Shine the dark ages

Recent WMAP results indicate quite early reionization of the universe. Here we discuss possible implications on CMB anisotropies and CMB polarization of the early reionization.     

Gravitational wave background from neutrino-driven gamma-ray bursts

We study cosmic microwave background (CMB) secondary anisotropies produced by inhomogeneous reionization by means of cosmological simulations coupled with the radiative transfer code crash . The reionization history is consistent with the Wilkinson Microwave Anisotropy Probe Thomson optical depth determination. We find that the signal arising from this process dominates over the primary CMB component for   l ≳ 4000  and reaches a maximum amplitude of   l ( l + 1) C_l /2π≃ 1.6 × 10⁻¹³  on arcmin scales (i.e. l as large as several thousands). We then cross-correlate secondary CMB anisotropy maps with neutral hydrogen 21-cm line emission fluctuations obtained from the same simulations. The two signals are highly anticorrelated on angular scales corresponding to the typical size of H  ii regions (including overlapping) at the 21-cm map redshift. We show how the CMB/21-cm cross-correlation can be used: (i) to study the nature of the reionization sources; (ii) to reconstruct the cosmic reionization history; (iii) to infer the mean cosmic ionization level at any redshift. We discuss the feasibility of the proposed experiment with forthcoming facilities.     

Cosmic microwave background anisotropies resulting from feedback-regulated inhomogeneous reionization

We calculate the secondary anisotropies in the cosmic microwave background (CMB) produced by inhomogeneous reionization from simulations in which the effects of radiative and stellar feedback effects on galaxy formation have been included. This allows us to determine self-consistently the beginning ( z _i≈30), the duration ( δz ≈20) and the (non-linear) evolution of the reionization process for a critical density cold dark matter (CDM) model. In addition, from the simulated spatial distribution of ionized regions, we are able to calculate the evolution of the two-point ionization correlation function, C _χ , and obtain the power spectrum of the anisotropies, C _ℓ, in the range 5000<ℓ<10⁶. The power spectrum has a broad maximum around ℓ≈30 000, where it reaches the value 2×10⁻¹². We also show that the ionization correlation function C _χ is not Gaussian, but at separation angles θ ≲10⁻⁴ rad it can be approximated by a modified Lorentzian shape; at larger separations an anticorrelation signal is predicted for both C _χ and C ( θ ). Detection of signals as above will be possible with future millimetre-wavelength interferometers like the Atacama Large Millimeter Array (ALMA) , which appears as an optimum instrument to search for signatures of inhomogeneous reionization.     

Cosmology from 3 years of WMAP CMB data

The combined 3 year observations from the Wilkinson Microwave Anisotropy Probe (WMAP) have yielded full-sky temperature and polarization maps in five frequency bands (K, Ka, Q, V, W) between 23 and 94 GHz. In this article we discuss the cosmological implications of these observations. The combination of temperature and polarization data leads to a significant improvement in the measurement of the reionization optical depth τ = 0.093 ± 0.029. This, in turn, breaks a number of key degeneracies present in the constraints from temperature measurements alone allowing the WMAP CMB data on its own to offer a powerful insight into the universe’s constituents and the processes that generated the initial conditions for structure formation.     

Modeling the WMAP large-angle anomalies as an effect of a local density inhomogeneity

We investigate large-angle scale temperature anisotropy in the Cosmic Microwave Background (CMB) with the Wilkinson Microwave Anisotropy Probe (WMAP) data and model the large-angle anomalies as the effect of the CMB quadrupole anisotropies caused by the local density inhomogeneities. The quadrupole caused by the local density inhomogeneities is different from the special relativity kinematic quadrupole. If the observer inhabits a strong inhomogeneous region, the local quadrupole should not be neglected. We ...     

Measuring statistical isotropy of CMB anisotropy

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson microwave anisotropy probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian and Souradeep [Hajian, A., Souradeep, T. (2003) Astrophys. J. Lett. 597, L5] for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian and Souradeep [Basak, S., Hajian, A., Souradeep, T. (2006) Phys. Rev. D74, 02130(R)]. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released first WMAP polarization maps, however, indicate significant violation of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.     

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.     

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.     

Detection of OH and wide H i absorption toward B0218+357

Large-scale polarization of the cosmic microwave background measured by the WMAP satellite requires a mean optical depth to Thomson scattering,  τ_e∼ 0.17  . The reionization of the Universe must therefore have begun at relatively high redshift. We have studied the reionization process using supercomputer simulations of a large and representative region of a universe which has cosmological parameters consistent with the WMAP results (  Ω_m= 0.3, Ω_Λ= 0.7, h = 0.7, Ω_b= 0.04, n = 1  and  σ₈= 0.9  ). Our simulations follow both the radiative transfer of ionizing photons and the formation and evolution of the galaxy population which produces them. A previously published model with ionizing photon production as expected for zero-metallicity stars distributed according to a standard stellar initial mass function (IMF) (10⁶¹ photons per unit solar mass of formed stars) and with a moderate photon escape fraction from galaxies (5 per cent), produces  τ_e= 0.104  , which is within 1.0 to  1.5σ  of the 'best' WMAP value. Values of up to 0.16 can be produced by taking larger escape fractions or a top-heavy IMF. The data do not require a separate populations of 'miniquasars' or of stars forming in objects with total masses below  10⁹ M_⊙  . Reconciling such early reionization with the observed Gunn–Peterson troughs in   z > 6  quasars may be challenging. Possible resolutions of this problem are discussed.     

