The effect of reionization on the cosmic microwave background–density correlation

In this paper, we show how the rescattering of cosmic microwave background photons after cosmic reionization can give a significant linear contribution to the temperature–matter cross-correlation measurements. These anisotropies, which arise via a late-time Doppler effect, are on scales much larger than the typical scale of non-linear effects at reionization; they can contribute to degree scale cross-correlations and could affect the interpretation of similar correlations resulting from the integrated Sachs–Wolfe effect. While expected to be small at low redshifts, these correlations can be large given a probe of the density at high redshift, and so could be a useful probe of the cosmic reionization history.     

Estimating non-Gaussianity in the microwave background

The bispectrum of the microwave background sky is a possible discriminator between inflationary and defect models of structure formation in the Universe. The bispectrum, which is the analogue of the temperature three-point correlation function in harmonic space, is zero for most inflationary models, but non-zero for non-Gaussian models. The expected departures from zero are small, and easily masked by noise, so it is important to be able to estimate the bispectrum coefficients as accurately as possible, and to know the errors and correlations between the estimates so that they may be used in combination as a diagnostic to rule out non-Gaussian models. This paper presents a method for estimating in an unbiased way the bispectrum from a microwave background map in the near-Gaussian limit. The method is optimal, in the sense that no other method can have smaller error bars, and, in addition, the covariances between the bispectrum estimates are calculated explicitly. The method deals automatically with partial sky coverage and arbitrary noise correlations without modification. A preliminary application to the Cosmic Background Explorer 4-yr data set shows no evidence for non-Gaussian behaviour.     

Full-sky correlations of peaks in the microwave background

We compute precise predictions for the two-point correlation function of local maxima (or minima) in the temperature of the microwave background, under the assumption that it is a random Gaussian field. For a given power spectrum and peak threshold there are no adjustable parameters, and since this analysis does not make the small-angle approximation of Heavens & Sheth, it is essentially complete. We find oscillatory features which are absent in the temperature autocorrelation function, and we also find that the small-angle approximation to the peak–peak correlation function is accurate to better than 0.01 on all scales. These high-precision predictions can form the basis of a sensitive test of the Gaussian hypothesis with upcoming all-sky microwave background experiments MAP and Planck , affording a thorough test of the inflationary theory of the early Universe. To illustrate the effectiveness of the technique, we apply it to simulated maps of the microwave sky arising from the cosmic string model of structure formation, and compare the two-point correlation function of peaks with the bispectrum as a non-Gaussian discriminant. We also show how peak statistics can be a valuable tool in assessing and statistically removing contamination of the map by foreground point sources.     

The correlation of peaks in the microwave background

We present accurate small-angle predictions of the correlation function of hotspots in the microwave background radiation for Gaussian theories such as those predicted in most inflation models. The correlation function of peaks above a certain threshold depends only on the threshold and the power spectrum of temperature fluctuations. Since these are both potentially observable quantities in a microwave background map, there are no adjustable parameters in the predictions. These correlations should therefore provide a powerful test of the Gaussian hypothesis, and provide a useful discriminant between inflation and topological defect models such as the cosmic string model. The correlations have a number of oscillatory features, which should be detectable at high signal-to-noise ratio with future satellite experiments such as MAP and Planck .     

Cosmic microwave background anisotropy: deviations from Gaussianity caused by non-linear gravity

Non-linear evolution of cosmological energy density fluctuations triggers deviations from Gaussianity in the temperature distribution of the cosmic microwave background. A method to estimate these deviations is proposed. N -body simulations – in a Λ cold dark matter cosmology – are used to simulate the strongly non-linear evolution of cosmological structures. It is proved that these simulations can be combined with the potential approximation to calculate the statistical moments of the cosmic microwave background anisotropies produced by non-linear gravity. Some of these moments are computed and the resulting values are different from those corresponding to Gaussianity.     

Fast parameter estimation from the cosmic microwave background power spectrum

The statistical properties of a map of the primary fluctuations in the cosmic microwave background (CMB) may be specified to high accuracy by a few thousand power spectra measurements, provided the fluctuations are Gaussian, yet the number of parameters relevant for the CMB is probably no more than ∼10–20. Consequently, there is a large degree of redundancy in the power spectrum data. In this paper, we show that the moped data compression technique can reduce the CMB power spectrum measurements to ∼10–20 numbers (one for each parameter), from which the cosmological parameters can be estimated virtually as accurately as from the complete power spectrum. Combined with recent advances in the speed of generation of theoretical power spectra, this offers opportunities for very fast parameter estimation from real and simulated CMB skies. The evaluation of the likelihood itself, at Planck resolution, is speeded up by factors up to ∼10⁸, ensuring that this step will not be the dominant part of the data analysis pipeline.     

Non-Gaussian cosmic microwave background temperature fluctuations from peculiar velocities of clusters

We use numerical simulations of a (480 Mpc  h ⁻¹)³ volume to show that the distribution of peak heights in maps of the temperature fluctuations from the kinematic and thermal Sunyaev–Zeldovich (SZ) effects will be highly non-Gaussian, and very different from the peak-height distribution of a Gaussian random field. We then show that it is a good approximation to assume that each peak in either SZ effect is associated with one and only one dark matter halo. This allows us to use our knowledge of the properties of haloes to estimate the peak-height distributions. At fixed optical depth, the distribution of peak heights resulting from the kinematic effect is Gaussian, with a width that is approximately proportional to the optical depth; the non-Gaussianity comes from summing over a range of optical depths. The optical depth is an increasing function of halo mass and the distribution of halo speeds is Gaussian, with a dispersion that is approximately independent of halo mass. This means that observations of the kinematic effect can be used to put constraints on how the abundance of massive clusters evolves, and on the evolution of cluster velocities. The non-Gaussianity of the thermal effect, on the other hand, comes primarily from the fact that, on average, the effect is larger in more massive haloes, and the distribution of halo masses is highly non-Gaussian. We also show that because haloes of the same mass may have a range of density and velocity dispersion profiles, the relation between halo mass and the amplitude of the thermal effect is not deterministic, but has some scatter.     

A measurement at the first acoustic peak of the cosmic microwave background with the 33-GHz interferometer

This paper presents the results from the Jodrell BankInstituto de Astrofisicia de Canarias (IAC) two-element 33-GHz interferometer operated with an element separation of 32.9 wavelengths and hence sensitive to 1°-scale structure on the sky. The level of cosmic microwave background (CMB) fluctuations, assuming a flat CMB spatial power spectrum over the range of multipoles =208±18, was found using a likelihood analysis to be at the 68 per cent confidence level, after the subtraction of the contribution of monitored point sources. Other possible foreground contributions have been assessed and are expected to have negligible impact on this result.