The Planck Surveyor mission and gravitational lenses

An extremely sensitive all-sky survey will be carried out in the millimetre/submillimetre waveband by the forthcoming ESA mission Planck Surveyor . The main scientific goal of the mission is to make very accurate measurements of the spatial power spectrum of primordial anisotropies in the cosmic microwave background radiation; however, hundreds of thousands of distant dusty galaxies and quasars will also be detected. These sources are much more likely to be gravitationally lensed by intervening galaxies compared with sources discovered in surveys in other wavebands. Here the number of lenses expected in the survey is estimated, and techniques for discriminating between lensed and unlensed sources are discussed. A practical strategy for this discrimination is presented, based on exploiting the remarkable sensitivity and resolving power of large ground-based millimetre/submillimetre-wave interferometer arrays. More than a thousand gravitational lenses could be detected: a sample that would be an extremely valuable resource in observational cosmology.     

The scalar, vector and tensor contributions of a stochastic background of magnetic fields to cosmic microwave background anisotropies

We study the contribution of a stochastic background (SB) of primordial magnetic fields (PMFs) on the anisotropies in temperature and polarization of the cosmic microwave background (CMB) radiation. A SB of PMF modelled as a fully inhomogeneous component induces non-Gaussian scalar, vector and tensor metric linear perturbations. We give the exact expressions for the Fourier spectra of the relevant energy–momentum components of such a SB, given a power-law dependence parametrized by a spectral index   n_B   for the magnetic field power spectrum cut at a damping scale k _D. For all the values of   n_B   considered here, the contribution to the CMB temperature pattern by such a SB is dominated by the scalar contribution and then by the vector one at higher multipoles. We also give an analytic estimate of the scalar contribution to the CMB temperature pattern.     

Features in the primordial power spectrum: constraints from the cosmic microwave background and the limitation of the 2dF and SDSS redshift surveys to detect them

We allow a more general (step-function) form of the primordial power spectrum than the usual featureless power-law Harrison–Zeldovich (with spectral index   n =1)  power spectrum, and fit it to the latest cosmic microwave background data sets. Although the best-fitting initial power spectrum can differ significantly from the power-law shape, and contains a dip at scales   k ∼0.003  h  Mpc^-1  , we find that  Ω_m≈0.24  , consistent with previous analyses that assume power-law initial fluctuations. We also explore the feasibility of the early releases of the 2dF and Sloan Digital Sky Survey (SDSS) galaxy redshifts surveys to see these features, and we find that even if features exist in the primordial power spectrum, they are washed out by the window functions of the redshift surveys on scales   k <0.03  h  Mpc^-1  .     

Limits on isocurvature perturbations from non-Gaussianity in WMAP temperature anisotropy

We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB) temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable  σ,  S =σ²−〈σ²〉  , can give the same signal-to-noise ratio as   f _NL= 30  even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum α. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction  α < 0.070  (95 per cent CL) for a scale-invariant spectrum which is comparable to the limit obtained from the power spectrum.     

Galactic magnetic turbulence from radio data

Fluctuations in the Galactic synchrotron emission can be traced by the angular power spectrum of radio maps at low multipoles. At frequencies below few GHz, large-scale anisotropies are mainly induced by magnetic field turbulence, since non-thermal electrons radiating at these frequencies are uniformly distributed over the scales of magnetic field inhomogeneities. By performing an analysis of five radio maps, we extract constraints on turbulence spectral index and halo scale. Results favour a power spectrum significantly flatter than for 3D Kolmogorov-like turbulence, and a thin halo. This can be interpreted as an indication supporting non-conventional models of propagation of cosmic-ray particles in the Galaxy, or as a suggestion of a spectral-index break in the observed magnetic turbulence power spectrum.     

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model. II

We examine the effect produced by the variation of cosmological parameters on the power spectra of one-dimensional cross-sections of the cosmic microwave background maps in a narrow range of spatial frequencies. Variation of the Ω _b and Ω_Λ density parameters has little effect on the power spectrum deviation from the one expected within the ΛCDM model. At the same time, variations in the spectral index of primordial fluctuations significantly affect the amplitude of the power spectrum of one-dimensional cross-sections. We observe a lack of signal generated by the even harmonics in the ILC map as compared with model expectations.     

