Cosmic Background Radiation Field Research Articles

The chemistry and excitation of H2 and HD in the early Universe

ABSTRACT We have critically reviewed the literature pertaining to reactions that are significant for the chemistry of hydrogen-, deuterium-, and helium-bearing species in the homogeneous early Universe. For each reaction rate coefficient, we provide a fit in the modified-Arrhenius form, specifying the corresponding uncertainty and temperature range. This new network, limited to 21 reactions, should be the most reliable to date. Combined with accurate state-to-state rate coefficients for inelastic and reactive collisions involving H2 and HD, it allows us for the first time to follow the evolution of the abundances of atomic and molecular species, level populations of H2 and HD, and the ortho:para ratio (OPR) of H2, in a self-consistent fashion during the adiabatic expansion of the universe. The abundances of H2 and HD change only marginally compared to previous models, indicating that the uncertainties on the main reaction rate coefficients have essentially been removed. We also find that the adiabatic expansion has a dramatic effect on the OPR of H2, which freezes-out at redshifts z ≲ 50. In contrast, at higher redshifts, the populations of the rotational levels of H2 and HD are predicted to be fully thermalized at the temperature of the cosmic background radiation field, a result that conflicts with some recent, independent calculations. This new network allows the chemistry of primordial gas to be followed during the early phase of collapse towards Population III star progenitors.

Ultra-High-energy Cosmic Rays from beyond the Greisen–Zatsepin–Kuz’min Horizon

Abstract Ultra-high-energy (UHE) cosmic rays (CRs) of energies ∼(1018–1020) eV, accelerated in violent astrophysical environments, interact with cosmic background radiation fields via photo-hadronic processes, leading to strong attenuation. Typically, the Universe would become “opaque” to UHE CRs after several tens of megaparsecs, setting the boundary of the Greisen–Zatsepin–Kuz’min (GZK) horizon. In this work, we investigate the contribution of sources beyond the conventional GZK horizon to the UHE CR flux observed on Earth, when photospallation of the heavy nuclear CRs is taken into account. We demonstrate that this contribution is substantial, despite the strong attenuation of UHE CRs. A significant consequence is the emergence of an isotropic background component in the observed flux of UHE CRs, coexisting with the anisotropic foreground component that is associated with nearby sources. Multi-particle CR horizons, which evolve over redshift, are determined by the CR nuclear composition. Thus, they are dependent on the source populations and source evolutionary histories.

Cosmological parameter forecasts by a joint 2D tomographic approach to CMB and galaxy clustering

The cross-correlation between the cosmic microwave background (CMB) fields and matter tracers carries important cosmological information. In this paper, we forecast by a signal-to-noise ratio analysis the information contained in the cross-correlation of the CMB anisotropy fields with source counts for future cosmological observations and its impact on cosmological parameters uncertainties, using a joint tomographic analysis. We include temperature, polarization and lensing for the CMB fields and galaxy number counts for the matter tracers. By restricting ourselves to quasi-linear scales, we forecast by a Fisher matrix formalism the relative importance of the cross-correlation of source counts with the CMB in the constraints on the parameters for several cosmological models. We obtain that the CMB-number counts cross-correlation can improve the dark energy Figure of Merit (FoM) at most up to a factor $\sim 2$ for LiteBIRD+CMB-S4 $\times$ SKA1 compared to the uncorrelated combination of both probes and will enable the Euclid-like photometric survey to reach the highest FoM among those considered here. We also forecast how CMB-galaxy clustering cross-correlation could increase the FoM of the neutrino sector, also enabling a statistically significant ($\gtrsim$ 3$\sigma$ for LiteBIRD+CMB-S4 $\times$ SPHEREx) detection of the minimal neutrino mass allowed in a normal hierarchy by using quasi-linear scales only. Analogously, we find that the uncertainty in the local primordial non-Gaussianity could be as low as $\sigma (f_{\rm NL}) \sim 1.5-2$ by using two-point statistics only with the combination of CMB and radio surveys such as EMU and SKA1. Our results highlight the additional constraining power of the cross-correlation between CMB and galaxy clustering from future surveys which is mainly based on quasi-linear scales and therefore sufficiently robust to non-linear effects.

