Non-linear evolution of suppressed dark matter primordial power spectra

We address the degree and rapidity of generation of small-scale power over the course of structure formation in cosmologies where the primordial power spectrum is strongly suppressed beyond a given wavenumber. We first summarize the situations where one expects such suppressed power spectra and point out their diversity. We then employ an exponential cut-off, which characterizes warm dark matter (WDM) models, as a template for the shape of the cut-off and focus on damping scales ranging from 10⁶ to  10⁹  h ⁻¹ M_⊙  . Using high-resolution simulations, we show that the suppressed part of the power spectrum is quickly (re)generated and catches up with both the linear and the non-linear evolution of the unsuppressed power spectrum. From   z = 2  onwards, a power spectrum with a primordial cut-off at  10⁹  h ⁻¹ M_⊙  becomes virtually indistinguishable from an evolved cold dark matter (CDM) power spectrum. An attractor such as that described in Zaldarriaga, Scoccimarro & Hui for power spectra with different spectral indices also emerges in the case of truncated power spectra. Measurements of   z ∼ 0  non-linear power spectra at  ∼100  h ⁻¹ kpc  cannot rule out the possibility of linear power spectra damped below  ∼10⁹  h ⁻¹ M_⊙  . Therefore, WDM or scenarios with similar features should be difficult to exclude in this way.     

Power spectrum analysis of the ESO Slice Project galaxy redshift survey

We measure the power spectrum of the galaxy distribution in the ESO Slice Project (ESP) galaxy redshift survey. We develop a technique to describe the survey window function analytically, and then deconvolve it from the measured power spectrum using a variant of the Lucy method. We test the whole deconvolution procedure on ESP mock catalogues drawn from large N -body simulations, and find that it is reliable for recovering the correct amplitude and shape of P ( k ) at k >0.065  h  Mpc⁻¹. In general, the technique is applicable to any survey composed of a collection of circular fields with an arbitrary pattern on the sky, as typical of surveys based on fibre spectrographs. The estimated power spectrum has a well-defined power-law shape k ⁿ with n ≃−2.2 for k ≥0.2  h  Mpc⁻¹, and a smooth bend to a flatter shape ( n ≃−1.6) for smaller k . The smallest wavenumber where a meaningful reconstruction can be performed ( k ∼0.06  h  Mpc⁻¹) does not allow us to explore the range of scales where other power spectra seem to show a flattening and hint at a turnover. We also find, by a direct comparison of the Fourier transforms, that the estimate of the two-point correlation function ξ ( s ) is much less sensitive to the effect of a problematic window function, such as that of the ESP, than the power spectrum. Comparison with other surveys shows an excellent agreement with estimates from blue-selected surveys. In particular, the ESP power spectrum is virtually indistinguishable from that of the Durham–UKST survey over the common range of k , an indirect confirmation of the quality of the deconvolution technique applied.     

The real-space power spectrum of the PSCz survey from 0.01 to 300 h Mpc−1

We report a measurement of the real-space (not redshift-space) power spectrum of galaxies over four and a half decades of wavenumber, 0.01 to 300  h  Mpc⁻¹, from the IRAS Point Source Catalog Redshift Survey (PSC z ). Since estimates of power are highly correlated in the non-linear regime, we also report results for the pre-whitened power spectrum, which is less correlated. The inferred bias between optically selected APM and IRAS -selected PSC z galaxies is about 1.15 at linear scales ≲0.3  h  Mpc⁻¹, increasing to about 1.4 at non-linear scales ≳1  h  Mpc⁻¹. The non-linear power spectrum of PSC z shows a near power-law behaviour to the smallest scales measured, with possible mild upward curvature in the broad vicinity of   k ∼2  h  Mpc⁻¹  . Contrary to the prediction of unbiased dark matter models, there is no prominent inflection at the linear to non-linear transition scale, and no turnover at the transition to the virialized regime. The non-linear power spectrum of PSC z requires scale-dependent bias: all Dark Matter models without scale-dependent bias are ruled out with high confidence.     