Constraints on large-scale inhomogeneities from WMAP5 and SDSS: confrontation with recent observations

Measurements of the Type Ia supernovae Hubble diagram which suggest that the Universe is accelerating due to the effect of dark energy may be biased because we are located in a 200–300 Mpc underdense 'void' which is expanding 20–30 per cent faster than the average rate. With the smaller global Hubble parameter, the Wilkinson Microwave Anisotropy Probe 5 data on cosmic microwave background (CMB) anisotropies can be fitted without requiring dark energy if there is some excess power in the spectrum of primordial perturbations on 100 Mpc scales. The Sloan Digital Sky Survey (SDSS) data on galaxy clustering can also be fitted if there is a small component of hot dark matter in the form of 0.5 eV mass neutrinos. We show however that if the primordial fluctuations are Gaussian, the expected variance of the Hubble parameter and the matter density are far too small to allow such a large local void. Nevertheless, many such large voids have been identified in the SDSS Luminous Red Galaxy survey in a search for the late integrated Sachs–Wolfe effect due to dark energy. The observed CMB temperature decrements imply that they are nearly empty, thus these real voids too are in gross conflict with the concordance Λ cold dark matter model. The recently observed high peculiar velocity flow presents another challenge for the model. Therefore, whether a large local void actually exists must be tested through observations and cannot be dismissed a priori.     

Measurement of a Peak in the Cosmic Microwave Background Power Spectrum from the North American Test Flight of Boomerang

We describe a measurement of the angular power spectrum of anisotropies in the cosmic microwave background (CMB) at scales of 0&fdg;3 to 5 degrees from the North American test flight of the Boomerang experiment. Boomerang is a balloon-borne telescope with a bolometric receiver designed to map CMB anisotropies on a long-duration balloon flight. During a 6 hr test flight of a prototype system in 1997, we mapped more than 200 deg(2) at high Galactic latitudes in two bands centered at 90 and 150 GHz with a resolution of 26&arcmin; and 16&farcm;5 FWHM, respectively. Analysis of the maps gives a power spectrum with a peak at angular scales of 1 degrees with an amplitude 70 μK(CMB).     

The Sunyaev–Zel'dovich effect and Faraday rotation contributions of galaxy groups to the CMB angular power spectrum

The Sunyaev–Zel'dovich (SZ) effect and the Faraday rotation from haloes are examined over a wide mass range, including gas condensation and magnetic field evolution. Contributions to the cosmic microwave background (CMB) angular power spectrum are evaluated for galaxy clusters, galaxy groups and galaxies. Smaller mass haloes are found to play a more important role than massive haloes for the B -mode polarization associated with the SZ CMB anisotropies. The B modes from the Faraday rotation dominate the secondary B modes caused by gravitational lensing at  ℓ > 3000  . Measurement of B -mode polarization in combination with the SZ power spectrum can potentially provide important constraints on intracluster magnetic field and gas evolution at early epochs.     

Cosmology after COBE

The measured anisotropies in the temperature of the cosmic microwave background radiation (CMB) by the Cosmic Background Explorer (COBE) are consistent with models of gravitational collapse for the formation of large scale structure in the universe. The amplitude of cosmological fluctuations on the largest scales is fixed by COBE. From COBE's data it is also possible to test for the shape of the primordial spectrum. Statistical tests using COBE's two year data and based on the geometric characteristics of anisotropy spots taking into account cosmic variance and the relevant experimental details indicate that the primordial spectrum has a slope in the rangen = 0.8 – 1.3. Possible identification of hot and cold spots of cosmological origin is also given.Presented at the Fourth United Nations/European Space Agency Workshop on Basic Space Science. Cairo, Egypt, 27 June - 1 July 1994.     

The power spectrum of rich clusters of galaxies on large spatial scales

We present an analysis of the redshift-space power spectrum, P ( k ), of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that P ( k ) can be approximated by a power law, P ( k )∝ kⁿ , with n ≈−1.6 over the wavenumber range 0.04< k <0.1 h Mpc⁻¹. Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution, but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale k ∼0.03 h Mpc⁻¹. We compare the power spectra estimated from simulated APM cluster catalogues with those estimated directly from cubical N -body simulation volumes, and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers k ≳0.02 h Mpc⁻¹. These results suggest that the observed turnover in the power spectrum may be a real feature of the cluster distribution, and that we have detected the transition to a near-scale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turnover in the cluster power spectrum is in good agreement with the scale of the turnover observed in the power spectrum of APM galaxies.     