The POLARBEAR Fourier transform spectrometer calibrator and spectroscopic characterization of the POLARBEAR instrument.

We describe the Fourier Transform Spectrometer (FTS) used for in-field testing of the POLARBEAR receiver, an experiment located in the Atacama Desert of Chile which measures the cosmic microwave background (CMB) polarization. The POLARBEAR-FTS (PB-FTS) is a Martin-Puplett interferometer designed to couple to the Huan Tran Telescope (HTT) on which the POLARBEAR receiver is installed. The PB-FTS measured the spectral response of the POLARBEAR receiver with signal-to-noise ratio >20 for ∼69% of the focal plane detectors due to three features: a high throughput of 15.1 sr cm2, optimized optical coupling to the POLARBEAR optics using a custom designed output parabolic mirror, and a continuously modulated output polarizer. The PB-FTS parabolic mirror is designed to mimic the shape of the 2.5 m-diameter HTT primary reflector, which allows for optimum optical coupling to the POLARBEAR receiver, reducing aberrations and systematics. One polarizing grid is placed at the output of the PB-FTS and modulated via continuous rotation. This modulation allows for decomposition of the signal into different harmonics that can be used to probe potentially pernicious sources of systematic error in a polarization-sensitive instrument. The high throughput and continuous output polarizer modulation features are unique compared to other FTS calibrators used in the CMB field. In-field characterization of the POLARBEAR receiver was accomplished using the PB-FTS in April 2014. We discuss the design, construction, and operation of the PB-FTS and present the spectral characterization of the POLARBEAR receiver. We introduce future applications for the PB-FTS in the next-generation CMB experiment, the Simons Array.

Bayesian delensing of CMB temperature and polarization

We develop the first algorithm able to jointly compute the maximum {\it a posteriori} estimate of the Cosmic Microwave Background (CMB) temperature and polarization fields, the gravitational potential by which they are lensed, and cosmological parameters such as the tensor-to-scalar ratio, $r$. This is an important step towards sampling from the joint posterior probability function of these quantities, which, assuming Gaussianity of the CMB fields and lensing potential, contains all available cosmological information and would yield theoretically optimal constraints. Attaining such optimal constraints will be crucial for next-generation CMB surveys like CMB-S4, where limits on $r$ could be improved by factors of a few over currently used sub-optimal quadratic estimators. The maximization procedure described here depends on a newly developed lensing algorithm, which we term \textsc{LenseFlow}, and which lenses a map by solving a system of ordinary differential equations. This description has conceptual advantages, such as allowing us to give a simple non-perturbative proof that the lensing determinant is equal to unity in the weak-lensing regime. The algorithm itself maintains this property even on pixelized maps, which is crucial for our purposes and unique to \textsc{LenseFlow} as compared to other lensing algorithms we have tested. It also has other useful properties such as that it can be trivially inverted (i.e. delensing) for the same computational cost as the forward operation, and can be used to compute lensing adjoint, Jacobian, and Hessian operators. We test and validate the maximization procedure on flat-sky simulations covering up to 600\,deg$^2$ with non-uniform noise and masking.

Solving linear equations with messenger-field and conjugate gradient techniques: An application to CMB data analysis

We discuss linear system solvers invoking a messenger-field and compare them with (preconditioned) conjugate gradient approaches. We show that the messenger-field techniques correspond to fixed point iterations of an appropriately preconditioned initial system of linear equations. We then argue that a conjugate gradient solver applied to the same preconditioned system, or equivalently a preconditioned conjugate gradient solver using the same preconditioner and applied to the original system, will in general ensure at least a comparable and typically better performance in terms of the number of iterations to convergence and time-to-solution. We illustrate our conclusions with two common examples drawn from the cosmic microwave background (CMB) data analysis: Wiener filtering and map-making. In addition, and contrary to the standard lore in the CMB field, we show that the performance of the preconditioned conjugate gradient solver can depend significantly on the starting vector. This observation seems of particular importance in the cases of map-making of high signal-to-noise ratio sky maps and therefore should be of relevance for the next generation of CMB experiments.

