The integrated Sachs–Wolfe effect in cosmologies with coupled dark matter and dark energy

The subject of this paper is the derivation of the integrated Sachs–Wolfe (iSW) effect in cosmologies with coupled dark matter and dark energy fluids. These couplings influence the iSW effect in three ways: the Hubble function assumes a different scaling, the structure growth rate shows a different time evolution and, in addition, the Poisson equation, which relates the density perturbations to fluctuations in the gravitational potential, is changed, due to the violation of the scaling  ρ∝ a ⁻³  of the matter density ρ with scalefactor a . Exemplarily, I derive the iSW spectra for a model in which dark matter decays into dark energy, investigate the influence of the dark matter decay rate and the dark energy equation of state on the iSW signal, and discuss the analogies for gravitational lensing. Quite generally, iSW measurements should reach similar accuracy in determining the dark energy equation of state parameter and the coupling constant.     

Implications of bias evolution on measurements of the integrated Sachs–Wolfe effect: errors and biases in parameter estimation

The subject of this paper is a quantification of the impact of uncertainties in bias and bias evolution on the interpretation of measurements of the integrated Sachs–Wolfe (ISW) effect, in particular on the estimation of cosmological parameters. We carry out a Fisher matrix analysis for quantifying the degeneracies between the parameters of a dark energy cosmology and bias evolution, for the combination of the PLANCK microwave sky survey with the EUCLID main galaxy sample, where bias evolution   b ( a ) = b ₀+ (1 − a ) b_a   is modelled with two parameters b ₀ and   b_a   . Using a realistic bias model introduces a characteristic suppression of the ISW spectrum on large angular scales, due to the altered distance-weighting functions. The errors in estimating cosmological parameters if the data with evolving bias is interpreted in the framework of cosmologies with constant bias are quantified in an extended Fisher formalism. We find that the best-fitting values of all parameters are shifted by an amount comparable to the statistical accuracy: the estimation bias in units of the statistical accuracy amounts to 1.19 for Ω_m, 0.27 for σ₈ and 0.72 for w for bias evolution with   b_a = 1  . Leaving   b_a   open as a free parameter deteriorates the statistical accuracy, in particular on Ω_m and w .     

Weak lensing in the second post-Newtonian approximation: gravitomagnetic potentials and the integrated Sachs–Wolfe effect

Dark matter currents in the large-scale structure give rise to gravitomagnetic terms in the metric, which affect the light propagation. Corrections to the weak-lensing power spectrum due to these gravitomagnetic potentials are evaluated by perturbation theory. A connection between gravitomagnetic lensing and the integrated Sachs–Wolfe (iSW) effect is drawn, which can be described by a line-of-sight integration over the divergence of the gravitomagnetic vector potential. This allows the power spectrum of the iSW-effect to be derived within the framework of the same formalism as derived for gravitomagnetic lensing and reduces the iSW-effect to a second-order lensing phenomenon. The three-dimensional power spectra are projected by means of a generalized Limber-equation to yield the angular power spectra. Gravitomagnetic corrections to the weak-lensing spectrum are negligible at currently accessible scales, and cosmic-variance considerations suggest that the detection of the iSW-effect's contribution to the cosmic microwave background angular power spectrum is too small to be detectable at multipoles probed by the Planck satellite.     

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.     

Statistics of the Sunyaev–Zel'dovich effect power spectrum

Using large numbers of simulations of the microwave sky, incorporating the cosmic microwave background (CMB) and the Sunyaev–Zel'dovich (SZ) effect due to clusters, we investigate the statistics of the power spectrum at microwave frequencies between spherical multipoles of 1000 and 10 000. From these virtual sky maps, we find that the spectrum of the SZ effect has a larger standard deviation by a factor of 3 than would be expected from purely Gaussian realizations, and has a distribution that is significantly skewed towards higher values, especially when small map sizes are used. The standard deviation is also increased by around 10 per cent compared to the trispectrum calculation due to the clustering of galaxy clusters. We also consider the effects of including residual point sources and uncertainties in the gas physics. This has implications for the excess power measured in the CMB power spectrum by the Cosmic Background Imager (CBI) and Berkeley–Illinois–Maryland Association (BIMA) experiments. Our results indicate that the observed excess could be explained using a lower value of σ₈ than previously suggested, however the effect is not enough to match  σ₈= 0.825  . The uncertainties in the gas physics could also play a substantial role. We have made our maps of the SZ effect available online.     

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.     

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 bispectrum and slow-roll inflation

Recent tentative findings of non-Gaussian structure in the COBE -DMR data set have triggered renewed attention on candidate models from which such intrinsic signature could arise. In the framework of slow-roll inflation with built-in non-linearities in the inflaton field evolution, we present expressions for both the cosmic microwave background (CMB) skewness and the full angular bispectrum _ℓ1ℓ₂ℓ₃ in terms of the slow-roll parameters. We use an estimator for the angular bispectrum recently proposed in the literature and calculate its variance for an arbitrary ℓ _i multipole combination. We stress that a real detection of non-Gaussianity in the CMB would imply that an important component of the anisotropies arises from processes other than primordial quantum fluctuations. We further investigate the behaviour of the signal-to-(theoretical) noise ratio and demonstrate for generic inflationary models that it decreases in the limited range of small ℓs considered for increasing multipole ℓ, while the opposite applies for the standard _ℓs.     

The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, ξ and ζ , in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10  h ⁻¹ Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function   Q ₃∼ ζ / ξ ²  . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ≃20 Mpc  h ⁻¹. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading-order PT become important at smaller scales   r ≃10 Mpc  h ^-1  , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.     

Bayesian calibrated significance levels applied to the spectral tilt and hemispherical asymmetry

Bayesian model selection provides a formal method of determining the level of support for new parameters in a model. However, if there is not a specific enough underlying physical motivation for the new parameters it can be hard to assign them meaningful priors, an essential ingredient of Bayesian model selection. Here we look at methods maximizing the prior so as to work out what is the maximum support the data could give for the new parameters. If the maximum support is not high enough then one can confidently conclude that the new parameters are unnecessary without needing to worry that some other prior may make them significant. We discuss a computationally efficient means of doing this which involves mapping p-values on to upper bounds of the Bayes factor (or odds) for the new parameters. A p-value of 0.05 (1.96σ) corresponds to odds less than or equal to 5:2, which is below the 'weak' support at best threshold. A p-value of 0.0003 (3.6σ) corresponds to odds of less than or equal to 150:1, which is the 'strong' support at best threshold. Applying this method we find that the odds on the scalar spectral index being different from one are 49:1 at best. We also find that the odds that there is primordial hemispherical asymmetry in the cosmic microwave background are 9:1 at best.