Phenomenological models of cosmic phase transitions II. Application of the classical nucleation theory

Classical nucleation theory is applied to follow the thermal history of a homogeneous and isotropic universe during a first-order phase transition. The dependence of possible supercooling and reheating scenarios on the surface tension and growth velocity of bubbles is discussed.     

Scalar statistics on the sphere: application to the cosmic microwave background

A method to compute several scalar quantities of cosmic microwave background (CMB) maps on the sphere is presented. We consider here four type of scalars: the Hessian matrix scalars, the distortion scalars, the gradient-related scalars and the curvature scalars. Such quantities are obtained directly from the spherical harmonic coefficients   a _{ℓ m}   of the map. We also study the probability density function of these quantities for the case of a homogeneous and isotropic Gaussian field, which are functions of the power spectrum of the initial field. From these scalars it is possible to construct a new set of scalars which are independent of the power spectrum of the field. We test our results using simulations and find good agreement between the theoretical probability density functions and those obtained from simulations. Therefore, these quantities are proposed to investigate the presence of non-Gaussian features in CMB maps. Finally, we show how to compute the scalars in the presence of anisotropic noise and realistic masks.     

Scalar quantities as detectors of non-Gaussianity in cosmic microwave background maps

We study the power of several scalar quantities constructed on the sphere (presented in Monteserín et al.) to detect non-Gaussianity in the temperature distribution of the cosmic microwave background (CMB). The test has been performed using non-Gaussian CMB simulations with injected skewness or kurtosis generated through the Edgeworth expansion. We have also taken into account in the analysis the effect of anisotropic noise and the presence of a Galactic mask. We find that the best scalars to detect an excess of skewness in the simulations are the derivative of the gradient, the fractional isotropy, the Laplacian and the shape index. For the kurtosis case, the fractional anisotropy, the Laplacian and the determinant are the quantities that perform better.     

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.     

Spectroscopic surveys of cosmic evolution

ALMA will be the premier instrument for the study of galaxy evolution in the early universe—enabling studies of the gas content, dynamics and dynamical masses, and star formation with unparalleled resolution and sensitivity. Galaxy evolution and AGN growth in the early universe are believed to be strongly driven by merging and dynamical interactions. Thus, a full exploration of the environmental influence is absolutely essential. The Cosmic Evolution Survey (COSMOS) is specifically designed to probe the correlated coevolution of galaxies, star formation, active galactic nuclei (AGN) and dark matter (DM) large-scale structure (LSS) over the redshift range z>0.5 to 3. In this contribution I review the characteristics of the COSMOS survey and very exciting initial results on mapping large scale structure in galaxies and dark matter. The survey includes multi-wavelength imaging and spectroscopy from X-ray to radio wavelengths covering a 2 square degree equatorial field. Given the very high sensitivity and resolution of these datasets, COSMOS will provide unprecedented samples of objects at z>3 for followup studies wit ALMA.     

Reionization and the large-scale 21-cm cosmic microwave background cross-correlation

Of the many probes of reionization, the 21-cm line and the cosmic microwave background (CMB) are among the most effective. We examine how the cross-correlation of the 21-cm brightness and the CMB Doppler fluctuations on large angular scales can be used to study this epoch. We employ a new model of the growth of large-scale fluctuations of the ionized fraction as reionization proceeds. We take into account the peculiar velocity field of baryons and show that its effect on the cross-correlation can be interpreted as a mixing of Fourier modes. We find that the cross-correlation signal is strongly peaked towards the end of reionization and that the sign of the correlation should be positive because of the inhomogeneity inherent to reionization. The signal peaks at degree scales (ℓ∼ 100) and comes almost entirely from large physical scales ( k ∼ 10⁻² Mpc). Since many of the foregrounds and noise that plague low-frequency radio observations will not correlate with CMB measurements, the cross-correlation might appear to provide a robust diagnostic of the cosmological origin of the 21-cm radiation around the epoch of reionization. Unfortunately, we show that these signals are actually only weakly correlated and that cosmic variance dominates the error budget of any attempted detection. We conclude that the detection of a cross-correlation peak at degree-size angular scales is unlikely even with ideal experiments.     

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.     

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.     

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.     

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.     

Correlations of cosmic tidal fields

We study correlations amongst tidal fields originated by the large-scale distribution of matter in the Universe. The two-point tidal correlation is described as a rank-4 tensor, the elements of which can be written in terms of four fundamental scalar functions ranging, with respect to the spatial separation, from purely transversal to purely longitudinal correlations. Tidal fields, on both galaxy and cluster scales, are revealed to be correlated over distances larger than the mass–density correlation length, although traceless tidal fields show anti-correlation between diagonal terms along orthogonal directions. The cross-correlation between mass and tidal field is also analysed. These results are relevant for galaxy formation and the interpretation of large-scale weak lensing phenomena.     

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.     

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.