Median Statistics, H_0, and the Accelerating Universe

(Abridged) We develop median statistics that provide powerful alternatives to chi-squared likelihood methods and require fewer assumptions about the data. Applying median statistics to Huchra's compilation of nearly all estimates of the Hubble constant, we find a median value H_0=67 km/s/Mpc. Median statistics assume only that the measurements are independent and free of systematic errors. This estimate is arguably the best summary of current knowledge because it uses all available data and, unlike other estimates, makes no assumption about the distribution of measurement errors. The 95% range of purely statistical errors is +/- 2 km/s/Mpc. The statistical precision of this result leads us to analyze the range of possible systematic errors in the median, which we estimate to be roughly +/- 5 km/s/Mpc (95% limits), dominating over the statistical errors. A Bayesian median statistics treatment of high-redshift Type Ia supernovae (SNe Ia) apparent magnitude versus redshift data from Riess et al. yields a posterior probability that the cosmological constant Lambda > 0 of 70 or 89%, depending on the prior information used. The posterior probability of an open universe is about 47%. Analysis of the Perlmutter et al. high-redshift SNe Ia data show the best-fit flat-Lambda model favored over the best-fit Lambda = 0 open model by odds of 366:1; corresponding Riess et al. odds are 3:1 (assuming prior odds of 1:1).Median statistics analyses of the SNe Ia data do not rule out a time-variable Lambda model, and may even favor it over a time-independent Lambda and a Lambda = 0 open model.Comment: Significant revisions include discussion of systematic errors in the median of H_0. Accepted for publication in The Astrophysical Journal, v548, February 20, 2001 issue. 47 pages incl. figures and table

Cosmological Parameter Determination from Counts of Galaxies

We study constraints that anticipated DEEP survey galaxy counts versus redshift data will place on cosmological model parameters in models with and without a constant or time-variable cosmological constant $\Lambda$. This data will result in fairly tight constraints on these parameters. For example, if all other parameters of a spatially-flat model with a constant $\Lambda$ are known, the galaxy counts data should constrain the nonrelativistic matter density parameter $\Omega_0$ to about 5% (10%, 1.5%) at 1 $\sigma$ with neutral (worst case, best case) assumptions about data quality.Comment: 15 pages, 6 figure

Supernovae Ia Constraints on a Time-Variable Cosmological "Constant"

The energy density of a scalar field $\phi$ with potential $V(\phi) \propto \phi^{-\alpha}$, $\alpha > 0$, behaves like a time-variable cosmological constant that could contribute significantly to the present energy density. Predictions of this spatially-flat model are compared to recent Type Ia supernovae apparent magnitude versus redshift data. A large region of model parameter space is consistent with current observations. (These constraints are based on the exact scalar field model equations of motion, not on the widely used time-independent equation of state fluid approximation equations of motion.) We examine the consequences of also incorporating constraints from recent measurements of the Hubble parameter and the age of the universe in the constant and time-variable cosmological constant models. We also study the effect of using a non-informative prior for the density parameter.Comment: Accepted for publication in Ap

On the Degeneracy Inherent in Observational Determination of the Dark Energy Equation of State

Using a specific model for the expansion rate of the Universe as a function of scale factor, it is demonstrated that the equation of state of the dark energy cannot be determined uniquely from observations at redshifts $z\lesssim{\rm a few}$ unless the fraction of the mass density of the Universe in nonrelativistic particles, $\Omega_M$, somehow can be found independently. A phenomenological model is employed to discuss the utility of additional constraints from the formation of large scale structure and the positions of CMB peaks in breaking the degeneracy among models for the dark energy.Comment: 12 pages, 3 figures. Several references adde

A new cosmological tracker solution for Quintessence

In this paper we propose a quintessence model with the potential $V(\Phi )=V_{o}[ \sinh {(\alpha \sqrt{\kappa_{o}}\Delta \Phi})] ^{\beta}$, which asymptotic behavior corresponds to an inverse power-law potential at early times and to an exponential one at late times. We demonstrate that this is a tracker solution and that it could have driven the Universe into its current inflationary stage. The exact solutions and the description for a complete evolution of the Universe are also given. We compare such model with the current cosmological observations.Comment: 13 pages REVTeX, 5 eps color figure

