Probing quintessence: reconstruction and parameter estimation from supernovae

We explore the prospects for using future supernova observations to probe the dark energy. We focus on quintessence, an evolving scalar field that has been suggested as a candidate for the dark energy. After simulating the observations that would be expected from the proposed SuperNova / Acceleration Probe satellite ( SNAP ), we investigate two methods for extracting information concerning quintessence from such data. First, by expanding the quintessence equation of state as   w _Q ( z ) = w _Q (0) −α ln(1 + z )  , to fit the data, it is possible to reconstruct the quintessence potential for a wide range of smoothly varying potentials. Secondly, it will be possible to test the basic properties of the dark energy by constraining the parameters  Ω _Q , w _Q   and α. We show that it may be possible, for example, to distinguish between quintessence and the cosmological constant in this way. Furthermore, when supernova data are combined with other planned cosmological observations, the precision of reconstructions and parameter constraints is significantly improved, allowing a wider range of dark energy models to be distinguished.     

Cosmic acceleration and extra dimensions: constraints on modifications of the Friedmann equation

An alternative to dark energy as an explanation for the present phase of accelerated expansion of the Universe is that the Friedmann equation is modified, e.g. by extra dimensional gravity, on large scales. We explore a natural parametrization of a general modified Friedmann equation, and find that the present supernova Type Ia and cosmic microwave background data prefer a correction of the form 1/ H to the Friedmann equation over a cosmological constant.     

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.     

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.     

Probing the Universe with the Ly α forest — II. The column density distribution

I apply the well controlled hydro-PM (HPM) approximation of Gnedin &38; Hui to model the column density distribution of the Ly α forest for 25 different flat cosmological scenarios, including variants of the standard cold dark matter (CDM), tilted CDM, CDM with a cosmological constant, and cold + hot dark matter (CHDM) models. I show that, within the accuracy of the HPM approximation, the slope of the column density distribution reflects the degree of non-linearity of the cosmic gas distribution and is a function of the rms linear density fluctuation at the characteristic filtering scale only. The amplitude of the column density distribution, expressed as the value for the ionizing intensity, is derived as a function of the cosmological parameters (to about 40 per cent accuracy). The observational data are currently consistent with the value for the ionizing intensity being constant in the redshift interval z  ∼ −4.     

The clustering of Lyman-break galaxies

We calculate the statistical clustering of Lyman-break galaxies predicted in a selection of currently fashionable structure formation scenarios. These models are all based on the cold dark matter model, but vary in the amount of dark matter, the initial perturbation spectrum, the background cosmology and the presence or absence of a cosmological constant term. If Lyman-break galaxies form as a result of hierarchical merging, the amplitude of clustering depends quite sensitively on the minimum halo mass that can host such a galaxy. Interpretation of the recent observations by Giavalisco et al. would therefore be considerably clarified by a direct determination of the relevant halo properties. For a typical halo mass around 10¹¹  h ⁻¹ M⊙ the observations do not discriminate strongly between cosmological models, but if the appropriate mass is larger, say 10¹²  h ⁻¹ M⊙ (which seems likely on theoretical grounds), then the data strongly favour models with a low matter density.     

Linear perturbations in a universe with a cosmological constant

There is now evidence that the cosmological constant Λ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density ρ and the pressure p of this fluid are constrained by − ρ ≤ p ≲−0.6 ρ . As p =− ρ is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further.
We study the linear theory of perturbations in a Friedmann–Robertson–Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.     

Using bright ellipticals as dark energy cosmic clocks

The age of the Universe has been increasingly constrained by different techniques, such as the observations of type Ia supernovae (SNIa) at high redshift or dating the stellar populations of globular clusters. In this paper, we present a complementary approach using the colours of the brightest elliptical galaxies in clusters over a wide redshift range  ( z ≲ 1)  . We put new and independent bounds on the dark energy equation of state parametrized by a constant pressure-to-density ratio   w _Q  and by a parameter (ξ) which determines the scaling between the matter and dark energy densities. We find that accurate estimates of the metallicities of the stellar populations in moderate and high-redshift cluster galaxies can pose stringent constraints on the parameters that describe dark energy. Our results are in good agreement with the analysis of dark energy models using SNIa data as a constraint. Accurate estimates of the metallicities of stellar populations in cluster galaxies at   z ≲ 2  will make this approach a powerful complement to studies of cosmological parameters using high-redshift SNIa.     

