSFs. We present procedures that permit the use of efficient techniques even when this condition is not met. In particular, two methods are considered: a procedure based on a Kronecker approximation technique that can be implemented with the numerical methods used with symmetric PSFs but that has the limitation of requiring only mildly asymmetric PSFs. The second is a variant of the classic Tikhonov technique that works even with very asymmetric PSFs but that requires discarding the edges of the maps. We provide details for efficient implementations of the algorithms. Their performance is tested on simulated CMB maps.Comment: 9 pages, 13 Figure

On the observational determination of squeezing in relic gravitational waves and primordial density perturbations

We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a non-stationary character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in oscillatory behavior of the higher order multipoles C_l of the cosmic microwave background anisotropy. We start with the gravitational wave background and then apply the theory to primordial density perturbations. We derive an analytical formula for the positions of peaks and dips in the angular power spectrum l(l+1)C_l as a function of l. This formula shows that the values of l at the peak positions are ordered in the proportion 1:3:5:..., whereas at the dips they are ordered as 1:2:3:.... We compare the derived positions with the actually observed features, and find them to be in reasonably good agreement. It appears that the observed structure is better described by our analytical formula based on the (squeezed) metric perturbations associated with the primordial density perturbations, rather than by the acoustic peaks reflecting the existence of plasma sound waves at the last scattering surface. We formulate a forecast for other features in the angular power spectrum, that may be detected by the advanced observational missions, such as MAP and PLANCK. We tentatively conclude that the observed structure is a macroscopic manifestation of squeezing in the primordial metric perturbations.Comment: 34 pages, 3 figures; to appear in Phys. Rev. D66, 0435XX (2002); includes Note Added in Proofs: "The latest CBI observations (T.J.Pearson et al., astro-ph/0205388) have detected four peaks, at l ~ 550, 800, 1150, 1500, and four dips, at l ~ 400, 700, 1050, 1400. These positions are in a very good agreement with the theoretical formula (6.35) of the present paper. We interpret this data as confirmation of our conclusion that it is gravity, and not acoustics, that is responsible for the observed structure.

Variations of the spectral index of dust emissivity from Hi-GAL observations of the Galactic plane

Original article can be found at: http://www.aanda.org/ Copyright The European Southern ObservatoryContext. Variations in the dust emissivity are critical for gas mass determinations derived from far-infrared observations, but also for separating dust foreground emission from the Cosmic Microwave Background (CMB). Hi-GAL observations allow us for the first time to study the dust emissivity variations in the inner regions of the Galactic plane at resolution below 1°. Aims. We present maps of the emissivity spectral index derived from the combined Herschel PACS 160 μm, SPIRE 250 μm, 350 μm, and 500 μm data, and the IRIS 100 μm data, and we analyze the spatial variations of the spectral index as a function of dust temperature and wavelength in the two science demonstration phase Hi-GAL fields, centered at l = 30° and l = 59°. Methods. Applying two different methods, we determine both dust temperature and emissivity spectral index between 100 and 500 μm, at an angular resolution (θ) of 4'. Results. Combining both fields, the results show variations of the emissivity spectral index in the range 1.8–2.6 for temperatures between 14 and 23 K. The median values of the spectral index are similar in both fields, i.e. 2.3 in the range 100–500 μm, while the median dust temperatures are equal to 19.1 K and 16.0 K in the l = 30° and l = 59° field, respectively. Statistically, we do not see any significant deviations in the spectra from a power law emissivity between 100 and 500 μm. We confirm the existence of an inverse correlation between the emissivity spectral index and dust temperature, found in previous analyses.Peer reviewe