The size distribution of void filaments in a ΛCDM cosmology

The size distribution of minifilaments in voids has been derived from the Millennium Run halo catalogues at redshifts   z = 0, 0.5, 1  and 2. It is assumed that the primordial tidal field originated the presence of filamentary substructures in voids and that the void filaments have evolved only little, keeping the initial memory of the primordial tidal field. Applying the filament-finding algorithm based on the minimal spanning tree (MST) technique to the Millennium voids, we identify the minifilaments running through voids and measure their sizes at each redshift. Then, we calculate the comoving number density of void filaments as a function of their sizes in the logarithmic interval and determine an analytic fitting function for it. It is found that the size distribution of void minifilaments in the logarithmic interval,  d N /d log  S   , has an almost universal shape, insensitive to the redshift. In the short-size section, it is well approximated as a power law,  d N /d log  S ≈ S   , while in the long-size section it decreases exponentially as  d N /dlog  S ≈ exp(− S ^α)  . We expect that the universal size distribution of void filaments may provide a useful cosmological probe without resorting to the rms density fluctuations.     

The lepton asymmetry: the last chance for a critical-density cosmology?

We use a wide range of observations to constrain cosmological models possessing a significant asymmetry in the lepton sector, which offer perhaps the best chance of reconciling a critical-density Universe with current observations. The simplest case, with massless neutrinos, fails to fit many experimental data and does not lead to an acceptable model. If the neutrinos have mass of order 1 eV (which is favoured by some neutrino observations), then models can be implemented which prove a good fit to the microwave anisotropies and large-scale structure data. However, taking into account the latest microwave anisotropy results, especially those from BOOMERANG, we show that the model can no longer accommodate the observed baryon fraction in clusters. Together with the observed acceleration of the present Universe, this puts considerable pressure on such critical-density models.     

General relativistic self-similar solutions in cosmology

We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, p , and energy density, μ, in the shock-heated matter are assumed to obey   p = w μ  , where w is a positive constant. Consistent solutions are found for shocks propagating from the symmetry centre of a region of a positive density excess over the background. In these solutions, shocks exist outside the radius marking the event horizon of the black hole which would be present in a shock-less collapse. For large jumps in the energy density at the shock, a black hole is avoided altogether and the solutions are regular at the centre. The shock-heated gas does not contain any sonic points, provided the motion of the cold gas ahead of the shock deviates significantly from the Hubble flow. For shocks propagating in the uniform background, sonic points always appear for small jumps in the energy density. We also discuss self-similar solutions without shocks in fluids with   w < −1/3  .     

On the least action principle in cosmology

Given the present distribution of mass tracing objects in an expanding universe, we develop and test a fast method for recovering their past orbits using the least action principle. In this method, termed FAM for fast action minimization, the orbits are expanded in a set of orthogonal time basis functions satisfying the appropriate boundary conditions at the initial and final times. The conjugate gradient method is applied to locate the extremum of the action in the space of the expansion coefficients of the orbits. The treecode gravity solver routine is used for computing the gravitational field appearing in the action and the potential field appearing in the gradient of the action. The time integration of the Lagrangian is done using Gaussian quadratures. FAM allows us to increase the number of galaxies over previous numerical action principle implementations by more than one order of magnitude. For example, orbits for the 15 000 IRAS PSC z galaxies can be recovered in 12 000 CPU seconds on a 400-MHz DEC-Alpha machine. FAM can recover the present peculiar velocities of particles and the initial fluctuations field. It successfully recovers the flow field down to cluster scales, where deviations of the flow from the Zel'dovich solution are significant. We also show how to recover orbits from the present distribution of objects in redshift space by direct minimization of a modified action, without iterating the solution between real and redshift spaces.     

Evolution of the cosmological density distribution function

We present a new calculation for the evolution of the one-point probability distribution function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman–Kolmogorov equation and second-order Eulerian perturbation theory we propagate the initial density distribution into the non-linear regime. Our calculations yield the moment generating function, allowing a straightforward derivation of the skewness of the PDF to second order. We find a new dependence on the initial perturbation spectrum. We compare our results with other approximations to the one-point PDF, and with N -body simulations. We find that our distribution accurately models the evolution of the one-point PDF of dark matter.     

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.     

Sources of contamination to weak lensing three-point statistics: constraints from N-body simulations

We investigate the impact of the observed correlation between a galaxy's shape and its surrounding density field on the measurement of third-order weak lensing shear statistics. Using numerical simulations, we estimate the systematic error contribution to a measurement of the third-order moment of the aperture mass statistic (GGG) from three-point intrinsic ellipticity correlations (III), and the three-point coupling between the weak lensing shear experienced by distant galaxies and the shape of foreground galaxies (GGI and GII). We find that third-order weak lensing statistics are typically more strongly contaminated by these physical systematics compared to second-order shear measurements, contaminating the measured three-point signal for moderately deep surveys with a median redshift   z _m∼ 0.7  by ∼15 per cent. It has been shown that accurate photometric redshifts will be crucial to correct for this effect, once a model and the redshift dependence of the effect can be accurately constrained. To this end we provide redshift-dependent fitting functions to our results and propose a new tool for the observational study of intrinsic galaxy alignments. For a shallow survey with   z _m∼ 0.4  we find III to be an order of magnitude larger than the expected cosmological GGG shear signal. Compared to the two-point intrinsic ellipticity correlation which is similar in amplitude to the two-point shear signal at these survey depths, third-order statistics therefore offer a promising new way to constrain models of intrinsic galaxy alignments. Early shallow data from the next generation of very wide weak lensing surveys will be optimal for this type of study.     

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 .     

Determination of the linear mass power spectrum from the mass function of galaxy clusters

We develop a new method to determine the linear mass power spectrum using the mass function of galaxy clusters. We obtain the rms mass fluctuation  σ( M )  using the expression for the mass function in the Press & Schechter, Sheth, Mo & Tormen and Jenkins et al. formalisms. We apply different techniques to recover the adimensional power spectrum  Δ²( k )  from  σ( M )  namely the   k _eff  approximation, the singular value decomposition and the linear regularization method. The application of these techniques to the τCDM and ΛCDM GIF simulations shows a high efficiency in recovering the theoretical power spectrum over a wide range of scales. We compare our results with those derived from the power spectrum of the spatial distribution of the same sample of clusters in the simulations obtained by application of the classical Feldman, Kaiser & Peacock (FKP) method. We find that the mass function based method presented here can provide a very accurate estimate of the linear power spectrum, particularly for low values of k . This estimate is comparable to, or even better behaved than, the FKP solution.
The principal advantage of our method is that it allows the determination of the linear mass power spectrum using the joint information of objects of a wide range of masses without dealing with specific assumptions on the bias relative to the underlying mass distribution.