Time delay and extended halo for constraints on the intergalactic magnetic field

Primary gamma rays emitted from extragalactic very-high-energy (VHE) sources, such as blazars, will generate cascade radiation in intergalactic space with a scale of ∼ 100 Mpc, for z ∼ 0.1 and Eγ ∼ 1TeV. These cascades proceed through electron-positron pair production and inverse Compton (IC) scattering in the cosmic background radiation fields, mainly cosmic microwave background (CMB) radiation and extragalactic background light in the voids of the universe. The existence of an intergalactic magnetic field (IGMF) would deflect paths of electron-positron pairs that scatter CMB photons, causing some observable effects, such as time delay, an extended halo, and a spectral change. Here we reanalyze the diffusion of an electron jet deflected by IGMF and propose a unified semi-analytical model. By using publicly available data from the Fermi/LAT detector and contemporaneous TeV observations, we find that the cascade photon flux is not significantly affected by the IGMF strength for non-variable blazars when the IGMF is weaker than ∼ 10−16 G. This result is clearly different from previous works that analyzed the extended halo and time delay separately for non-variable blazars and flaring blazars. By applying our model to two extreme blazars (1ES 0229+200 and 1ES 1218+304), we obtain the IGMF lower limit of order ≳ 10−13 ∼ 10−14 G in the non-variable case, which is a stronger constraint on the IGMF strength than previous works (≳ 10−16 ∼ 10−18 G), and ≳ 10−18 ∼ 10−19 G in the case of flaring blazars. Furthermore, we study the light curves and extended halo of the cascade photons by considering the effects of the IGMF.

Galactic PeV neutrinos

The IceCube experiment has detected two neutrinos with energies between 1 and 10PeV. They might have originated from Galactic or extragalactic sources of cosmic rays. In the present work we consider hadronic interactions of the diffuse very high energy cosmic rays with the interstellar matter within our Galaxy to explain the PeV neutrino events detected in IceCube. We also expect PeV gamma ray events along with the PeV neutrino events if the observed PeV neutrinos were produced within our Galaxy in hadronic interactions. PeV gamma rays are unlikely to reach us from sources outside our Galaxy due to pair production with cosmic background radiation fields. We suggest that in future with simultaneous detections of PeV gamma rays and neutrinos it would be possible to distinguish between Galactic and extragalactic origins of very high energy neutrinos.

ON MEASURING THE COSMIC MICROWAVE BACKGROUND TEMPERATURE AT REDSHIFT 0.89

We report on a measurement of the temperature of the cosmic microwave background radiation field, T_CMB, at z = 0.88582 by imaging HC3N (3-2) and (5-4) absorption in the foreground galaxy of the gravitationally lens magnified radio source PKS 1830-211 using the Very Long Baseline Array and the phased Very Large Array. Low-resolution imaging of the data yields a value of Trot = 5.6+2.5-0.9 K, for the rotational temperature, Trot, which is consistent with the temperature of the cosmic microwave background at the absorber's redshift of 2.73(1+z) K. However, our high-resolution imaging reveals that the absorption peak position of the foreground gas is offset from the continuum peak position of the synchrotron radiation from PKS 1830-211 SW, which indicates that the absorbing cloud is covering only part of the emission from PKS 1830-211, rather than the entire core-jet region. This changes the line-to-continuum ratios, and we find Trot between 1.1 and 2.5 K, which is lower than the expected value. This shows that previous, Trot, measurements could be biased due to unresolved structure.