Effects of destriping errors on estimates of the CMB power spectrum

Destriping methods for constructing maps of the cosmic microwave background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates for Planck -like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. Assuming Planck -like low-frequency noise, the noise power spectrum is accurately white at high multipoles  (ℓ≳ 50)  . Destriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis of Planck data and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic '1/ f ' noise.     

Large scale magnetic fields: Density power spectrum in redshift space

We compute the density redshift-space power spectrum in the presence of tangled magnetic fields and compare it with existing observations. Our analysis shows that if these magnetic fields originated in the early universe then it is possible to construct models for which the shape of the power spectrum agrees with the large scale slope of the observed power spectrum. However requiring compatibility with observed CMBR anisotropies, the normalization of the power spectrum is too low for magnetic fields to have significant impact on the large scale structure at present. Magnetic fields of a more recent origin generically give density power spectrumα k ⁴which doesn’t agree with the shape of the observed power spectrum at any scale. Magnetic fields generate curl modes of the velocity field which increase both the quadrupole and hexadecapole of the redshift space power spectrum. For curl modes, the hexadecapole dominates over quadrupole. So the presence of curl modes could be indicated by an anomalously large hexadecapole, which has not yet been computed from observation. It appears difficult to construct models in which tangled magnetic fields could have played a major role in shaping the large scale structure in the present epoch. However if they did, one of the best ways to infer their presence would be from the redshift space effects in the density power spectrum.     

On the influence of resonant scattering on cosmic microwave background polarization anisotropies

We implement the theory of resonant scattering in the context of cosmic microwave background (CMB) polarization anisotropies. We compute the changes in the E-mode polarization (EE) and temperature E-mode (TE) CMB power spectra introduced by the scattering on a resonant transition with a given optical depth τ_X and polarization coefficient E ₁. The latter parameter, accounting for how anisotropic the scattering is, depends on the exchange of angular momentum in the transition, enabling observational discrimination between different resonances. We use this formalism in two different scenarios: cosmological recombination and cosmological re-ionization. In the context of cosmological recombination, we compute predictions in frequency and multipole space for the change in the TE and EE power spectra introduced by scattering on the Hα and Pα lines of hydrogen. This constitutes a fundamental test of the standard model of recombination, and the sensitivity it requires is comparable to that needed in measuring the primordial CMB B-mode polarization component. In the context of re-ionization, we study the scattering off metals and ions produced by the first stars, and find that polarization anisotropies, apart from providing a consistency test for intensity measurements, give some insight on how re-ionization evolved. Since polarization anisotropies have memory of how anisotropic the line scattering is, they should be able to discern the O  i 63.2-μm transition from other possible transitions associated to O  iii , N  ii , N  iii , etc. The amplitude of these signals are, however, between 10 and 100 times below the (already challenging) level of CMB B-mode polarization anisotropies.     

Radial gradients and anisotropies due to galactic cosmic rays

Numerical calculations have been made of the radial gradients and the anisotropyvector atr=1 AU due to galactic cosmic-ray protons and helium nuclei. The model used assumes transport by convection and anisotropic diffusion, and includes the energy losses due to adiabatic deceleration. The present calculations are for the 1964–65 solar minimum. An important constraint applied ineach case was that the model reproduces the electron modulation known from deductions of the galactic spectrum and observations of the near-Earth spectrum; and also reproduces the near-Earth proton and helium nuclei spectra. The diffusion coefficients have been based upon those deduced from magnetic-field power spectra.The principal aim has been to provide estimates of radial gradients and anisotropies, particularly at kinetic energiesT100 MeV/nucleon, by the complete solution of realistic models. Typical values for protons, obtained with a galactic differential number density (total energy)^–2.5, atT50 MeV are: radial gradient, 25%/AU; radial anisotropy, –0.2%; azimuthal anisotropy, 0.2%. These values change markedly when the galactic spectrum is cut-off or greatly enhanced atT<150 MeV, but the intensity spectrum near Earth remains substantially unchanged.It has been shown that it is possible to obtain negative radial gradients and positive radial anisotropies atT50 MeV for galactic particles and thus to mimic solar sources. The radial gradient for 1964–65 reported by Anderson (1968) and by Krimigis and Venkatesan (1969) are shown to be consistent with the diffusion coefficient deduced from the magnetic-field power spectrum; those reported by O'Gallagher are higher than expected and that for 20T30 MeV protons appears to be inconsistent. More precise data on conditions throughout the solar cavity are required if more definitive gradients and anisotropies are to be determined.     

