Constraints on cosmological anisotropy out to z= 1 from Type Ia supernovae

A combined sample of 79 high- and low-redshift Type Ia supernovae (SNe) is used to set constraints on the degree of anisotropy in the Universe out to z ≃1. First, we derive the global most probable values of matter density Ω_M, the cosmological constant Ω_Λ and the Hubble constant H ₀, and find them to be consistent with the published results from the two data sets of Riess et al. and Perlmutter et al. We then examine the Hubble diagram (HD, i.e., the luminosity–redshift relation) in different directions on the sky by utilizing spherical harmonic expansion. In particular, via the analysis of the dipole anisotropy, we divide the sky into the two hemispheres that yield the most discrepant of the three cosmological parameters, and the scatter χ _HD² in each case. The most discrepant values roughly move along the locus −4Ω_M+3Ω_Λ=1 (cf. Perlmutter et al.), but by no more than Δ≈2.5 along this line. For a perfect Friedmann–Robertson–Walker universe, Monte Carlo realizations that mimic the current set of SNe yield values higher than the measured Δ in ∼1/5 of the cases (for Ω_M). We discuss implications for the validity of the Cosmological Principle, and possible calibration problems in the SNe data sets.     

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially flat cosmologies, varying the matter density Ω₀ (the flatness being restored by a cosmological constant), the Hubble parameter h and the spectral index n of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently favoured low-density model with Ω₀=0.3 and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits that we quote.     

The WARPS survey – IV. The X-ray luminosity–temperature relation of high-redshift galaxy clusters

We present a measurement of the cluster X-ray luminosity–temperature ( L – T ) relation out to high redshift ( z ∼0.8). Combined ROSAT PSPC spectra of 91 galaxy clusters detected in the Wide Angle ROSAT Pointed Survey (WARPS) are simultaneously fitted in redshift and luminosity bins. The resulting temperature and luminosity measurements of these bins, which occupy a region of the high-redshift L – T relation not previously sampled, are compared with existing measurements at low redshift in order to constrain the evolution of the L – T relation. We find the best fit to low-redshift ( z <0.2) cluster data, at T >1 keV, to be L ∝ T ^3.15±0.06. Our data are consistent with no evolution in the normalization of the L – T relation up to z ∼0.8. Combining our results with ASCA measurements taken from the literature, we find η =0.19±0.38 (for Ω₀=1, with 1 σ errors) where L _Bol∝(1+ z ) ^η T ^3.15, or η =0.60±0.38 for Ω₀=0.3. This lack of evolution is considered in terms of the entropy-driven evolution of clusters. Further implications for cosmological constraints are also discussed.     

On the errors on Ω0: Monte Carlo simulations of the EMSS cluster sample

We perform Monte Carlo simulations of synthetic EMSS cluster samples, to quantify the systematic errors and the statistical uncertainties on the estimate of Ω₀ derived from fits to the cluster number density evolution and to the X-ray temperature distribution up to z =0.83 . We identify the scatter around the relation between cluster X-ray luminosity and temperature to be a source of systematic error, of the order of Δ_systΩ₀=0.09 , if not properly taken into account in the modelling. After correcting for this bias, our best Ω₀ is 0.66. The uncertainties on the shape and normalization of the power spectrum of matter fluctuations imply relatively large uncertainties on this estimate of Ω₀, of the order of Δ_statΩ₀=0.1 at the 1 σ level. On the other hand, the statistical uncertainties due to the finite size of the high-redshift sample are twice as small. Therefore, what is needed in order to improve the accuracy of Ω₀ estimates based on cluster number density evolution is a more reliable measure of the local temperature function and a better understanding of the cluster observed properties both in the local Universe and at high redshift, that is the relation between cluster mass, temperature and luminosity. This requires detailed observations of X-ray selected cluster samples, in comparison with hydrodynamic simulations including refined physics.     