Microwave polarization in the direction of galaxy clusters induced by the CMB quadrupole anisotropy

Electron scattering induces a polarization in the cosmic microwave background (CMB) signal measured in the direction of a galaxy cluster owing to the presence of a quadrupole component in the CMB temperature distribution. Measuring the polarization towards distant clusters provides the unique opportunity to observe the evolution of the CMB quadrupole at moderate redshifts, z ∼0.5–3. We demonstrate that for the local cluster population the polarization degree will depend on the cluster celestial position. There are two extended regions in the sky, which are opposite to each other, where the polarization is maximal, ∼0.1( τ /0.02) μK in the Rayleigh–Jeans part of the CMB spectrum ( τ being the Thomson optical depth across the cluster). This value exceeds the polarization introduced by the cluster transverse peculiar motion if v _t<1300 km s⁻¹. One can hope to detect this small signal by measuring a large number of clusters, thereby effectively removing the systematic contribution from other polarization components produced in clusters. These polarization effects, which are of the order of ( v _t c )² τ , ( v _t c ) τ ² and ( kT _e m _e c ²) τ ², as well as the polarization owing to the CMB quadrupole, were previously given by Sunyaev and Zel'dovich for the Rayleigh–Jeans part of the spectrum. We fully confirm their earlier results and present exact frequency dependences for all these effects. The polarization degree is considerably higher in the Wien region.     

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.     

Wilkinson Microwave Anisotropy Probe 5-yr constraints on fnl with wavelets

We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f _nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ²  analysis. The  χ²  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f _nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f _nl parameter is constrained to  −8 < f _nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f _nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.     

Non-Gaussianity detections in the Bianchi VIIh corrected WMAP one-year data made with directional spherical wavelets

Many of the current anomalies reported in the WMAP text ( WMAP ) one-year data disappear after 'correcting' for the best-fitting embedded Bianchi type VII _h component, albeit assuming no dark energy component. We investigate the effect of this Bianchi correction on the detections of non-Gaussianity in the WMAP data that we previously made using directional spherical wavelets. We confirm that the deviations from Gaussianity in the kurtosis of spherical Mexican hat wavelet coefficients are eliminated once the data are corrected for the Bianchi component, as previously discovered by Jaffe et al. This is due to the reduction of the cold spot at Galactic coordinates  ( l , b ) = (209°, −57°)  , which Cruz et al. claimed to be the sole source of non-Gaussianity introduced in the kurtosis. Our previous detections of non-Gaussianity observed in the skewness of spherical wavelet coefficients are not reduced by the Bianchi correction. Indeed, the most significant detection of non-Gaussianity made with the spherical real Morlet wavelet at a significant level of 98.4 per cent remains (using a very conservative method to estimate the significance). Furthermore, we perform preliminary tests to determine if foregrounds or systematics are the source of this non-Gaussian signal, concluding that it is unlikely that these factors are responsible. We make our code to simulate Bianchi-induced temperature fluctuations publicly available.     

Primordial magnetic fields in the post-recombination era and early reionization

We explore the ways in which primordial magnetic fields influence the thermal and ionization history of the post-recombination Universe. After recombination, the Universe becomes mostly neutral, resulting also in a sharp drop in the radiative viscosity. Primordial magnetic fields can then dissipate their energy into the intergalactic medium via ambipolar diffusion and, for small enough scales, by generating decaying magnetohydrodynamics turbulence. These processes can significantly modify the thermal and ionization history of the post-recombination Universe. We show that the dissipation effects of magnetic fields, which redshifts to a present value   B ₀= 3 × 10⁻⁹ G  smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths  τ≳ 0.1  , although not in the range of redshifts needed to explain the recent Wilkinson Microwave Anisotropy Probe ( WMAP ) polarization observations. We also study the possibility that primordial fields could induce the formation of subgalactic structures for   z ≳ 15  . We show that early structure formation induced by nanoGauss magnetic fields is potentially capable of producing the early reionization implied by the WMAP data. Future cosmic microwave background observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength.     

Status of CMB polarization measurements from DASI and other experiments

We review the current status and future plans for polarization measurements of the cosmic microwave background radiation, as well as the cosmology these measurements will address. After a long period of increasingly sensitive upper limits, the DASI experiment has detected the E-mode polarization and both the DASI and WMAP experiments have detected the TE correlation. These detections provide confirmation of the standard model of adiabatic primordial density fluctuations consistent with inflationary models. The WMAP TE correlation on large angular scales provides direct evidence of significant reionization at higher redshifts than had previously been supposed. These detections mark the beginning of a new era in CMB measurements and the rich cosmology that can be gleaned from them.     