The power spectrum of flux-limited X-ray galaxy cluster surveys

We compute the redshift space power spectrum of two X-ray cluster samples: the X-ray Brightest Abell Cluster Sample (XBACS) and the Brightest Cluster Sample (BCS) using the method developed by Feldman, Kaiser & Peacock. The power spectra derived for these samples are in agreement with determinations of other optical and X-ray cluster samples. For XBACS we find the largest power spectrum amplitude expected, given the high richness of this sample ( R ≥2) . In the range 0.05< k <0.4  h  Mpc⁻¹ the power spectrum shows a power-law behaviour P ( k )∝ k ⁿ with an index n ≃−1.2 . In a similar range, 0.04< k <0.3  h  Mpc⁻¹ , the BCS power spectrum has a smaller amplitude with index n ≃−1.0 . We do not find significant evidence for a peak at k ≃0.05  h  Mpc⁻¹ , suggesting that claims such of feature detections in some cluster samples could rely on artificial inhomogeneities of the data. We compare our results with power spectrum predictions derived by Moscardini et al. within current cosmological models (LCDM and OCDM). For XBACS we find that both models underestimate the amplitude of the power spectrum but for BCS there is reasonably good agreement at k ≳0.03  h  Mpc⁻¹ for both models.     

Scale-dependent bias induced by local non-Gaussianity: a comparison to N-body simulations

We investigate the effect of primordial non-Gaussianity of the local f _NL type on the auto- and cross-power spectra of dark matter haloes using simulations of the Λ cold dark matter cosmology. We perform a series of large N -body simulations of both positive and negative f _NL, spanning the range between 10 and 100. Theoretical models predict a scale-dependent bias correction  Δ b ( k , f _NL)  that depends on the linear halo bias   b ( M )  . We measure the power spectra for a range of halo mass and redshifts covering the relevant range of existing galaxy and quasar populations. We show that auto- and cross-correlation analyses of bias are consistent with each other. We find that for low wavenumbers with   k < 0.03  h  Mpc⁻¹  the theory and the simulations agree well with each other for biased haloes with   b ( M ) > 1.5  . We show that a scale-independent bias correction improves the comparison between theory and simulations on smaller scales, where the scale-dependent effect rapidly becomes negligible. The current limits on f _NL from Slosar et al. come mostly from very large scales   k < 0.01  h  Mpc⁻¹  and, therefore, remain valid. For the halo samples with   b ( M ) < 1.5 − 2  , we find that the scale-dependent bias from non-Gaussianity actually exceeds the theoretical predictions. Our results are consistent with the bias correction scaling linearly with f _NL.     

Scale-dependent galaxy bias in the Sloan Digital Sky Survey as a function of luminosity and colour

It has been known for a long time that the clustering of galaxies changes as a function of galaxy type. This galaxy bias acts as a hindrance to the extraction of cosmological information from the galaxy power spectrum or correlation function. Theoretical arguments show that a change in the amplitude of the clustering between galaxies and mass on large scales is unavoidable, but cosmological information can be easily extracted from the shape of the power spectrum or correlation function if this bias is independent of scale. Scale-dependent bias is generally small on large scales,   k < 0.1  h  Mpc⁻¹  , but on smaller scales can affect the recovery of  Ω_m h   from the measured shape of the clustering signal, and have a small effect on the Baryon Acoustic Oscillations. In this paper, we investigate the transition from scale-independent to scale-dependent galaxy bias as a function of galaxy population. We use the Sloan Digital Sky Survey Data Release 5 sample to fit various models, which attempt to parametrize the turn-off from scale-independent behaviour. For blue galaxies, we find that the strength of the turn-off is strongly dependent on galaxy luminosity, with stronger scale-dependent bias on larger scales for more luminous galaxies. For red galaxies, the scale dependence is a weaker function of luminosity. Such trends need to be modelled in order to optimally extract the information available in future surveys, and can help with the design of such surveys.     

Redshift-space bias and β from the halo model

We analyse scale dependence of redshift-space bias b and β  ≡ Ω_m^0.6/ b in the context of the halo model. We show that linear bias is a good approximation only on large scales, for k <0.1  h  Mpc⁻¹ . On intermediate scales the virial motions of galaxies cause a suppression of the power spectrum relative to the linear one and the suppression differs from the same effect in dark matter. This can potentially mimic the effect of massive neutrinos, and the degeneracy can only be broken if the power spectrum is measured for k ≪0.1  h  Mpc⁻¹ . Different methods to determine β converge for k <0.1  h  Mpc⁻¹ , but give drastically different results on smaller scales, which explains some of the trends observed in the real data. We also assess the level of stochasticity by calculating the cross-correlation coefficient between the reconstructed velocity field divergence and the galaxies, and show that the two fields decorrelate for k >0.1  h  Mpc⁻¹ . Most problematic are galaxies predominantly found in groups and clusters, such as bright, red or elliptical galaxies, where we find poor convergence to a constant bias or β even on large scales.     