The matter power spectrum from the Lyα forest: an optical depth estimate

We measure the matter power spectrum from 31 Lyα spectra spanning the redshift range of 1.6–3.6. The optical depth, τ, for Lyα absorption of the intergalactic medium is obtained from the flux using the inversion method of Nusser & Haehnelt. The optical depth is converted to density by using a simple power-law relation,  τ∝ (1 +δ)^α  . The non-linear 1D power spectrum of the gas density is then inferred with a method that makes simultaneous use of the one- and two-point statistics of the flux and compared against theoretical models with a likelihood analysis. A cold dark matter model with standard cosmological parameters fits the data well. The power-spectrum amplitude is measured to be (assuming a flat Universe),  σ₈= (0.92 ± 0.09) × (Ω_m/0.3)^−0.3  , with α varying in the range of 1.56–1.8 with redshift. Enforcing the same cosmological parameters in all four redshift bins, the likelihood analysis suggests some evolution in the temperature–density relation and the thermal smoothing length of the gas. The inferred evolution is consistent with that expected if reionization of He  ii occurred at   z ∼ 3.2  . A joint analysis with the Wilkinson Microwave Anisotropy Probe results together with a prior on the Hubble constant as suggested by the Hubble Space Telescope key project data, yields values of Ω_m and σ₈ that are consistent with the cosmological concordance model. We also perform a further inversion to obtain the linear 3D power spectrum of the matter density fluctuations.     

Measuring Ω0 using cluster evolution

The evolution of the abundance of galaxy clusters depends sensitively on the value of the cosmological density parameter, Ω₀. Recent ASCA data are used to quantify this evolution as measured by the cluster X-ray temperature function. A χ² minimization fit to the cumulative temperature function, as well as a maximum-likelihood estimate (which requires additional assumptions about cluster luminosities), leads to the estimate Ω₀ ≈ 0.45 ± 0.25 (1σ statistical error). Various systematic uncertainties are considered, none of which significantly enhances the probability that Ω₀ = 1. These conclusions hold for models with or without a cosmological constant, i.e., with Λ₀ = 0 or Λ₀ = 1 − Ω₀. The statistical uncertainties are at least as large as any of the individual systematic errors that have been considered here, suggesting that additional temperature measurements of distant clusters will allow an improvement in this estimate. An alternative method that uses the highest redshift clusters to place an upper limit on Ω₀ is also presented and tentatively applied, with the result that Ω₀  1 can be ruled out at the 98 per cent confidence level. Whilst this method does not require a well-defined statistical sample of distant clusters, there are still modelling uncertainties that preclude a firmer conclusion at this time.     

The XMM Cluster Survey: forecasting cosmological and cluster scaling-relation parameter constraints

We forecast the constraints on the values of  σ₈, Ω_m  and cluster scaling-relation parameters which we expect to obtain from the XMM Cluster Survey (XCS). We assume a flat Λ cold dark matter Universe and perform a Monte Carlo Markov Chain analysis of the evolution of the number density of galaxy clusters that takes into account a detailed simulated selection function. Comparing our current observed number of clusters shows good agreement with predictions. We determine the expected degradation of the constraints as a result of self-calibrating the luminosity–temperature relation (with scatter), including temperature measurement errors, and relying on photometric methods for the estimation of galaxy cluster redshifts. We examine the effects of systematic errors in scaling relation and measurement error assumptions. Using only  ( T , z )  self-calibration, we expect to measure Ω_m to ±0.03 (and  Ω_Λ  to the same accuracy assuming flatness), and σ₈ to ±0.05, also constraining the normalization and slope of the luminosity–temperature relation to ±6 and ±13 per cent (at 1σ), respectively, in the process. Self-calibration fails to jointly constrain the scatter and redshift evolution of the luminosity–temperature relation significantly. Additional archival and/or follow-up data will improve on this. We do not expect measurement errors or imperfect knowledge of their distribution to degrade constraints significantly. Scaling-relation systematics can easily lead to cosmological constraints 2σ or more away from the fiducial model. Our treatment is the first exact treatment to this level of detail, and introduces a new 'smoothed ML' (Maximum Likelihood) estimate of expected constraints.     

The angular-diameter distance maximum and its redshift as constraints on Λ≠ 0 Friedmann–Lemaître–Robertson–Walker models

The plethora of recent cosmologically relevant data has indicated that our Universe is very well fitted by a standard Friedmann–Lemaître–Robertson–Walker (FLRW) model, with     and  Ω_Λ≈ 0.73  – or, more generally, by nearly flat FLRW models with parameters close to these values. Additional independent cosmological information, particularly the maximum of the angular-diameter (observer area) distance and the redshift at which it occurs, would improve and confirm these results, once sufficient precise Type Ia supernovae data in the range  1.5 < z < 1.8  become available. We obtain characteristic FLRW-closed functional forms for   C = C ( z )  and     , the angular-diameter distance and the density per source counted, respectively, when  Λ≠ 0  , analogous to those we have for  Λ= 0  . More importantly, we verify that for flat FLRW models z _max– as is already known but rarely recognized – the redshift of C _max, the maximum of the angular-diameter distance, uniquely gives  Ω_Λ  , the amount of vacuum energy in the universe, independent of H ₀, the Hubble parameter. For non-flat models, determination of both z _max and C _max gives both  Ω_Λ  and Ω_M, the amount of matter in the universe, as long as we know H ₀ independently. Finally, determination of C _max automatically gives a very simple observational criterion for whether or not the universe is flat – presuming that it is FLRW.     