Non-Gaussian structure of the lensed CMB power spectra covariance matrix

Gravitational lensing of the cosmic microwave background (CMB) encodes cosmological information in the observed anisotropies of temperature and polarization. Accurate extraction of this additional information requires precise modeling of the covariance matrix of the power spectra of observed CMB fields. We introduce a new analytical model to describe the non-Gaussian structure of this covariance matrix and display the importance of second-order terms that were previously neglected. When compared with direct numerical simulations our model captures parameter errors to better than a few percent for cases where the non-Gaussianity causes an order unity degradation in errors. We also provide a detailed comparison between the information content of lensed CMB power spectra and ideal reconstruction of the lensing potential. We illustrate the impact of the non-Gaussian terms in the power spectrum covariance by providing Fisher errors on the sum of the masses of the neutrinos, the dark energy equation of state, and the curvature of the Universe.

Particle Pair Production in Cosmological General Relativity

The Cosmological General Relativity (CGR) of Carmeli, a 5-dimensional (5-D) theory of time, space and velocity, predicts the existence of an acceleration a 0=c/τ due to the expansion of the universe, where c is the speed of light in vacuum, τ=1/h is the Hubble-Carmeli time constant, where h is the Hubble constant at zero distance and no gravity. The Carmeli force on a particle of mass m is F c =ma 0, a fifth force in nature. In CGR, the effective mass density ρ eff =ρ−ρ c , where ρ is the matter density and ρ c is the critical mass density which we identify with the vacuum mass density ρ vac =−ρ c . The fields resulting from the weak field solution of the Einstein field equations in 5-D CGR and the Carmeli force are used to hypothesize the production of a pair of particles. The mass of each particle is found to be m=τc 3/4G, where G is Newton’s constant. The vacuum mass density derived from the physics is ρ vac =−ρ c =−3/8πGτ 2. We make a connection between the cosmological constant of the Friedmann-Robertson-Walker model and the vacuum mass density of CGR by the relation Λ=−8πGρ vac =3/τ 2. Each black hole particle defines its own volume of space enclosed by the event horizon, forming a sub-universe. The cosmic microwave background (CMB) black body radiation at the temperature T o =2.72548 K which fills that volume is found to have a relationship to the ionization energy of the Hydrogen atom. Define the radiation energy ϵ γ =(1−g)mc 2/N γ , where (1−g) is the fraction of the initial energy mc 2 which converts to photons, g is a function of the baryon density parameter Ω b and N γ is the total number of photons in the CMB radiation field. We make the connection with the ionization energy of the first quantum level of the Hydrogen atom by the hypothesis 1 $$ \epsilon_{\gamma} = \frac{ ( 1 - g ) m c^2 }{ N_{\gamma} } = \frac{\alpha^2 \mu c^2}{2}, $$ where α is the fine-structure constant and μ=m p f/(1+f), where f=m e /m p with m e the electron mass and m p the proton mass. We give a model for g≈Ω b (1+f)m p /m n , where m n is the neutron mass. Then ratio η of the number of baryons N b to photons N γ is given by 2 $$ \eta = \frac{N_b}{N_{\gamma}} \approx \frac{ \alpha^2 \varOmega_b f m_p / m_n}{ 2 ( 1 + f ) [ 1 - \varOmega_b ( 1 + f ) m_p / m_n ] } $$ with a value of η≈6.708×10−10. The Bekenstein-Hawking black hole entropy S is given by S=(kc 3 A)/(4ħG), where k is Boltzmann’s constant, ħ is Planck’s constant over 2π and A is the area of the event horizon. For our black hole sub-universe of mass m the entropy is given by 3 $$ S = \frac{\pi k \tau^2 c^5 }{ \hbar G }, $$ which can be put into the form relating to the vacuum mass density 4 $$ \rho_{vac} = \frac{\rho_P }{ ( S / k ) }, $$ where the cosmological Planck mass density $\rho_{P} = -\mathcal{M}_{P} / L^{3}_{P}$ . The cosmological Planck mass $\mathcal{M}_{P} = \sqrt{ \sqrt{ 3 / 8 } \hbar c / G}$ and length $L_{P} = \hbar / \mathcal{M}_{P} c$ . The value of (S/k)≈1.980×10122.

