On the structure of the BBGKY hierarchy for a Boltzmann gas

Structure of BBGKY hierarchy for Boltzmann gas and particle distribution

Future Type Ia Supernova Data as Tests of Dark Energy from Modified Friedmann Equations

In the Cardassian model, dark energy density arises from modifications to the Friedmann equation, which becomes H^2 = g(\rhom), where g(\rhom) is a new function of the energy density. The universe is flat, matter dominated, and accelerating. The distance redshift relation predictions of generalized Cardassian models can be very different from generic quintessence models, and can be differentiated with data from upcoming pencil beam surveys of Type Ia Supernovae such as SNAP. We have found the interesting result that, once $\Omega_m$ is known to 10% accuracy, SNAP will be able to determine the sign of the time dependence of the dark energy density. Knowledge of this sign (which is related to the weak energy condition) will provide a first discrimination between various cosmological models that fit the current observational data (cosmological constant, quintessence, Cardassian expansion). Further, we have performed Monte Carlo simulations to illustrate how well one can reproduce the form of the dark energy density with SNAP. To be concrete we study a class of two parameter ($n$,$q$) generalized Cardassian models that includes the original Cardassian model (parametrized by $n$ only) as a special case. Examples are given of MP Cardassian models that fit current supernovae and CMB data, and prospects for differentiating between MP Cardassian and other models in future data are discussed. We also note that some Cardassian models can satisfy the weak energy condition $w>-1$ even with a dark energy component that has an effective equation of state $w_X < -1$.Comment: revised version accepted by Ap

Gravitational Lensing Statistics in Universes Dominated by Dark Energy

We study lens statistics in flat, low-density universes with different equations of state $w=p_Q/\rho_Q$ for the dark energy component. Dark energy modifies the distance-redshift relation and the mass function of dark matter halos leading to changes in the lensing optical depth as a function of image separation. Those effects must, however, be distinguished from effects associated with the structure of dark matter halos. Baryonic cooling causes galaxy-mass halos to have different central density profiles than group- and cluster-mass halos, which causes the distribution of normal arcsecond-scale lenses to differ from the distribution of ``wide-separation'' (\Delta\theta \gtrsim 4\arcsec) lenses. Fortunately, the various parameters related to cosmology and halo structure have very different effects on the overall image separation distribution: (1) the abundance of wide-separation lenses is exremely sensitive (by orders of magnitude) to the distribution of ``concentration'' parameters for massive halos modeled with the Navarro-Frenk-White profile; (2) the transition between normal and wide-separation lenses depends mainly on the mass scale where baryonic cooling ceases to be efficient; and (3) dark energy has effects at all image separation scales. While current lens samples cannot usefully constrain all of the parameters, ongoing and future imaging surveys should discover hundreds or thousands of lenses and make it possible to disentangle the various effects and constrain all of the parameters simultaneously. (abridged)Comment: 15 pages, 11 figures, accepted for publication in Ap

Large-Scale Bulk Motions Complicate the Hubble Diagram

We investigate the extent to which correlated distortions of the luminosity distance-redshift relation due to large-scale bulk flows limit the precision with which cosmological parameters can be measured. In particular, peculiar velocities of type 1a supernovae at low redshifts may prevent a sufficient calibration of the Hubble diagram necessary to measure the dark energy equation of state to better than 10%, and diminish the resolution of the equation of state time-derivative projected for planned surveys. We consider similar distortions of the angular-diameter distance, as well as the Hubble constant. We show that the measurement of correlations in the large-scale bulk flow at low redshifts using these distance indicators may be possible with a cumulative signal-to-noise ratio of order 7 in a survey of 300 type 1a supernovae spread over 20,000 square degrees.Comment: 6 pages; 4 figure