Cosmological implications of the PSCz PDF and its moments

We compare the probability density function (PDF) and its low-order moments (variance and skewness) of the smoothed IRAS Point Source Catalogue Redshift Survey (PSC z ) galaxy density field and of the corresponding simulated PSC z look-alikes, generated from N -body simulations of six different dark matter models: four structure-normalized with     and     , one COBE -normalized, and the old standard cold dark matter model. The galaxy distributions are smoothed with a Gaussian window at three different smoothing scales,     , 10 and 15  h ⁻¹ Mpc. We find that the simulation PSC z look-alike PDFs are sensitive only to the normalization of the power spectrum, probably owing to the shape similarity of the simulated galaxy power spectrum on the relevant scales. We find that the only models that are consistent, at a high significance level, with the observed PSC z PDF are models with a relatively low power spectrum normalization     . From the phenomenologically derived σ ₈–moments relation, fitted from the simulation data, we find that the PSC z moments suggest     .     

Testing deprojection algorithms on mock angular catalogues: evidence for a break in the power spectrum

We produce mock angular catalogues from simulations with different initial power spectra to test methods that recover measures of clustering in three dimensions, such as the power spectrum, variance and higher order cumulants. We find that the statistical properties derived from the angular mock catalogues are in good agreement with the intrinsic clustering in the simulations. In particular, we concentrate on the detailed predictions for the shape of the power spectrum, P ( k ). We find that there is good evidence for a break in the galaxy P ( k ) at scales in the range 0.02< k <0.06 h Mpc⁻¹, using an inversion technique applied to the angular correlation function measured from the APM Galaxy Survey. For variants on the standard cold dark matter (CDM) model, a fit at the location of the break implies Ω h =0.45±0.10, where Ω is the ratio of the total matter density to the critical density, and Hubble's constant is parametrized as H ₀=100 h km s⁻¹ Mpc⁻¹. On slightly smaller, though still quasi-linear scales, there is a feature in the APM power spectrum where the local slope changes appreciably, with the best match to CDM models obtained for Ω h ≃0.2. Hence the location and narrowness of the break in the APM power spectrum combined with the rapid change in its slope on quasi-linear scales cannot be matched by any variant of CDM, including models that have a non-zero cosmological constant or a tilt to the slope of the primordial P ( k ). These results are independent of the overall normalization of the CDM models or any simple bias that exists betwen the galaxy and mass distributions.     

The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales   k _NL∼ 1 h Mpc⁻¹  . On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population.
We find an average bias   b = 1.24 ± 0.18  for the I -selected galaxies, and a cross-correlation coefficient   r = 0.75 ± 0.23  . Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy–galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter   h ≡ r / b = 0.57 ± 0.16  , suggesting that dynamical masses estimated using galaxies systematically underestimate total mass.
Ongoing surveys, such as the Canada–France–Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.     

CDM models with a BSI step-like primordial spectrum and a cosmological constant

A class of spatially flat models with cold dark matter (CDM), a cosmological constant and a broken-scale-invariant (BSI) step-like primordial (initial) spectrum of adiabatic perturbations, generated in an exactly solvable inflationary model where the inflaton potential has a rapid change of its first derivative at some point, is confronted with existing observational data on angular fluctuations of the CMB temperature, galaxy clustering and peculiar velocities of galaxies. If we locate the step in the initial spectrum at k  ≃ 0.05  h Mpc⁻¹, where a feature in the spectrum of Abell clusters of galaxies was found that could reflect a property of the initial spectrum, and if the large-scale flat plateau of the spectrum is normalized according to the COBE data, the only remaining parameter of the spectrum is p — the ratio of amplitudes of the metric perturbations between the small-scale and large-scale flat plateaux. Allowed regions in the plane of parameters (Ω = 1 − Ω_Λ,  H ₀) satisfying all data have been found for p lying in the region (0.8–1.7). Especially good agreement of the form of the present power spectrum in this model with the form of the cluster power spectrum is obtained for the inverted step ( p  < 1,  p  = 0.7–0.8), when the initial spectrum has slightly more power on small scales.     

