Constraints on perfect fluid and scalar field dark energy models from future redshift surveys

We discuss the constraints that future photometric and spectroscopic redshift surveys can put on dark energy through the baryon oscillations of the power spectrum. We model the dark energy either with a perfect fluid or a scalar field and take into account the information contained in the linear growth function. We show that the growth function helps to break the degeneracy in the dark energy parameters and reduce the errors on   w ₀, w ₁  roughly by 30 per cent, making more appealing multicolour surveys based on photometric redshifts. We find that a 200-deg² spectroscopic survey reaching   z ≈ 3  can constrain   w ₀, w ₁  to within  Δ w ₀= 0.21, Δ w ₁= 0.26  , to  Δ w ₀= 0.39, Δ w ₁= 0.54  using photometric redshifts with an absolute uncertainty of 0.02, and to  Δ w ₀= 0.43, Δ w ₁= 0.66  with an uncertainty of 0.04. In the scalar field case, we show that the slope n of the inverse power-law potential for dark energy can be constrained to  Δ n = 0.26  (spectroscopic redshifts) or  Δ n = 0.40  (photometric redshifts), i.e. better than with future ground-based supernovae surveys or cosmic microwave background data.     

Modified Chaplygin gas and constraints on its B parameter from cold dark matter and unified dark matter energy cosmological models

We study modified Chaplygin gas (MCG) as a candidate for dark energy and predict the values of parameters of the gas for a physically viable cosmological model. The equation of state of MCG     involves three parameters: B , A and α. The permitted values of these parameters are determined with the help of a dimensionless age parameter  ( H ₀ t ₀)  and   H ( z ) − z   data. Specifically, we study the allowed ranges of values of the B parameter in terms of α and   A_s   (   A_s   is defined in terms of the parameters in the theory). We explore the constraints of the parameters in the cold dark matter and unified dark matter energy models, respectively.     

Smoothing supernova data to reconstruct the expansion history of the Universe and its age

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel in order to reconstruct important cosmological quantities including   H ( z )  and   w ( z )  in a model-independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future Supernova Acceleration Probe ( SNAP ). We find that the Hubble parameter is especially well determined and useful for this purpose. The look-back time of the Universe may also be determined to a very high degree of accuracy (≲0.2 per cent) using this method. By refining the method, it is also possible to obtain reasonable bounds on the equation of state of dark energy. We explore a new diagnostic of dark energy – the ' w -probe'– which can be calculated from the first derivative of the data. We find that this diagnostic is reconstructed extremely accurately for different reconstruction methods even if Ω_{0 m} is marginalized over. The w -probe can be used to successfully distinguish between Λ cold dark matter and other models of dark energy to a high degree of accuracy.     

Consequences for some dark energy candidates from the type Ia supernova SN 1997ff

We examine the status of various dark energy models in light of the recently observed SN 1997ff at   z ≈1.7  . The modified data still fit a pure cosmological constant Λ or a quintessence with an equation of state similar to that of Λ. The kinematical Λ models,  Λ∼ S ^-2  and  Λ∼ H ²  , also fit the data reasonably well and require less dark energy density (hence more matter energy density) than is required by the constant Λ model. However, the model  Λ∼ S ^-2  with low energy density becomes unphysical as it cannot accommodate higher redshift objects.
We also examine an alternative explanation of the data, namely the absorption by the intervening whisker-like dust, and find that the quasi-steady state (QSS) model and the Friedmann–Robertson–Walker (FRW) model  Ω_m0=0.33  without any dark energy also fit the data reasonably well.
We notice that the addition of SN 1997ff to the old data has worsened the fit to most of the models, except a closed FRW model with a constant Λ and a closed quintessence model with   ω _φ =-0.82  , and the models have started departing from each other as we go above   z =1  . However, to make a clear discrimination possible, a few more supernovae with   z >1  are required.
We have also calculated the age of the Universe in these models and find that, in the models with a constant Λ, the expansion age is uncomfortably close to the age of the globular clusters. Quintessence models show even lower age. The kinematical Λ models are, however, interesting in this connection (especially the model  Λ∼ H ²)  , as they give a remarkably large age of the Universe.     

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.     

