The cosmic microwave background for a nearly flat compact hyperbolic universe

The fluctuations of the cosmic microwave background (CMB) are investigated for a hyperbolic universe with finite volume. Four-component models with radiation, matter, vacuum energy and an extra spatially constant dark energy X -component are considered. The general solution of the Friedmann equation for the cosmic scalefactor a ( η ) is given for the four-component models in terms of the Weierstrass ℘-function. The lower parts of the angular power spectra C _l of the CMB anisotropy are computed for nearly flat models with Ω_tot≤0.95. It is shown that the particular compact fundamental cell that is considered in this paper leads to a suppression in C _l for l ≲10 and Ω_tot≲0.9.     

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.     

Ironing out primordial temperature fluctuations with polarization: optimal detection of cosmic structure imprints

Secondary anisotropies of the cosmic microwave background (CMB) can be detected by using the cross-correlation between the large-scale structure (LSS) and the CMB temperature fluctuations. In such studies, chance correlations of primordial CMB fluctuations with the LSS are the main source of uncertainty. We present a method for reducing this noise by exploiting information contained in the polarization of CMB photons. The method is described in general terms and then applied to our recently proposed optimal method for measuring the integrated Sachs–Wolfe (ISW) effect. We obtain an expected signal-to-noise ratio of up to 8.5. This corresponds to an enhancement of the signal-to-noise ratio by 23 per cent as compared to the standard method for ISW detection, and by 16 per cent w.r.t. our recently proposed method, both for the best-case scenario of having perfect (noiseless) CMB and LSS data.     

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.     

Is the CMB shift parameter connected with the growth of cosmological perturbations?

We verify numerically that in the context of general relativity (GR), flat models which have the same Ω_m and cosmic microwave background (CMB) shift parameter R but different   H ( a )  and w ( a ) also have very similar (within less than 8 per cent) growth of perturbations even though the dark energy density evolution is quite different. This provides a direct connection between geometrical and dynamical tests of dark energy and may be used as a cosmological test of GR.     

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.     

On the APM power spectrum and the CMB anisotropy: evidence for a phase transition during inflation?

Adams et al. have noted that according to our current understanding of the unification of fundamental interactions, there should have been phase transitions associated with spontaneous symmetry breaking during the inflationary era. This may have resulted in the breaking of scale-invariance of the primordial density perturbation for brief periods. A possible such feature was identified in the power spectrum of galaxy clustering in the automated plate measurement (APM) survey at the scale k  ∼ 0.1  h  Mpc ^− 1 and it was shown that the secondary acoustic peaks in the power spectrum of the cosmic microwave background (CMB) anisotropy should consequently be suppressed. We demonstrate that this prediction is confirmed by the recent Boomerang and Maxima observations, which favour a step-like spectral feature in the range k  ∼ (0.06–0.6)  h  Mpc ^− 1 , independently of the similar previous indication from the APM data. Such a spectral break enables an excellent fit to both APM and CMB data with a baryon density consistent with the big bang nucleosynthesis (BBN) value. It also allows the possibility of a matter-dominated universe with zero cosmological constant, which we show can now account for even the evolution of the abundance of rich clusters.     

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 .     

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.     

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.     

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 .     

Mixed three-point correlation functions of the non-linear integrated Sachs–Wolfe effect and their detectability

In this paper, I investigate the family of mixed three-point correlation functions  〈τ ^q γ^{3− q} 〉, q = 0, 1, 2  , between the integrated Sachs–Wolfe (iSW) temperature perturbation τ and the galaxy overdensity γ as a tool for detecting the gravitational interaction of cosmic microwave background (CMB) photons with the potentials of non-linearly evolving cosmological structures. Both the iSW-effect and the galaxy overdensity are derived in hyperextended perturbation theory to second order and I emphasize the different parameter sensitivities of the linear and non-linear iSW-effect. I examine the configuration dependence of the relevant bispectra, quantify their sensitivities and discuss their degeneracies with respect to the cosmological parameters  Ω_m, σ₈, h   and the dark energy equation of state parameter w . I give detection significances for combining Planck CMB data and galaxy sample of a survey like Dark UNiverse Explorer (DUNE) by using a quadratic approximation for the likelihood with Λ cold dark matter (ΛCDM) as the fiducial cosmology: the combination of Planck with DUNE should be able to reach a cumulative signal-to-noise ratio of ≃0.6 for the bispectrum  〈τγ²〉  up to ℓ= 2000, which is too weak to be detected. The most important noise source is the primary CMB fluctuations as the Poisson noise in the galaxy number density is almost negligible for a survey like DUNE.     

Can non-linear structure form at the era of decoupling?

The effects of large-scale fluctuations on small-scale isothermal modes at the epoch of recombination are analysed. We find the following. (a) Albeit the fact that primordial fluctuations were at this epoch still well in the linear regime, a significant non-linear radiation hydrodynamic interaction could have taken place. (b) Short-wavelength isothermal fluctuations are unstable. Their growth rate is an exponential function of the amplitude of the large-scale fluctuations and is therefore very sensitive to the initial conditions. (c) The observed cosmic microwave background radiation (CMBR) fluctuations are of order of the limit above which the effect should be significant. Thus, depending on their exact value, the effect may be negligible or lead to structure formation out of the isothermal fluctuations within the period of recombination. (d) If the cosmological parameters are within the prescribed regime, the effect should be detectable through induced deviations in the Planck spectrum. (e) The sensitivity of the effect to the initial conditions provides a tool to set limits on various cosmological parameters with emphasis on the type and amplitude of the primordial fluctuation spectrum. (f) Under proper conditions, the effect may be responsible for the formation of sub-globular-cluster sized objects at particularly high redshifts. (g) Under certain circumstances, it can also affect horizon-sized large-scale structure.