An enlarged cosmic shear survey with the William Herschel Telescope

We report the results of a cosmic shear survey using the 4.2-m William Herschel Telescope on La Palma, to a depth of   R = 25.8 ( z ≈ 0.8)  , over 4 deg². The shear correlation functions are measured on scales from 1 to 15 arcmin, and are used to constrain cosmological parameters. We ensure that our measurements are free from instrumental systematic effects by performing a series of tests, including a decomposition of the signal into E - and B -modes. We also reanalyse the data independently, using the shear measurement pipeline developed for the COMBO-17 survey. This confirms our results and also highlights various effects introduced by different implementations of the basic 'Kaiser–Squires–Broadhurst' shear measurement method. We find that the normalization of the matter power spectrum on 8  h ⁻¹ Mpc scales is  σ₈= (1.02 ± 0.15)(0.3/Ω _m )^1/2  , where the 68 per cent confidence limit error includes noise, sample variance, covariance between angular scales, systematic effects, redshift uncertainty and marginalization over other parameters. We compare these results with other cosmic shear surveys and with recent constraints from the Wilkinson Microwave Anisotropy Probe experiment.     

Cosmic rays and the primordial gas

One of the most-outstanding problems in the gravitational collapse scenario of early structure formation is the cooling of primordial gas to allow for small-mass objects to form. As the neutral primordial gas is a poor radiator at temperatures   T ≤ 10⁴ K  , molecular hydrogen is needed for further cooling down to temperatures   T ∼ 100 K  . The formation of molecular hydrogen is catalyzed by the presence of free electrons, which could be provided by the ionization due to an early population of cosmic rays (CRs). In order to investigate this possibility, we developed a code to study the effects of ionizing CRs on the thermal and chemical evolution of primordial gas. We found that CRs can provide enough free electrons needed for the formation of molecular hydrogen, and therefore can increase the cooling ability of such primordial gas under following conditions. A dissociating photon flux with   F < 10⁻¹⁸ erg cm⁻² Hz⁻¹ s⁻¹  , initial temperature of the gas  ∼10³ K  , total gas number densities   n ≥ 1 cm⁻³  , and cosmic-ray sources with     .     

Neutralino annihilations and the gas temperature in the dark ages

Assuming that the dark matter is entirely made up of neutralinos, we re-visit the role of their annihilation on the temperature of diffuse gas in the high-redshift universe  ( z > 10)  , before the formation of luminous structures. We consider neutralinos of particle mass 36 and 100 GeV. The former is able to produce  ∼7  e ⁻ e ⁺  particles per annihilation through the fremionic channel, and the latter ∼53 particles assuming a purely bosonic channel. High-energy   e ⁻ e ⁺  particles up-scatter the cosmic microwave background (CMB) photons into higher energies via the inverse-Compton scattering. The process produces a power-law   e ⁻ e ⁺  energy spectrum of index −1 in the energy range of interest, independent of the initial energy distribution. The corresponding energy spectrum of the up-scattered photons is a power law of index −1/2, if absorption by the gas is not included. The scattered photons photoheat the gas by releasing electrons which deposit a fraction (14 per cent) of their energy as heat into the ambient medium. For uniformly distributed neutralinos, the heating is insignificant. The effect is greatly enhanced by the clumping of neutralinos into dense haloes. We use a time-dependent clumping model which takes into account the damping of density fluctuations on mass-scales smaller than  ∼10⁻⁶ M_⊙  . With this clumping model, the heating mechanism boosts the gas temperature above that of the CMB after a redshift of   z ∼ 30  . By   z ≈ 10  , the gas temperature is nearly 100 times its temperature when no heating is invoked. Similar increase is obtained for the two neutralino masses considered.     

Clustering of X-ray selected active galactic nuclei

A total of 235 active galactic nuclei (AGN) from two different soft X-ray surveys [the ROSAT Deep Survey (DRS) and the ROSAT International X-ray Optical Survey (RIXOS)] with redshifts between 0 and 3.5 are used to study the clustering of X-ray selected AGN and its evolution. A 2σ significant detection of clustering of such objects is found on scales < 40–80 h ⁻¹ Mpc in the RIXOS sample, while no clustering is detected on any scales in the DRS sample. Assuming a single power-law model for the spatial correlation function (SCF), quantitative limits on the AGN clustering have been obtained: a comoving correlation length 1.5 ≲  r ₀ ≲ 3.3  h ⁻¹ Mpc is implied for comoving evolution, while 1.9 ≲  r ₀ ≲ 4.8 for stable clustering and 2.2 ≲  r ₀ ≲ 5.5 for linear evolution. These values are consistent with the correlation lengths and evolutions obtained for galaxy samples, but imply smaller amplitude or faster evolution than recent ultraviolet and optically selected AGN samples. We also constrain the ratio of bias parameters between X-ray selected AGN and IRAS galaxies to be ≲ 1.7 on scales ≲ 10  h ⁻¹ Mpc, a somewhat smaller value than is inferred from local large-scale dynamical studies.     