Covariance of dark energy parameters and sound speed constraints from large H i surveys

An interesting probe of the nature of dark energy is the measure of its sound speed, c _s. We review the significance for constraining sound speed models of dark energy using large neutral hydrogen (H  i ) surveys with the square kilometre array (SKA). Our analysis considers the effect on the sound speed measurement that arises from the covariance of c _s with the dark energy density, Ω_de, and a time-varying equation of state,   w ( a ) = w ₀+ (1 − a ) w _a   . We find that the approximate degeneracy between dark energy parameters that arises in power spectrum observations is lifted through redshift tomography of the H  i -galaxy angular power spectrum, resulting in sound speed constraints that are not severely degraded. The cross-correlation of the galaxy and the integrated Sachs Wolfe (ISW) effect spectra contributes approximately 10 per cent of the information that is needed to distinguish variations in the dark energy parameters, and most of the discriminating signal comes from the galaxy auto-correlation spectrum. We also find that the sound speed constraints are weakly sensitive to the H  i bias model. These constraints do not improve substantially for a significantly deeper H  i survey since most of the clustering sensitivity to sound speed variations arises from   z ≲ 1.5  . A detection of models with sound speeds close to zero,   c _s≲ 0.01,  is possible for dark energy models with   w ≳−0.9  .     

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.     

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.     

Investigating cosmological weak lensing with the ray-bundle method

Using the ray-bundle method for calculating gravitational lens magnifications, we outline a method by which the magnification probability may be determined specifically in the weak lensing limit for cosmological models obtained from N -body simulations.
16 different models are investigated, which are variations on three broad classes of cold dark matter model: the standard model with  (Ω₀, λ ₀)=(1.0,0.0)  , the open model with  (Ω₀, λ ₀)=(0.3,0.0)  and the lambda model, which is a flat model with a cosmological constant  (Ω₀, λ ₀)=(0.3,0.7)  .
The effects of varying the Hubble parameter, H ₀, the power spectrum shape parameter, Γ, and the cluster mass normalization, σ ₈, are studied. It is shown that there is no signature of these parameters in the weak lensing magnification distributions. The magnification probability distributions are also shown to be independent of the numerical parameters such as the lens mass and simulation box size in the N -body simulations.     

Implications of bias evolution on measurements of the integrated Sachs–Wolfe effect: errors and biases in parameter estimation

The subject of this paper is a quantification of the impact of uncertainties in bias and bias evolution on the interpretation of measurements of the integrated Sachs–Wolfe (ISW) effect, in particular on the estimation of cosmological parameters. We carry out a Fisher matrix analysis for quantifying the degeneracies between the parameters of a dark energy cosmology and bias evolution, for the combination of the PLANCK microwave sky survey with the EUCLID main galaxy sample, where bias evolution   b ( a ) = b ₀+ (1 − a ) b_a   is modelled with two parameters b ₀ and   b_a   . Using a realistic bias model introduces a characteristic suppression of the ISW spectrum on large angular scales, due to the altered distance-weighting functions. The errors in estimating cosmological parameters if the data with evolving bias is interpreted in the framework of cosmologies with constant bias are quantified in an extended Fisher formalism. We find that the best-fitting values of all parameters are shifted by an amount comparable to the statistical accuracy: the estimation bias in units of the statistical accuracy amounts to 1.19 for Ω_m, 0.27 for σ₈ and 0.72 for w for bias evolution with   b_a = 1  . Leaving   b_a   open as a free parameter deteriorates the statistical accuracy, in particular on Ω_m and w .     

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.     

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.     

The Hubble Deep Field North reveals a supernova at z∼0.95

We report the discovery of a variable object in the Hubble Deep Field North (HDF-N) which brightened, during the 8.5 d sampled by the data, by more than 0.9 mag in I ₈₁₄ and about 0.7 mag in V ₆₀₆, remaining stable in B ₄₅₀. Subsequent observations of the HDF-N show that two years later this object has dimmed to about its original brightness in I ₈₁₄. The colours of this object, its brightness, its time behaviour in the various filters and the evolution of its morphology are consistent with it being a Type Ib supernova in a faint galaxy at z .     

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 Hα luminosity function and star formation rate up to z ∼ 1

We describe ISAAC/ESO-VLT observations of the Hαλ6563 Balmer line of 33 field galaxies from the Canada–France Redshift Survey (CFRS) with redshifts selected between 0.5 and 1.1. We detect Hα in emission in 30 galaxies and compare the properties of this sample with the low-redshift sample of CFRS galaxies at   z ∼ 0.2  . We find that the Hα luminosity,   L (Hα)  , is tightly correlated to   M ( B _AB)  in the same way for both the low- and high-redshift samples.   L (Hα)  is also correlated to L ([O  ii ]λ3727), and again the relation appears to be similar at low and high redshifts. The ratio L (lsqb;O  ii ])/   L (Hα)  decreases for brighter galaxies by as much as a factor of 2 on average. Derived from the Hα luminosity function, the comoving Hα luminosity density increases by a factor 12 from  〈 z 〉= 0.2  to  〈 z 〉= 1.3  . Our results confirm a strong rise of the star formation rate (SFR) at   z < 1.3  , proportional to  (1 + z )^4.1±0.3  (with   H ₀= 50 km s⁻¹ Mpc⁻¹, q ₀= 0.5  ). We find an average  SFR(2800 Å)/SFR (Hα)  ratio of 3.2 using the Kennicutt SFR transformations. This corresponds to the dust correction that is required to make the near-ultraviolet data consistent with the reddening-corrected Hα data within the self-contained, I -selected CFRS sample.     