A dark energy view of inflation

Traditionally, inflationary models are analyzed in terms of parameters such as the scalar spectral index ns and the tensor to scalar ratio r, while dark energy models are studied in terms of the equation of state parameter w. Motivated by the fact that both deal with periods of accelerated expansion, we study the evolution of w during inflation, in order to derive observational constraints on its value during an earlier epoch likely dominated by a dynamic form of dark energy. We find that the cosmic microwave background and large-scale structure data is consistent with w_inflation=-1 and provides an upper limit of 1+w <~ 0.02. Nonetheless, an exact de Sitter expansion with a constant w=-1 is disfavored since this would result in ns=1.Comment: 5 pages, 4 figures; v2: minor modifications to match published versio

Domain Bubbles of Extra Dimensions

``Dimension bubbles'' of the type previously studied by Blau and Guendelman [S.K. Blau and E.I. Guendelman, Phys. Rev. D40, 1909 (1989)], which effectively enclose a region of 5d spacetime and are surrounded by a region of 4d spacetime, can arise in a 5d theory with a compact extra dimension that is dimensionally reduced to give an effective 4d theory. These bubbles with thin domain walls can be stabilized against total collapse in a rather natural way by a scalar field which, as in the case with ``ordinary'' nontopological solitons, traps light scalar particles inside the bubble.Comment: 13 pages, no figures; to appear in Phys.Rev.

Optimising Spectroscopic and Photometric Galaxy Surveys: Efficient Target Selection and Survey Strategy

The next generation of spectroscopic surveys will have a wealth of photometric data available for use in target selection. Selecting the best targets is likely to be one of the most important hurdles in making these spectroscopic campaigns as successful as possible. Our ability to measure dark energy depends strongly on the types of targets that we are able to select with a given photometric data set. We show in this paper that we will be able to successfully select the targets needed for the next generation of spectroscopic surveys. We also investigate the details of this selection, including optimisation of instrument design and survey strategy in order to measure dark energy. We use color-color selection as well as neural networks to select the best possible emission line galaxies and luminous red galaxies for a cosmological survey. Using the Fisher matrix formalism we forecast the efficiency of each target selection scenario. We show how the dark energy figures of merit change in each target selection regime as a function of target type, survey time, survey density and other survey parameters. We outline the optimal target selection scenarios and survey strategy choices which will be available to the next generation of spectroscopic surveys.Comment: 16 pages, 22 figures, accepted to MNRAS in dec 201

Model-Independent Constraints on Dark Energy Density from Flux-averaging Analysis of Type Ia Supernova Data

We reconstruct the dark energy density $\rho_X(z)$ as a free function from current type Ia supernova (SN Ia) data (Tonry et al. 2003; Barris et al. 2003; Knop et al. 2003), together with the Cosmic Microwave Background (CMB) shift parameter from CMB data (WMAP, CBI, and ACBAR), and the large scale structure (LSS) growth factor from 2dF galaxy survey data. We parametrize $\rho_X(z)$ as a continuous function, given by interpolating its amplitudes at equally spaced $z$ values in the redshift range covered by SN Ia data, and a constant at larger $z$ (where $\rho_X(z)$ is only weakly constrained by CMB data). We assume a flat universe, and use the Markov Chain Monte Carlo (MCMC) technique in our analysis. We find that the dark energy density $\rho_X(z)$ is constant for 0 \la z \la 0.5 and increases with redshift $z$ for 0.5 \la z \la 1 at 68.3% confidence level, but is consistent with a constant at 95% confidence level. For comparison, we also give constraints on a constant equation of state for the dark energy. Flux-averaging of SN Ia data is required to yield cosmological parameter constraints that are free of the bias induced by weak gravitational lensing \citep{Wang00b}. We set up a consistent framework for flux-averaging analysis of SN Ia data, based on \cite{Wang00b}. We find that flux-averaging of SN Ia data leads to slightly lower $\Omega_m$ and smaller time-variation in $\rho_X(z)$. This suggests that a significant increase in the number of SNe Ia from deep SN surveys on a dedicated telescope \citep{Wang00a} is needed to place a robust constraint on the time-dependence of the dark energy density.Comment: Slightly revised in presentation, ApJ accepted. One color figure shows rho_X(z) reconstructed from dat