Early reionization with primordial magnetic fields

Early reionization of the intergalactic medium (IGM), which is favoured from the WMAP temperature–polarization cross-correlations, contests the validity of the standard scenario of structure formation in the cold dark matter (CDM) cosmogony. It is difficult to achieve early enough star formation without rather extreme assumptions such as a very high escape fraction of ionizing photons from protogalaxies or a top-heavy initial mass function (IMF). Here, we propose an alternative scenario that additional fluctuations on small scales induced by primordial magnetic fields trigger early structure formation. We found that ionizing photons from Population III stars formed in dark haloes can easily reionize the Universe by   z ≃ 15  if the strength of primordial magnetic fields is between 0.7 and  1.5 × 10⁻⁹ G  .     

Old high-redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at z  ≃ 1.5 which have apparent stellar ages of ≳ 3 Gyr, based on detailed spectroscopy in the rest-frame ultraviolet. In order for galaxies to have existed at the high collapse redshifts indicated by these ages, there must be a minimum level of power in the density fluctuation spectrum on galaxy scales. This paper compares the required power with that inferred from other high-redshift populations: damped Lyα absorbers and Lyman-limit galaxies at z  ≃ 3.2. If the collapse redshifts for the old red galaxies are in the range z _c ≃ 6–8, there is general agreement between the various tracers on the required inhomogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately ν ≃ 3.0 fluctuations, implying a very large bias parameter b  ≃ 6. If the collapse redshifts of the red galaxies are indeed in the range z _c = 6–8 required for power spectrum consistency, their implied ages at z  ≃ 1.5 are between 3 and 3.8 Gyr for essentially any model universe of current age 14 Gyr. The age of these objects as deduced from gravitational collapse thus provides independent support for the ages estimated from their stellar populations. Such early-forming galaxies are rare, and their contribution to the cosmological stellar density is consistent with an extrapolation to higher redshifts of the star formation rate measured at z  < 5; there is no evidence for a general era of spheroid formation at extreme redshifts.     

Seed magnetic Fields Generated by Primordial Supernova Explosions

The origin of the magnetic field in galaxies is an open question in astrophysics. Several mechanisms have been proposed related, in general, to the generation of small seed fields amplified by a dynamo mechanism. In general, these mechanisms have difficulty in satisfying both the requirements of a sufficiently high strength for the magnetic field and the necessary large coherent scales. We show that the formation of dense and turbulent shells of matter, in the multiple explosion scenario of Miranda &38; Opher for the formation of the large-scale structures of the Universe, can naturally act as a seed for the generation of a magnetic field. During the collapse and explosion of Population III objects, a temperature gradient not parallel to a density gradient can naturally be established, producing a seed magnetic field through the Biermann battery mechanism. We show that seed magnetic fields ∼ 10⁻¹²–10⁻¹⁴ G can be produced in this multiple explosion scenario on scales of the order of clusters of galaxies (with coherence length L  ∼ 1.8 Mpc) and up to ∼ 4.5 × 10⁻¹⁰ G on scales of galaxies ( L  ∼ 100 kpc).     

Self-consistent gravitational lens reconstruction

We present a new method for directly determining accurate, self-consistent cluster lens mass and shear maps in the strong lensing regime from the magnification bias of background galaxies. The method relies upon pixellization of the surface mass density distribution which allows us to write down a simple, solvable set of equations. We also show how pixellization can be applied to methods of mass determination from measurements of shear and present a simplified method of application. The method is demonstrated with cluster models and applied to magnification data from the lensing cluster Abell 1689.     

Large-scale magnetic fields: galaxy two-point correlation function

We study the effect of large-scale tangled magnetic fields on the galaxy two-point correlation function in the redshift space. We show that (i) the magnetic field effects can be comparable to the gravity-induced clustering for present magnetic field strength   B ₀≃ 5 × 10⁻⁸ G  , (ii) the absence of this signal from the present data gives an upper bound   B ₀≲ 3 × 10⁻⁸ G  and (iii) the future data can probe the magnetic fields of  ≃10⁻⁸ G  . A comparison with other constraints on the present magnetic field shows that they are marginally compatible. However, if the magnetic fields corresponding to   B ₀≃ 10⁻⁸ G  existed at the last scattering surface, they will cause unacceptably large cosmic microwave background radiation anisotropies.     

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.     