The distance–redshift equation in quintessence cosmology and the estimation of H0 through time delays

We calculate analytically and numerically the distance–redshift equation in perfect fluid quintessence models and give an accurate fit to the numerical solutions for all the values of the density parameter and the quintessence equation of state. Then we apply our solutions to the estimation of H ₀ from multiple image time delays and find that the inclusion of quintessence modifies significantly the likelihood distribution of H ₀, generally reducing the best estimate with respect to a pure cosmological constant. Marginalizing over the other parameters (Ω _m and the quintessence equation of state) we obtain H ₀=71±6 km s⁻¹ Mpc⁻¹ for an empty beam and H ₀=64±4 km s⁻¹ Mpc⁻¹ for a filled beam. These errors, however, do not take into account the uncertainty on the modelling of the lens. We also discuss the future prospects for distinguishing quintessence from a cosmological constant with time delays.     

Constraints on cosmological and biasing models using active galactic nucleus clustering

We attempt to put constraints on different cosmological and biasing models by combining the recent clustering results of X-ray sources in the local ( z ≤0.1) and distant Universe ( z ∼1) . To this end we compare the measured angular correlation function for bright (Akylas et al.) and faint (Vikhlinin & Forman) ROSAT X-ray sources respectively with those expected in three spatially flat cosmological models. Taking into account the different functional forms of the bias evolution, we find that there are two cosmological models which match the data well. In particular, low-Ω_○ cosmological models (Ω_Λ=1−Ω_○=0.7) that contain either (i) high σ ₈^mass=1.13 value with galaxy merging bias, b ( z )∝(1+ z )^1.8 or (ii) low σ ₈^mass=0.9 with non-bias, b ( z ) ≡ 1 best reproduce the AGN clustering results, while τ CDM models with different bias behaviour are ruled out at a high significance level.     

Measuring Ω0 from the entropy evolution of clusters

In this paper we have extended the entropy-driven model of cluster evolution developed by Bower in order to be able to predict the evolution of galaxy clusters for a range of cosmological scenarios. We have applied this model to recent measurements of the evolution of the L _x− T normalization and X-ray luminosity function in order to place constraints on cosmological parameters. We find that these measurements alone do not select a particular cosmological framework. An additional constraint is required on the effective slope of the power spectrum to break the degeneracy that exists between this and the background cosmology. We therefore include a theoretical calculation of the Ω₀ dependence on the power spectrum, based on the cold dark matter paradigm, which infers Ω₀<0.55 (0.1<Ω₀<0.7 for Ω₀+Λ₀=1), at the 95 per cent confidence level. Alternatively, an independent measurement of the slope of the power spectrum from galaxy clustering requires Ω₀<0.6 (Ω₀<0.65 for Ω₀+Λ₀=1), again to 95 per cent confidence. The rate of entropy evolution is insensitive to the values of Ω₀ considered, although it is sensitive to changes in the distribution of the intracluster medium.     

The Δθ–zs relation for gravitational lenses as a cosmological test

Recently, Park &38; Gott claimed that there is a statistically significant, strong, negative correlation between the image separation Δθ and source redshift z _s for gravitational lenses. This is somewhat puzzling if one believes in a flat ( k  = 0) universe, since in this case the typical image separation is expected to be independent of the source redshift, while one expects a negative correlation in a k  = −1 universe and a positive one in a k  = +1 universe. Park &38; Gott explored several effects that could cause the observed correlation, but no combination of these can explain the observations with a realistic scenario. Here, I explore this test further in three ways. First, I show that in an inhomogeneous universe a negative correlation is expected regardless of the value of k . Secondly, I test whether the Δθ– z _s relation can be used as a test to determine λ₀ and Ω₀, rather than just the sign of k . Thirdly, I compare the results of the test from the Park &38; Gott sample with those using other samples of gravitational lenses, which can illuminate (unknown) selection effects and probe the usefulness of the Δθ– z _s relation as a cosmological test.     