Decay of the vacuum energy into cosmic microwave background photons

We examine the possibility of the decay of the vacuum energy into a homogeneous distribution of a thermalized cosmic microwave background (CMB), which is characteristic of an adiabatic vacuum energy decay into photons. It is shown that observations of the primordial density fluctuation spectrum, obtained from CMB and galaxy distribution data, restrict the possible decay rate. When photon creation due to an adiabatic vacuum energy decay takes place, the standard linear temperature dependence   T ( z ) = T ₀(1 + z )  is modified, where T ₀ is the present CMB temperature, and can be parametrized by a modified CMB temperature dependence     . From the observed CMB and galaxy distribution data, a strong limit on the maximum value of the decay rate is obtained by placing a maximum value  β_max≃ 3.4 × 10⁻³  on the β parameter.     

New limits on the possible variation of physical constants

Recent detections of high-redshift absorption by both atomic hydrogen and molecular gas in the radio spectra of quasars have provided a powerful tool for measuring possible temporal and spatial variations of physical 'constants' in the universe.
We compare the frequency of high-redshift hydrogen 21-cm absorption with that of associated molecular absorption in two quasars to place new (1σ) upper limits on any variation in y≡g_pα² (where α is the fine-structure constant, and g_p is the proton g -factor of
   
at redshifts z = 0.25 and 0.68. These quasars are separated by a comoving distance of 3000 Mpc ( H ₀= 75 km s⁻¹ Mpc⁻¹ and q ₀). We also derive limits on the time rates of change
   
    between the present epoch and z = 0.68. These limits are more than an order of magnitude smaller than previous results derived from high-redshift measurements.     

Photometric redshifts for weak lensing tomography from space: the role of optical and near infrared photometry

We study in detail the photometric redshift requirements needed for tomographic weak gravitational lensing in order to measure accurately the dark energy equation of state. In particular, we examine how ground-based photometry  ( u , g , r , i , z , y )  can be complemented by space-based near-infrared (near-IR) photometry  ( J , H )  , e.g. onboard the planned DUNE satellite. Using realistic photometric redshift simulations and an artificial neural network photo- z method we evaluate the figure of merit for the dark energy parameters  ( w ₀, w _a )  . We consider a DUNE -like broad optical filter supplemented with ground-based multiband optical data from surveys like the Dark Energy Survey, Pan-STARRS and LSST. We show that the dark energy figure of merit would be improved by a factor of 1.3–1.7 if IR filters are added onboard DUNE . Furthermore we show that with IR data catastrophic photo- z outliers can be removed effectively. There is an interplay between the choice of filters, the magnitude limits and the removal of outliers. We draw attention to the dependence of the results on the galaxy formation scenarios encoded into the mock galaxies, e.g. the galaxy reddening. For example, very deep u -band data could be as effective as the IR. We also find that about  10⁵–10⁶  spectroscopic redshifts are needed for calibration of the full survey.     

The redshift evolution of clustering in the Hubble Deep Field

We present a correlation function analysis for the catalogue of photometric redshifts obtained from the Hubble Deep Field image by Fernandez-Soto, Lanzetta & Yahil. By dividing the catalogue into redshift bins of width Δ z =0.4 we measured the angular correlation function w ( θ ) as a function of redshift up to z ∼4.8. From these measurements we derive the trend of the correlation length r ₀. We find that r ₀( z ) is roughly constant with look-back time up to z ≃2, and then increases to higher values at z ≳2.4. We estimate the values of r ₀, assuming ξ ( r , z )=[ r r ₀( z )]^{− γ} , γ =1.8 and various geometries. For Ω₀=1 we find r ₀( z =3)≃7.00±4.87  h ⁻¹ Mpc, in good agreement with the values obtained from analysis of the Lyman break galaxies.     

The location of cosmic microwave background peaks in a universe with dark energy

The locations of the peaks of the cosmic microwave background (CMB) spectrum are sensitive indicators of cosmological parameters, yet there is no known analytic formula which accurately describes their dependence on them. We parametrize the location of the peaks as   l _m = l _A( m - φ _m )  , where l _A is the analytically calculable acoustic scale and m labels the peak number. Fitting formulae for the phase shifts φ _m for the first three peaks and the first trough are given. It is shown that in a wide range of parameter space, the acoustic scale l _A can be retrieved from actual CMB measurements of the first three peaks within 1 per cent accuracy. This can be used to speed up likelihood analysis. We describe how the peak shifts can be used to distinguish between different models of dark energy.