Dark energy and the evolution of spherical overdensities

We use the non-linear spherical model in cold dark matter (CDM) cosmologies with dark energy to investigate the effects of dark energy on the growth of structure and the formation of virialized structures. We consider dark energy models with a constant equation-of-state parameter w . For  −1 < w < −1/3  , clusters form earlier and are more concentrated in quintessence than in ΛCDM models, but they form later and are less concentrated than in the corresponding open model with the same matter density and no dark energy. We point out some confusion in the literature around the expression of the collapse factor (ratio of the radius of the sphere at virialization to that at turnaround) derived from the virial theorem. We use the Sheth & Tormen extension of the Press–Schechter framework to calculate the evolution of the cluster abundance in different models and show the sensitivity of the cluster abundance to both the amplitude of the mass fluctuations, σ₈, and the σ₈– w normalization, selected to match either the cosmic microwave background observations or the abundance of X-ray clusters.     

Recovery of the cosmological peculiar velocity from the density field in the weakly non-linear regime

Using third-order perturbation theory, we derive a relation between the divergence of the peculiar velocity and the density. Specifically, we compute the expectation value of the divergence given density. Our calculations assume Gaussian initial conditions and are valid for Gaussian filtering of the evolved density and velocity fields. The mean velocity divergence turns out to be a third-order polynomial in the density contrast. We test the power-spectrum dependence of the coefficients of the polynomial for scale-free and standard CDM spectra and find it rather weak. Over scales larger than about 5  h ⁻¹ Mpc, the scatter in the relation is small compared with that introduced by random errors in the observed density and velocity fields. The relation can be useful for recovering the peculiar velocity from the associated density field, and also for non-linear analyses of the anisotropies of structure in redshift surveys.     

Tests for primordial non-Gaussianity

We investigate the relative sensitivities of several tests for deviations from Gaussianity in the primordial distribution of density perturbations. We consider models for non-Gaussianity that mimic that which comes from inflation as well as that which comes from topological defects. The tests we consider involve the cosmic microwave background (CMB), large-scale structure, high-redshift galaxies, and the abundances and properties of clusters. We find that the CMB is superior at finding non-Gaussianity in the primordial gravitational potential (as inflation would produce), while observations of high-redshift galaxies are much better suited to find non-Gaussianity that resembles that expected from topological defects. We derive a simple expression that relates the abundance of high-redshift objects in non-Gaussian models to the primordial skewness.     

Towards breaking the Ω-bias degeneracy in density–velocity comparisons

I derive a second-order local relation between the redshift-space mass density field and the real-space velocity field. This relation can be useful for comparisons between the cosmic density and peculiar velocity fields, for a number of reasons. First, relating the real-space velocity directly to the redshift-space density enables one to avoid the Ω-dependent reconstruction of the density field in real space. Secondly, the reconstruction of the three-dimensional velocity field in redshift space, questionable because of its vorticity, is also unnecessary. Finally, a similar relation between the galaxy density field and the velocity field offers a way to break the Ω-bias degeneracy in density–velocity comparisons, when combined with an additional measurement of the redshift-space galaxy skewness. I derive the latter relation under the assumption of non-linear but local bias; accounting for stochasticity of bias is left for further study.     

Angular cross-correlation of galaxies: a probe of gravitational lensing by large-scale structure

The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise as a result of spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line of sight. The lensing contribution to the two-point autocorrelation function is typically small compared with the gravitational clustering. However, the cross-correlation between two galaxy samples is almost unaffected by gravitational clustering provided that their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias resulting from lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of ≃0.3 and 1, we find a cross-correlation signal of ≃1 per cent on arcmin scales and ≃3 per cent on scales of a few arcsec. The dependence on the cosmological parameters Ω and Λ, the dark matter power spectrum and the bias factor of the foreground galaxy population is explored.     

A primordial feature at the scale of superclusters of galaxies

We investigate a spatially flat cold dark matter model (with the matter density parameter     with a primordial feature in the initial power spectrum. We assume that there is a bump in the power spectrum of density fluctuations at wavelengths     , which corresponds to the scale of superclusters of galaxies . There are indications for such a feature in the power spectra derived from redshift surveys and also in the power spectra derived from peculiar velocities of galaxies. We study the mass function of clusters of galaxies, the power spectrum of the cosmic microwave background (CMB) temperature fluctuations, the rms bulk velocity and the rms peculiar velocity of clusters of galaxies. The baryon density is assumed to be consistent with the big bang nucleosynthesis value. We show that with an appropriately chosen feature in the power spectrum of density fluctuations at the scale of superclusters, the mass function of clusters, the CMB power spectrum, the rms bulk velocity and the rms peculiar velocity of clusters are in good agreement with the observed data.