The time evolution of cosmological redshift as a test of dark energy

The variation of the expansion rate of the Universe with time produces an evolution in the cosmological redshift of distant sources (e.g. quasar Lyman α absorption lines) that might be directly observed by future ultrastable, high-resolution spectrographs (such as the COsmic Dynamics Experiment) coupled to extremely large telescopes (such as the European Southern Observatory's Extremely Large Telescope). This would open a new window to explore the physical mechanism responsible for the current acceleration of the Universe. We investigate the evolution of cosmological redshift from a variety of dark energy models, and compare it with simulated data. We perform a Fisher matrix analysis and discuss the prospects for constraining the parameters of these models and for discriminating among competing candidates. We find that, because of parameter degeneracies, and the inherent technical difficulties involved in this kind of observations, the uncertainties on parameter reconstruction can be rather large unless strong external priors are assumed. However, the method could be a valuable complementary cosmological tool, and give important insights on the dynamics of dark energy, not obtainable using other probes.     

Constraints on structure formation models from the Sunyaev–Zel'dovich effect

In the context of cold dark matter (CDM) cosmological models, we have simulated images of the brightness temperature fluctuations in the cosmic microwave background (CMB) sky owing to the Sunyaev–Zel'dovich (S–Z) effect in a cosmological distribution of clusters. We compare the image statistics with recent ATCA limits on arcmin-scale CMB anisotropy. The S–Z effect produces a generically non-Gaussian field and we compute the variance in the simulated temperature-anisotropy images, after convolution with the ATCA beam pattern, for different cosmological models. All the models are normalized to the 4-yr COBE data. We find an increase in the simulated-sky temperature variance with increase in the cosmological density parameter Ω₀. A comparison with the upper limits on the sky variance set by the ATCA appears to rule out our closed-universe model: low-Ω₀ open-universe models are preferred. The result is independent of any present day observations of σ ₈.     

Tracing the nature of dark energy with galaxy distribution

Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Λ and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z , the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N -body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable differences.     

Testing dark energy with the Advanced Liquid-mirror Probe of Asteroids, Cosmology and Astrophysics

The Advanced Liquid-mirror Probe of Asteroids, Cosmology and Astrophysics (ALPACA) is a proposed 8-m liquid-mirror telescope surveying  ∼1000 deg²  of the Southern hemisphere sky. It will be a remarkably simple and inexpensive telescope that none the less will deliver a powerful sample of optical data for studying dark energy. The bulk of the cosmological data consist of nightly, high signal-to-noise ratio, multiband light curves of Type Ia supernovae (SNe Ia). At the end of the 3-yr run, ALPACA is expected to collect  ≳100 000  SNe Ia up to   z ∼ 1  . This will allow us to reduce present systematic uncertainties affecting the standard-candle relation. The survey will also provide several other data sets such as the detection of baryon acoustic oscillations in the matter power spectrum and shear weak-lensing measurements. In this preliminary analysis, we forecast constraints on dark energy parameters from SNe Ia and baryon acoustic oscillations. The combination of these two data sets will provide competitive constraints on the dark energy parameters under minimal prior assumptions. Further studies are needed to address the accuracy of weak-lensing measurements.     

Large-scale cosmic microwave background anisotropies and dark energy

In this paper we investigate the effects of perturbations in a dark energy component with a constant equation of state on large-scale cosmic microwave background (CMB) anisotropies. The inclusion of perturbations increases the large-scale power. We investigate more speculative dark energy models with   w < −1  and find the opposite behaviour. Overall the inclusion of perturbations in the dark energy component increases the degeneracies. We generalize the parametrization of the dark energy fluctuations to allow for an arbitrary constant sound speed, and we show how constraints from CMB experiments change if this is included. Combining CMB with large-scale structure, Hubble parameter and supernovae observations we obtain   w =−1.02 ± 0.16 (1σ)  as a constraint on the equation of state, which is almost independent of the sound speed chosen. With the presented analysis we find no significant constraint on the constant speed of sound of the dark energy component.     

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.     

Anisotropic universe and observational constraint on the dark energy models with the cosmological redshift drift

This study set out to examine the effect of anisotropy on the various dark energy models by using the observational data, including the Sandage-Loeb test, Strongly gravitationally lensing, observational Hubble data, and Baryon Acoustic Oscillations data. In particular, we consider three cases of dark energy models: the cosmological constant model, which is most favored by current observations, the wCDM model where dark energy is introduced with constant w equation of state parameter and in Chevalier-Polarski-Linder parametrization where ω is allowed to evolve with redshift. With an anisotropy framework, a maximum likelihood method to constrain the cosmological parameters was implemented. With an anisotropic universe, we also study the behavior of different cosmological parameters such as Hubble parameter, EoS parameter, and deceleration parameter of dark energy models mentioned. The results indicate that the Bianchi type I model for the dark energy models are consistent with the combined observational data.     