Limits on isocurvature perturbations from non-Gaussianity in WMAP temperature anisotropy

We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB) temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable  σ,  S =σ²−〈σ²〉  , can give the same signal-to-noise ratio as   f _NL= 30  even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum α. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction  α < 0.070  (95 per cent CL) for a scale-invariant spectrum which is comparable to the limit obtained from the power spectrum.     

The cross-correlation of the CMB polarization and the 21-cm line fluctuations from cosmic reionization

The cosmic microwave background (CMB) polarization and the 21-cm line fluctuations are powerful probes of cosmological reionization. We study how the cross-correlation between the CMB polarization ( E modes) and the 21-cm line fluctuations can be used to gain further understanding of the reionization history, within the framework of inhomogeneous reionization. Since the E -mode polarization reflects the amplitude of the quadrupole component of the CMB temperature fluctuations, the angular power spectrum of the cross-correlation exhibits oscillations at all multipoles. The first peak of the power spectrum appears at the scale corresponding to the quadrupole at the redshift, which is probed by the 21-cm line fluctuations. The peak reaches its maximum value in redshift when the average ionization fraction of the universe is about half. On the other hand, on small scales, there is a damping that depends on the duration of reionization. Thus, the cross-correlation between the CMB polarization and the 21-cm line fluctuations has the potential to accurately constrain the epoch and the duration of reionization.     

Fossil H ii regions: self-limiting star formation at high redshift

Recent results from the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite suggest that the intergalactic medium (IGM) was significantly reionized at redshifts as high as   z ∼ 17  . At this early epoch, the first ionizing sources probably appeared in the shallow potential wells of mini-haloes with virial temperatures   T _vir < 10⁴ K  . Once such an ionizing source turns off, its surrounding H ii region Compton cools and recombines. None the less, we show that the 'fossil' H ii regions left behind remain at high adiabats, prohibiting gas accretion and cooling in subsequent generations of mini-haloes. This greatly amplifies feedback effects explored in previous studies, and early star formation is self-limiting. We quantify this effect to show that star formation in mini-haloes cannot account for the bulk of the electron scattering opacity measured by WMAP , which must be due to more massive objects. We argue that gas entropy, rather than IGM metallicity, regulates the evolution of the global ionizing emissivity and impedes full reionization until lower redshifts. We discuss several important consequences of this early entropy floor for reionization. It reduces gas clumping, curtailing the required photon budget for reionization. An entropy floor also prevents H₂ formation and cooling, due to reduced gas densities: it greatly enhances feedback from ultraviolet photodissociation of H₂. An early X-ray background would also furnish an entropy floor to the entire IGM; thus, X-rays impede rather than enhance H₂ formation. Future 21-cm observations may probe the topology of fossil H ii regions.     

Lensed CMB temperature and polarization maps from the Millennium Simulation

We have constructed the first all-sky cosmic microwave background (CMB) temperature and polarization lensed maps based on a high-resolution cosmological N -body simulation, the Millennium Simulation (MS). We have exploited the lensing potential map obtained using a previously developed map-making procedure which integrates along the line-of-sight the MS dark matter distribution by stacking and randomizing the simulation boxes up to   z = 127  , and which semi-analytically supplies the large-scale power in the angular lensing potential that is not correctly sampled by the N -body simulation. The lensed sky has been obtained by properly modifying the latest version of the LensPix code to account for the MS structures. We have also produced all-sky lensed maps of the so-called  ψ _E   and  ψ _B   potentials, which are directly related to the electric and magnetic types of polarization. The angular power spectra of the simulated lensed temperature and polarization maps agree well with semi-analytic estimates up to   l ≤ 2500  , while on smaller scales we find a slight excess of power which we interpret as being due to non-linear clustering in the MS. We also observe how non-linear lensing power in the polarized CMB is transferred to large angular scales by suitably misaligned modes in the CMB and the lensing potential. This work is relevant in view of the future CMB probes, as a way to analyse the lensed sky and disentangle the contribution from primordial gravitational waves.     

An Australia Telescope survey for CMB anisotropies

We have surveyed six distinct 'empty fields' using the Australia Telescope Compact Array (ATCA) in an ultracompact configuration with the aim of imaging, with a high brightness sensitivity, any arcminute-scale brightness-temperature anisotropies in the background radio sky. The six well-separated regions were observed at a frequency of 8.7 GHz, and the survey regions were limited by the ATCA primary beams which have a full width at half-maximum of 6 arcmin at this frequency; all fields were observed with a resolution of 2 arcmin and an rms thermal noise of 24 μJy beam⁻¹. After subtracting foreground confusion detected in higher resolution images of the fields, residual fluctuations in Stokes I images are consistent with the expectations from thermal noise and weaker (unidentified) foreground sources; the Stokes Q and U images are consistent with expectations from thermal noise.
Within the sensitivity of our observations, we have no reason to believe that there are any Sunyaev–Zeldovich holes in the microwave sky surveyed. Assuming Gaussian-form CMB anisotropy with a 'flat' spectrum, we derive 95 per cent confidence upper limits of Q _flat<10–11 μK in polarized intensity and Q _flat<25 μK in total intensity. The ATCA filter function peaks at l =4700 and has half-maximum values at l =3350 and 6050.