Hot stars in old stellar populations: a continuing need for intermediate ages

We present numerical investigations into the formation of massive stars from turbulent cores of density structure  ρ∝ r ^−1.5  . The results of five hydrodynamical simulations are described, following the collapse of the core, fragmentation and the formation of small clusters of protostars. We generate two different initial turbulent velocity fields corresponding to power-law spectra   P ∝ k ⁻⁴  and   P ∝ k ^−3.5  , and we apply two different initial core radii. Calculations are included for both completely isothermal collapse, and a non-isothermal equation of state above a critical density  (10⁻¹⁴ g cm⁻³)  . Our calculations reveal the preference of fragmentation over monolithic star formation in turbulent cores. Fragmentation was prevalent in all the isothermal cases. Although disc fragmentation was largely suppressed in the non-isothermal runs due to the small dynamic range between the initial density and the critical density, our results show that some fragmentation still persisted. This is inconsistent with previous suggestions that turbulent cores result in the formation of a single massive star. We conclude that turbulence cannot be measured as an isotropic pressure term.     

Recovering the initial conditions of our local Universe from NOG and PSCz catalogues

We apply the ztrace algorithm to the optical NOG and infrared PSC z galaxy catalogues to reconstruct the pattern of primordial fluctuations that have generated our local Universe. We check that the density fields traced by the two catalogues are well correlated, and consistent with a linear relation [either in δ or in  log (1 +δ)  ] with relative bias (of NOG with respect to PSC z )   b _rel= 1.1 ± 0.1  . The relative bias relation is used to fill the optical zone of avoidance at  | b | < 20°  using the PSC z galaxy density field.
We perform extensive testing on simulated galaxy catalogues to optimize the reconstruction. The quality of the reconstruction is predicted to be good at large scales, up to a limiting wavenumber   k _lim≃ 0.4 h Mpc⁻¹  beyond which all information is lost. We find that the improvement arising from the denser sampling of the optical catalogue is compensated by the uncertainties connected to the larger zone of avoidance.
The initial conditions reconstructed from the NOG catalogue are found (analogously to those from the PSC z ) to be consistent with a Gaussian paradigm. We use the reconstructions to produce sets of initial conditions ready to be used for constrained simulations of our local Universe.     

The one-point PDF of the initial conditions of our local Universe from the IRAS PSC redshift catalogue

The algorithm ztrace of Monaco & Efstathiou is applied to the IRAS PSCz catalogue to reconstruct the initial conditions of our local Universe with a resolution down to ~5  h ¹ Mpc. The one-point probability distribution function (PDF) of the reconstructed initial conditions is consistent with the assumptions that: (i) IRAS galaxies trace mass on scales of ~5  h ¹ Mpc and (ii) the statistics of the primordial density fluctuations are Gaussian. We use simulated PSCz catalogues, constructed from N -body simulations with Gaussian initial conditions, to show that local non-linear bias can cause the recovered initial PDF (assuming no bias) to be non-Gaussian. However, for plausible bias models, the distortions of the recovered PDF would be difficult to detect using the volume finely sampled by the PSCz catalogue. So, for Gaussian initial conditions, a range of bias models remain compatible with our PSCz reconstruction results.     

Study of corrections to the dust model via perturbation theory

This work reports on the application of the Eulerian perturbation theory to a recently proposed model of cosmological structure formation by gravitational instability. Its physical meaning is discussed in detail and put in perspective of previous works. The model incorporates in a systematic fashion corrections to the popular dust model owing to multistreaming and, more generally, the small-scale, virialized degrees of freedom. It features a time-dependent length-scale L ( t ) estimated to be   L / r ₀10^-1  [ r ₀( t ) is the non-linear scale, at which   ²=1]  . The model provides a new angle on the dust model and allows us to overcome some of its limitations. Thus, the scale L ( t ) works as a physically meaningful short-distance cut-off for the divergences appearing in the perturbation expansion of the dust model when there is too much initial power on small scales. The model also incorporates the generation of vorticity by tidal forces; according to the perturbational result, the filtered vorticity for standard cold dark matter initial conditions should be significant today only at scales below 1  h ¹ Mpc.