Cosmological Studies with Radio Galaxies and Supernovae

Physical sizes of extended radio galaxies can be employed as a cosmological "standard ruler", using a previously developed method. Eleven new radio galaxies are added to our previous sample of nineteen sources, forming a sample of thirty objects with redshifts between 0 and 1.8. This sample of radio galaxies are used to obtain the best fit cosmological parameters in a quintessence model in a spatially flat universe, a cosmological constant model that allows for non-zero space curvature, and a rolling scalar field model in a spatially flat universe. Results obtained with radio galaxies are compared with those obtained with different supernova samples, and with combined radio galaxy and supernova samples. Results obtained with different samples are consistent, suggesting that neither method is seriously affected by systematic errors. Best fit radio galaxy and supernovae model parameters determined in the different cosmological models are nearly identical, and are used to determine dimensionless coordinate distances to supernovae and radio galaxies, and distance moduli to the radio galaxies. The distance moduli to the radio galaxies can be combined with supernovae samples to increase the number of sources, particularly high-redshift sources, in the samples. The constraints obtained here with the combined radio galaxy plus supernovae data set in the rolling scalar field model are quite strong. The best fit parameter values suggest a value of omega is less than about 0.35, and the model parameter alpha is close to zero; that is, a cosmological constant provides a good description of the data. We also obtain new constraints on the physics of engines that power the large-scale radio emission.Comment: 32 pages. Accepted for publication in the Astrophysical Journa

Limitations in using luminosity distance to determine the equation of state of the universe

Supernova searches have been been suggested as a method for determining precisely the current value and time variation of the equation of state, $w$, of the dark energy component responsible for the accelerated expansion of the Universe. We show that the method is fundamentally limited by the fact that luminosity dista nce depends on $w$ through a multiple integral relation that smears out information about $w$ and its time variatio n. The effect degrades the resolution of $w$ that can be obtained from current d ata.Comment: 4 pages, 2 figures; corrected figure 1 (compared to preprint and published versions) and minor changes to tex

Unified dark energy models : a phenomenological approach

A phenomenological approach is proposed to the problem of universe accelerated expansion and of the dark energy nature. A general class of models is introduced whose energy density depends on the redshift $z$ in such a way that a smooth transition among the three main phases of the universe evolution (radiation era, matter domination, asymptotical de Sitter state) is naturally achieved. We use the estimated age of the universe, the Hubble diagram of Type Ia Supernovae and the angular size - redshift relation for compact and ultracompact radio structures to test whether the model is in agreement with astrophysical observation and to constrain its main parameters. Although phenomenologically motivated, the model may be straightforwardly interpreted as a two fluids scenario in which the quintessence is generated by a suitably chosen scalar field potential. On the other hand, the same model may also be read in the context of unified dark energy models or in the framework of modified Friedmann equation theories.Comment: 12 pages, 10 figures, accepted for publication on Physical Review

Unified phantom cosmology: inflation, dark energy and dark matter under the same standard

Phantom cosmology allows to account for dynamics and matter content of the universe tracing back the evolution to the inflationary epoch, considering the transition to the non-phantom standard cosmology (radiation/matter dominated eras) and recovering the today observed dark energy epoch. We develop the unified phantom cosmology where the same scalar plays the role of early time (phantom) inflaton and late-time Dark Energy. The recent transition from decelerating to accelerating phase is described too by the same scalar field. The (dark) matter may be embedded in this scheme, giving the natural solution of the coincidence problem. It is explained how the proposed unified phantom cosmology can be fitted against the observations which opens the way to define all the important parameters of the model.Comment: LaTeX file, 9 pages, no figure, version to appear in PL

Quintessence models in Supergravity

Scalar field models of quintessence typically require that the expectation value of the field today is of order the Planck mass, if we want them to explain the observed acceleration of the Universe. This suggests that we should be considering models in the context of supergravity. We discuss a particular class of supergravity models and analyze their behavior under different choices of the Kahler metric.Comment: 6 pages, revised version to appear in PR