Non-linear evolution of suppressed dark matter primordial power spectra

We address the degree and rapidity of generation of small-scale power over the course of structure formation in cosmologies where the primordial power spectrum is strongly suppressed beyond a given wavenumber. We first summarize the situations where one expects such suppressed power spectra and point out their diversity. We then employ an exponential cut-off, which characterizes warm dark matter (WDM) models, as a template for the shape of the cut-off and focus on damping scales ranging from 10⁶ to  10⁹  h ⁻¹ M_⊙  . Using high-resolution simulations, we show that the suppressed part of the power spectrum is quickly (re)generated and catches up with both the linear and the non-linear evolution of the unsuppressed power spectrum. From   z = 2  onwards, a power spectrum with a primordial cut-off at  10⁹  h ⁻¹ M_⊙  becomes virtually indistinguishable from an evolved cold dark matter (CDM) power spectrum. An attractor such as that described in Zaldarriaga, Scoccimarro & Hui for power spectra with different spectral indices also emerges in the case of truncated power spectra. Measurements of   z ∼ 0  non-linear power spectra at  ∼100  h ⁻¹ kpc  cannot rule out the possibility of linear power spectra damped below  ∼10⁹  h ⁻¹ M_⊙  . Therefore, WDM or scenarios with similar features should be difficult to exclude in this way.     

Cosmological science enabled by Planck

Planck will be the first mission to map the entire cosmic microwave background (CMB) sky with mJy sensitivity and resolution better than 10′. The science enabled by such a mission spans many areas of astrophysics and cosmology. In particular it will lead to a revolution in our understanding of primary and secondary CMB anisotropies, the constraints on many key cosmological parameters will be improved by almost an order of magnitude (to sub-percent levels) and the shape and amplitude of the mass power spectrum at high redshift will be tightly constrained.     

Weak lensing of the CMB: extraction of lensing information from the trispectrum

We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-Gaussian noise contributions, beyond the previously discussed dominant Gaussian noise. Non-Gaussian noise contributions are generated by lensing itself and by the correlation between the lensing effect and other foreground secondary anisotropies in the CMB such as the Sunyaev–Zel’dovich (SZ) effect. When the SZ effect is removed from temperature maps using its spectral dependence, we find these additional non-Gaussian noise contributions to be an order of magnitude lower than the dominant Gaussian noise. If the noise-bias due to the dominant Gaussian part of the temperature squared power spectrum is removed, then these additional non-Gaussian contributions provide the limiting noise level for the lensing reconstruction. The temperature squared power spectrum allows a high signal-to-noise extraction of the lensing deflections and a confusion-free separation of the curl (or B-mode) polarization due to inflationary gravitational waves from that due to lensed gradient (or E-mode) polarization. The small angular scale temperature and polarization anisotropy measurements provide a novel approach to weak lensing studies, complementing the approach based on galaxy ellipticities.     

Acceleration of ultrarelativistic electrons in the Crab Nebula

Ultrarelativistic electrons must be being accelerated in the Crab Nebula to maintain the synchrotron spectrum. Sufficient power to maintain the synchrotron spectrum is supplied by an observed damping of compressional motions in the central region of the nebula (the wisps of Baade). An acceleration mechanism which involves compressional motions, the gyrorelaxation effect and the removal of pitch angle anisotropies by the generation of hydromagnetic waves is formulated and applied to a model of the Crab Nebula with acceleration confined to a central region. This can account for the power supplied to the electrons, the overall shape of the spectrum and allows acceleration up to energies corresponding to the synchrotron emission of hard X-rays. The acceleration process tends to flatten an initial energy spectrum.