PHOTON-INDUCED EVOLUTIONARY RATES OF LiHe+(1Σ+) IN EARLY UNIVERSE FROM ACCURATE QUANTUM COMPUTATIONS

The radiative association rates for the formation of LiHe+ molecules in their ground electronic state have been calculated employing an accurate ab initio potential energy curve and the dipole moment function. The enhancement of this rate, which may arise from stabilizing emissions stimulated by the cosmic background radiation field, has also been calculated and analyzed in the context of early universe conditions. Direct photodissociation processes have also been studied using local thermal equilibrium cross sections and rates are reported for temperatures between 600 and 9000 K. These photochemical processes are in turn analyzed and discussed as a function of the redshift z that is expected to operate in the early universe chemical kinetics. All data suggest very low residual abundances of this molecule and therefore its marginal role within early universe chemistry.

The Astrophysics of Ultrahigh-Energy Cosmic Rays

The origin of the highest energy cosmic rays is still unknown. The discovery of their sources is expected to reveal the workings of the most energetic astrophysical accelerators in the Universe. Current observations show a spectrum consistent with an origin in extragalactic astrophysical sources. Candidate sources range from the birth of compact objects to explosions related to gamma-ray bursts or to events in active galaxies. We discuss the main effects of propagation from cosmologically distant sources, including interactions with cosmic background radiation and magnetic fields. We examine possible acceleration mechanisms leading to a survey of candidate sources and their signatures. New questions arise from an observed hint of sky anisotropies and an unexpected evolution of composition indicators. Future observations may reach the necessary sensitivity to achieve charged particle astronomy and to observe ultrahigh-energy photons and neutrinos, which may further illuminate the workings of the Universe at these extreme energies. In addition to fostering a new understanding of high-energy astrophysical phenomena, the study of ultrahigh-energy cosmic rays can constrain the structure of the Galactic and extragalactic magnetic fields as well as probe particle interactions at energies orders of magnitude higher than achieved in terrestrial accelerators.

GZK neutrinos after the Fermi-LAT diffuse photon flux measurement

Cosmogenic neutrinos originate from photo-hadronic interactions of cosmic ray protons with the cosmic microwave background (CMB). The neutrino production rate can be constrained through the accompanying electrons, positrons and gamma-rays that quickly cascade on the CMB and intergalactic magnetic fields to lower energies and generate a γ-ray background in the GeV–TeV region. Bethe–Heitler pair production by protons also contributes to the cascade and can tighten the neutrino constraints in models where extragalactic cosmic rays begin to dominate over the galactic component at a relatively low “crossover” energy. We investigate this issue in the light of the recent Fermi-LAT measurements of the diffuse extragalactic γ-ray background and illustrate by a fit to the HiRes spectrum how the prediction of the cosmogenic neutrino flux in all-proton models varies with the crossover energy. The neutrino flux is required to be smaller when the gamma-ray bound is applied, nevertheless such models are still consistent with HiRes and Fermi-LAT if one properly takes into account the energy uncertainty of cosmic ray measurements. The presently allowed flux is within reach of the IceCube neutrino telescope and other dedicated radio experiments.

