Large-scale cosmic microwave background anisotropies and dark energy

In this paper we investigate the effects of perturbations in a dark energy component with a constant equation of state on large-scale cosmic microwave background (CMB) anisotropies. The inclusion of perturbations increases the large-scale power. We investigate more speculative dark energy models with   w < −1  and find the opposite behaviour. Overall the inclusion of perturbations in the dark energy component increases the degeneracies. We generalize the parametrization of the dark energy fluctuations to allow for an arbitrary constant sound speed, and we show how constraints from CMB experiments change if this is included. Combining CMB with large-scale structure, Hubble parameter and supernovae observations we obtain   w =−1.02 ± 0.16 (1σ)  as a constraint on the equation of state, which is almost independent of the sound speed chosen. With the presented analysis we find no significant constraint on the constant speed of sound of the dark energy component.     

The statistical significance of the low cosmic microwave background mulitipoles

The Wilkinson Microwave Anisotropy Probe ( WMAP ) has measured lower amplitudes for the temperature quadrupole and octopole anisotropies than expected in the best fitting (concordance) Λ-dominated cold dark matter (ΛCDM) cosmology. Some authors have argued that this discrepancy may require new physics. However, the statistical significance of this result is not clear. Some authors have applied frequentist arguments and claim that the discrepancy would occur by chance about 1 time in 700, if the concordance model is correct. Other authors have used Bayesian arguments to claim that the data show marginal evidence for new physics. I investigate these confusing and apparently conflicting claims in this Letter using a frequentist analysis and a simplified Bayesian analysis. On either analysis, I conclude that the WMAP results are consistent with the concordance ΛCDM model.     

Constraints on cosmological parameters from recent measurements of cosmic microwave background anisotropy

A key prediction of cosmological theories for the origin and evolution of structure in the Universe is the existence of a 'Doppler peak' in the angular power spectrum of cosmic microwave background (CMB) fluctuations. We present new results from a study of recent CMB observations which provide the first strong evidence for the existence of a 'Doppler peak' localized in both angular scale and amplitude. This first estimate of the angular position of the peak is used to place a new direct limit on the curvature of the Universe, corresponding to a density of Ω = 0.7^+0.8_−0.5, consistent with a flat universe. Very low-density 'open' universe models are inconsistent with this limit unless there is a significant contribution from a cosmological constant. For a flat standard cold dark matter dominated universe we use our results in conjunction with big bang nucleosynthesis constraints to determine the value of the Hubble constant as H ₀ = 30 − 70 km s⁻¹ Mpc⁻¹ for baryon fractions Ω_b = 0.05 to 0.2. For H ₀ = 50 km s⁻¹ Mpc⁻¹ we find the primordial spectral index of the fluctuations to be n  = 1.1 ± 0.1, in close agreement with the inflationary prediction of n  ≃ 1.0.     

The location of cosmic microwave background peaks in a universe with dark energy

The locations of the peaks of the cosmic microwave background (CMB) spectrum are sensitive indicators of cosmological parameters, yet there is no known analytic formula which accurately describes their dependence on them. We parametrize the location of the peaks as   l _m = l _A( m - φ _m )  , where l _A is the analytically calculable acoustic scale and m labels the peak number. Fitting formulae for the phase shifts φ _m for the first three peaks and the first trough are given. It is shown that in a wide range of parameter space, the acoustic scale l _A can be retrieved from actual CMB measurements of the first three peaks within 1 per cent accuracy. This can be used to speed up likelihood analysis. We describe how the peak shifts can be used to distinguish between different models of dark energy.     

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.     

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.     

Principal-component analysis of the cosmic microwave background anisotropies: revealing the tensor degeneracy

A principal-component analysis of cosmic microwave background (CMB) anisotropy measurements is used to investigate degeneracies among cosmological parameters. The results show that a degeneracy with tensor modes – the 'tensor degeneracy'– dominates uncertainties in estimates of the baryon and cold dark matter densities,   ω _b=Ω_b  h ²  ,   ω _c=Ω_c  h ²  , ¹ from an analysis of CMB anisotropies alone. The principal-component analysis agrees well with a maximum-likelihood analysis of the observations, identifying the main degeneracy directions and providing an impression of the effective dimensionality of the parameter space.     

Decay of the vacuum energy into cosmic microwave background photons

We examine the possibility of the decay of the vacuum energy into a homogeneous distribution of a thermalized cosmic microwave background (CMB), which is characteristic of an adiabatic vacuum energy decay into photons. It is shown that observations of the primordial density fluctuation spectrum, obtained from CMB and galaxy distribution data, restrict the possible decay rate. When photon creation due to an adiabatic vacuum energy decay takes place, the standard linear temperature dependence   T ( z ) = T ₀(1 + z )  is modified, where T ₀ is the present CMB temperature, and can be parametrized by a modified CMB temperature dependence     . From the observed CMB and galaxy distribution data, a strong limit on the maximum value of the decay rate is obtained by placing a maximum value  β_max≃ 3.4 × 10⁻³  on the β parameter.     

Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.     

Circular scans for cosmic microwave background anisotropy observation and analysis

A number of experiments for measuring anisotropies of the cosmic microwave background (CMB) use scanning strategies in which temperature fluctuations are measured along circular scans on the sky. It is possible, from a large number of such intersecting circular scans, to build two-dimensional sky maps for subsequent analysis. However, since instrumental effects — especially the excess low-frequency 1/ f noise — project on to such two-dimensional maps in a non-trivial way, we discuss the analysis approach which focuses on information contained in the individual circular scans. This natural way of looking at CMB data from experiments scanning on the circles combines the advantages of elegant simplicity of Fourier series for the computation of statistics useful for constraining cosmological scenarios, and superior efficiency in analysing and quantifying most of the crucial instrumental effects.     

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially flat cosmologies, varying the matter density Ω₀ (the flatness being restored by a cosmological constant), the Hubble parameter h and the spectral index n of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently favoured low-density model with Ω₀=0.3 and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits that we quote.     

Large-scale structure, the cosmic microwave background and primordial non-Gaussianity

Cosmic microwave background and large-scale structure data will shortly improve dramatically with the Microwave Anisotropy Probe and Planck Surveyor , and the Anglo-Australian 2-Degree Field and Sloan Digital Sky Survey. It is therefore timely to ask which of the microwave background and large-scale structure will provide a better probe of primordial non-Gaussianity. In this paper we consider this question, using the bispectrum as a discriminating statistic. We consider several non-Gaussian models and find that in each case the microwave background will provide a better probe of primordial non-Gaussianity. Our results suggest that if microwave background maps appear Gaussian, then apparent deviations from Gaussian initial conditions in galaxy surveys can be attributed with confidence to the effects of biasing. We demonstrate this precisely for the spatial bispectrum induced by local non-linear biasing.