Determination of cosmology and evolution from K-band magnitude–redshift and number count observations

We determine cosmological and evolutionary parameters from the 3CR K -band Hubble diagram and K -band number counts, assuming that the galaxies in question undergo pure luminosity evolution. Separately the two data sets are highly degenerate with respect to choice of cosmological and evolutionary parameters, but in combination the degeneracy is resolved. Of models that either are flat or have  Ω_Λ=0  , the preferred ones are close to the canonical case  Ω_{cold  matter}=1  ,  Ω_Λ=0  , with luminosity evolution amounting to 1 mag brighter at   z =1  .     

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.     

Do Type Ia supernovae prove Λ>0?

The evidence for positive cosmological constant Λ from Type Ia supernovae is re-examined.
Both high redshift supernova teams are found to underestimate the effects of host galaxy extinction. The evidence for an absolute magnitude–decay time relation is much weakened if supernovae not observed before maximum light are excluded. Inclusion of such objects artificially suppresses the scatter about the mean relation.
With a consistent treatment of host galaxy extinction and elimination of supernovae not observed before maximum, the evidence for a positive lambda is not very significant  (3–4 σ )  . A factor which may contribute to apparent faintness of high- z supernovae is evolution of the host galaxy extinction with z .
The Hubble diagram using all high- z distance estimates, including SZ clusters and gravitational lens time-delay estimates, does not appear inconsistent with an  Ω_o=1  model.
Although a positive Λ can provide an (albeit physically unmotivated) resolution of the low curvature implied by cosmic microwave background (CMB) experiments and evidence that  Ω_o<1  from large-scale structure, the direct evidence from Type Ia supernovae seems at present to be inconclusive.     

A critical-density closed universe in BransDicke theory

In a BransDicke (BD) cosmological model, the energy density associated with some scalar field decreases as a ^{2[( o +1/2)/( _o +1)]} with the scalefactor a ( t ) of the universe, giving matter with an equation of state In this model, the universe could be closed but still have a non-relativistic matter density corresponding to its critical value, _o =1. Different cosmological expressions, such as luminosity distance, angular diameter, number count and ratio of the redshift thicknessangular size, are determined in terms of the redshift for this model.     

Constraining quasar host halo masses with the strength of nearby Lyα forest absorption

Using cosmological hydrodynamic simulations, we measure the mean transmitted flux in the Lyα forest for quasar sightlines that pass near a foreground quasar. We find that the trend of absorption with pixel quasar separation distance can be fitted using a simple power-law form including the usual correlation function parameters r ₀ and γ, so that     . From the simulations, we find the relation between r ₀ and quasar host mass, and formulate this as a way to estimate quasar host dark matter halo masses, quantifying uncertainties due to cosmological and IGM parameters, and redshift errors. With this method, we examine data for ∼9000 quasars from the Sloan Digital Sky Survey (SDSS) Data Release 5, assuming that the effect of ionizing radiation from quasars (the so-called transverse proximity effect) is unimportant (no evidence for it is seen in the data). We find that the best-fitting host halo mass for SDSS quasars with mean redshift z = 3 and absolute G -band magnitude −27.5 is  log  M /M_⊙= 12.68^+0.81_−0.67  . We also use the Lyman-Break Galaxy (LBG) and Lyα forest data of Adelberger et al. in a similar fashion to constrain the halo mass of LBGs to be  log₁₀  M /M_⊙= 11.41^+0.54_−0.59  , a factor of ∼20 lower than the bright quasars. In addition, we study the redshift distortions of the Lyα forest around quasars, using the simulations. We use the quadrupole to monopole ratio of the quasar Lyα forest correlation function as a measure of the squashing effect. We find its dependence on halo mass difficult to measure, but find that it may be useful for constraining cosmic geometry.     

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.     

Constraining the cosmic equation of state from old galaxies at high redshift

New limits on the cosmic equation of state are derived from age measurements of three recently reported old high-redshift galaxies (OHRG). The results are based on a flat Friedmann–Robertson–Walker (FRW) type cosmological model driven by non-relativistic matter plus a smooth component parametrized by its equation of state p _x ωρ _x ( ω −1). The range of ω is strongly dependent on the matter density parameter. For Ω_M∼0.3, as indicated from dynamical measurements, the age estimates of the OHRG restrict the cosmic parameter to ω −0.27. However, if Ω_M is the one suggested by some studies of field galaxies, i.e., Ω_M≃0.5, only a cosmological constant ( ω =−1) may be compatible with these data.