Non-Gaussianity in WMAP data due to the correlation of CMB lensing potential with secondary anisotropies

We measure the skewness power spectrum of the Cosmic Microwave Background (CMB) anisotropies optimized for a detection of the secondary bispectrum generated by the correlation of the CMB lensing potential with integrated Sachs-Wolfe effect and the Sunyaev-Zel'dovich effect. The covariance of our measurements is generated by Monte-Carlo simulations of Gaussian CMB fields with noise properties consistent with Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data. When interpreting multi-frequency measurements we also take into account the confusion resulting from unresolved radio point sources. We analyze Q, V and W-band WMAP 5-year raw and foreground-cleaned maps using the KQ75 mask out to l_max=600. We find no significant evidence for a non-zero non-Gaussian signal from the lensing-secondary correlation in all three bands and we constrain the overall amplitude of the cross power spectrum between CMB lensing potential and the sum of SZ and ISW fluctuations to be 0.42 \pm 0.86 and 1.19 \pm 0.86 in combined V and W-band raw and foreground-cleaned maps provided by the WMAP team, respectively. The point source amplitude at the bispectrum level measured with this skewness power spectrum is higher than previous measurements of point source non-Gaussianity. We also consider an analysis where we also account for the primordial non-Gaussianity in addition to lensing-secondary bispectrum and point sources. The focus of this paper is on secondary anisotropies. Consequently the estimator is not optimised for primordial non-Gaussianity and the limit we find on local non-Gaussianity from the foreground-cleaned V+W maps is f_NL = -13 \pm 62, when marginalized over point sources and lensing-ISW/SZ constributions to the total bispectrum.

Galaxy clusters as mirrors of the distant Universe

It is well known that Thomson scattering of cosmic microwave background (CMB) photons in galaxy clusters introduces new anisotropies in the CMB radiation field, but still little attention is payed to the fraction of CMB photons that are scattered <i>off<i/> the line of sight, causing a slight blurring of the CMB anisotropies present <i>at the moment<i/> of scattering. In this work we study this <i>blurring<i/> effect and find that it can provide an independent measurement of the cluster's gas mass. Likewise, this effect has a non-negligible impact on estimations of the kSZ effect: it induces a 10% correction in 20-40% of the clusters/groups and a dominant over kSZ correction in % of the clusters in an ideal (noiseless) experiment. For rich clusters, CMB, tSZ and X-ray observations can provide estimates for the amplitude and sign of the blurring effect that can be used for correcting kSZ estimations. We explore the possibility of using this blurring term to probe the CMB anisotropy field at different epochs in our Universe. In particular, we study the required precision in the removal of the kSZ which enables us to detect the blurring term in galaxy cluster populations placed at different redshift shells. By mapping this term in those shells, we provide a tomographic probe for the growth of the Integrated Sachs-Wolfe effect (ISW) during the late evolutionary stages of the Universe. We find that the required precision on the removal of the cluster's peculiar velocity is of the order of 100-200 km s<sup>-1<sup/> in the redshift range 0.2-0.8, after assuming that all clusters more massive than 10 are observable. These errors are comparable to the total expected linear line of sight velocity dispersion for clusters in WMAPV cosmogony and correspond to a residual level of roughly 900-1800 K per cluster, including all types of contaminants and systematics. Were this precision requirement achieved, then independent constraints on the intrinsic cosmological dipole would be simultaneously provided.

Impact of instrumental systematic contamination on the lensing mass reconstruction using the CMB polarization