Distance measurements as a probe of cosmic acceleration

A major recent development in observational cosmology has been an accurate measurement of the luminosity distance–redshift relation out to redshifts z =0.8 from Type Ia supernova standard candles. The results have been argued as evidence for cosmic acceleration. It is well known that this assertion depends on the assumption that we know the equation of state for all mass–energy other than normal pressureless matter; popular models are based either on the cosmological constant or on the more general quintessence formulation. However, this assertion also depends on a number of other assumptions, implicit in the derivation of the standard cosmological field equations: large-scale isotropy and homogeneity, the flatness of the Universe, and the validity of general relativity on cosmological scales (where it has not been tested). A detailed examination of the effects of these assumptions on the interplay between the luminosity distance–redshift relation and the acceleration of the Universe is not possible unless one can define the precise nature of the failure of any particular assumption. However a simple quantitative investigation is possible and reveals a number of considerations about the relative importance of the different assumptions. In this paper we present such an investigation. We find that the relationship between the distant-redshift relation and the sign of the deceleration parameter is fairly robust and is unaffected if only one of the assumptions that we investigate is invalid so long as the deceleration parameter is not close to zero (it would not be close to zero in the currently favoured Ω_Λ=1−Ω_matter=0.7 or 0.8 Universe, for example). Failures of two or more assumptions in concordance may have stronger effects.     

Gravitational lensing by elliptical galaxies

The fraction of high-redshift sources which are multiply imaged by intervening galaxies is strongly dependent on the cosmological constant, and so can be a useful probe of the cosmological model. However its power is limited by various systematic (and random) uncertainties in the calculation of lensing probabilities, one of the most important of which is the dynamical normalization of elliptical galaxies. Assuming ellipticals' mass distributions can be modelled as isothermal spheres, the mass normalization depends on the velocity anisotropy, the luminosity density, the core radius and the area over which the velocity dispersion is measured. The differences in the lensing probability and optical depth produced by using the correct normalization can be comparable to the differences between even the most extreme cosmological models. The existing data are not sufficient to determine the correct normalization with enough certainty to allow lensing statistics to be used to their full potential. However, as the correct lensing probability is almost certainly higher than is usually assumed, upper bounds on the cosmological constant are not weakened by these possibilities.     

Constraint on cosmological model with matter creation using complementary astronomical observations

The universe with adiabatic matter creation is considered. It is thought that the negative pressure caused by matter creation can play the role of a dark energy component, and drive the accelerating expansion of the universe. Using the Type Ia supernovae (SNe Ia) data, the observational Hubble parameter data, the Cosmic Microwave Background (CMB) data and the Baryonic Acoustic Oscillation (BAO) data, we make constraints on the cosmological parameters, assuming a spatially flat universe. Our results show that the model with matter creation is consistent with the SNe Ia data, while the joint constraints of all these observational data disfavor this model. If the cosmological constant is taken into account, a traditional model without matter creation is favored by the joint observations.     

A model of slingshot prominences in rapidly rotating stars

We analyse the spatial clustering properties of the ROSAT All-Sky Survey (RASS) 1 Bright Sample, an X-ray flux-limited catalogue of galaxy clusters selected from the southern part of the survey. The two-point correlation function ( r ) of the whole sample is well fitted (in an Einsteinde Sitter model) by the power law =( r r ₀) , with and (95.4 per cent confidence level with one fitting parameter). We use the RASS 1 Bright Sample as a first application of a theoretical model that aims to predict the clustering properties of X-ray clusters in flux-limited surveys for different cosmological scenarios. The model uses the theoretical and empirical relations between mass, temperature and X-ray cluster luminosity, and fully accounts for the redshift evolution of the underlying dark matter clustering and cluster bias factor. The comparison between observational results and theoretical predictions shows that the Einsteinde Sitter models display too low a correlation length, while models with a matter density parameter _0m=0.3 (with or without a cosmological constant) are successful in reproducing the observed clustering. The dependence of the correlation length r ₀ on the X-ray limiting flux and luminosity of the sample is generally consistent with the predictions of all our models. Quantitative agreement is however only reached for _0m=0.3 models. The model presented here can be reliably applied to future deeper X-ray cluster surveys: the study of the clustering properties will provide a useful complementary tool to the traditional cluster abundance analyses used to constrain the cosmological parameters.     

The Universe With Bulk Viscosity

Exact solutions for a model with variable G,A and bulk viscosity are obtained,Inflationary solutions with constant(de Sitter-type )and variable energy density are found.An expanding anisotropic universe is found to isotropize during its expansion but a static universe cannot isotropize.The gravitational constant is found to increase with time and the cosmological constant decreases with time as A∝t^-2。