In this paper, we study the effects of instrumental systematics on the reconstruction of the deflection angle power spectrum from weak lensing of cosmic microwave background (CMB) temperature and polarization observations. We consider 7 types of effects which are related to known instrumental systematics: calibration, rotation, pointing, spin-flip, monopole leakage, dipole leakage, and quadrupole leakage. These effects can result in the distortion in the CMB field and can be characterized by 11 distortion fields. Each of these systematic effects can mimic the effective projected matter power spectrum and hence contaminate the lensing reconstruction. To demonstrate the effect of these instrumental systematics on CMB lensing measurements, we consider two types of experiments: one with a detector noise level for polarization of $9.6\text{ }\text{ }\ensuremath{\mu}\mathrm{K}$ arcmin and FWHM of ${8.0}^{\ensuremath{'}}$, typical of upcoming ground and balloon-based CMB experiments; and a CMBPol-like instrument with a detector noise level for polarization of $2.0\text{ }\text{ }\ensuremath{\mu}\mathrm{K}$ arcmin and FWHM of ${4.0}^{\ensuremath{'}}$, typical of future space-based CMB experiments. For each systematics field, we consider various choices of coherence scale ${\ensuremath{\alpha}}_{s}$, starting from ${\ensuremath{\alpha}}_{s}={10}^{\ensuremath{'}}$ to the maximum of ${\ensuremath{\alpha}}_{s}={120}^{\ensuremath{'}}$. Among all the 11 systematic parameters, rotation $\ensuremath{\omega}$, and monopole leakage ${\ensuremath{\gamma}}_{a}$ ${\ensuremath{\gamma}}_{b}$ place the most stringent requirements, while quadrupole leakage $q$, pointing error ${p}_{a}$ and ${p}_{b}$, and calibration $a$ are among the least demanding. The requirements from lensing extraction are about 1--2 orders of magnitude less stringent than the requirements to measure the primordial $B$ modes with an inflationary energy scale of $1.0\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{GeV}$. On the other hand, the requirements for lensing reconstruction are comparable or even more stringent for some systematic parameters than the requirements to detect primordial $B$ modes with an inflationary scale of ${E}_{i}=3.0\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{GeV}$.

Polarized wavelets and curvelets on the sphere

The statistics of the temperature anisotropies in the primordial cosmic microwave background radiation field provide a wealth of information for cosmology and for estimating cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence being awaited with excitement. Multiscale methods, such as isotropic wavelets, steerable wavelets, or curvelets, have been proposed in the past to analyze the CMB temperature map. In this paper, we contribute to enlarging the set of available transforms for polarized data on the sphere. We describe a set of new multiscale decompositions for polarized data on the sphere, including decimated and undecimated Q-U or E-B wavelet transforms and Q-U or E-B curvelets. The proposed transforms are invertible and so allow for applications in data restoration and denoising.

Monitoring of the reflectors of ESA's Planck telescope by close-range photogrammetry

The Planck mission of the European Space Agency (ESA) is designed to image the anisotropies of the Cosmic Background Radiation Field over the whole sky. Planck's objective is to analyze, with the highest accuracy ever achieved, the remnants of the radiation that filled the universe immediately after the Big Bang, which we observe today as the cosmic microwave background. To achieve this aim well-manufactured reflectors are used as parts of the Planck telescope receiving system. The system consists of the Secondary and Primary Reflectors which are sections of two different ellipsoids of revolution with diameters of 1.1 and 1.9 meters. Deformations of the reflectors which influence the optical parameters and the gain of receiving signals are investigated in vacuum and at temperatures down to 95K, using close-range photogrammetric techniques. We have designed an optimal close-range photogrammetric network by heuristic simulation for the Primary and Secondary Reflectors with a mean relative precision better than 1:1,000,000 and 1:400,000, respectively, to achieve the requested accuracies. Special considerations have been taken into account in different steps of design, such as the determinability of additional parameters under the given network configuration, datum definition, reliability and precision issues as well as workspace limits and propagating errors from different sources of errors. A least squares best-fit ellipsoid was developed to determine the optical parameters of the reflector. We present our procedure and the results of processing the photogrammetric measurements of the Flight Models of the Primary and Secondary Reflectors which were executed by Thales Alenia Space France under ESA-ESTEC contract in vacuum and at very low temperatures.

Recombination of H 2 by Raman Association in the Early Universe

We investigate the contribution that Raman association makes to H2 production in the early universe at redshifts 10 ≤ z ≤ 104. The Raman process involves inelastic scattering of electromagnetic radiation off two colliding hydrogen atoms, taking away kinetic and binding energy and leaving bound H2. We calculate the inelastic cross sections and rate coefficients for this process and determine the Raman association rate in the cosmic background radiation field present during the early stages of the universe. A comparison with other H2-forming reactions is made.