Lensing and high-z supernova surveys

Gravitational lensing causes the distribution of observed brightnesses of standard candles at a given redshift to be highly non-gaussian. The distribution is strongly, and asymmetrically, peaked at a value less than the expected value in a homogeneous Robertson-Walker universe. Therefore, given any small sample of observations in an inhomogeneous universe, the most likely observed luminosity is at flux values less than the Robertson-Walker value. This paper explores the impact of this systematic error due to lensing upon surveys predicated on measuring standard candle brightnesses. We re-analyze recent results from the high-z supernova team (Riess et al. 1998), both when most of the matter in the universe is in the form of compact objects (represented by the empty-beam expression, corresponding to the maximal case of lensing), and when the matter is continuously distributed in galaxies. We find that the best-fit model remains unchanged (at Omega_m=0, Omega_Lambda=0.45), but the confidence contours change size and shape, becoming larger (and thus allowing a broader range of parameter space) and dropping towards higher values of matter density, Omega_m (or correspondingly, lower values of the cosmological constant, Omega_Lambda). These effects are slight when the matter is continuously distributed. However, the effects become considerably more important if most of the matter is in compact objects. For example, neglecting lensing, the Omega_m=0.5, Omega_Lambda=0.5 model is more than 2 sigma away from the best fit. In the empty-beam analysis, this cosmology is at 1 sigma.Comment: 11 pages, 3 ps figures. uses aaspp4.sty. accepted to ApJ Letters. includes analysis of lensing due to matter continuously distributed in galaxie

On the structure of the BBGKY hierarchy for a Boltzmann gas

Structure of BBGKY hierarchy for Boltzmann gas and particle distribution

Cosmology from supernova magnification maps

High-z Type Ia supernovae are expected to be gravitationally lensed by the foreground distribution of large-scale structure. The resulting magnification of supernovae is statistically measurable, and the angular correlation of the magnification pattern directly probes the integrated mass density along the line of sight. Measurements of cosmic magnification of supernovae therefore complements galaxy shear measurements in providing a direct measure of clustering of the dark matter. As the number of supernovae is typically much smaller than the number of sheared galaxies, the two-point correlation function of lensed Type Ia supernovae suffers from significantly increased shot noise. Neverthless, we find that the magnification map of a large sample of supernovae, such as that expected from next generation dedicated searches, will be easily measurable and provide an important cosmological tool. For example, a search over 20 sq. deg. over five years leading to a sample of ~ 10,000 supernovae would measure the angular power spectrum of cosmic magnification with a cumulative signal-to-noise ratio of ~20. This detection can be further improved once the supernova distance measurements are cross-correlated with measurements of the foreground galaxy distribution. The magnification maps made using supernovae can be used for important cross-checks with traditional lensing shear statistics obtained in the same fields, as well as help to control systematics. We discuss two applications of supernova magnification maps: the breaking of the mass-sheet degeneracy when estimating masses of shear-detected clusters, and constraining the second-order corrections to weak lensing observables.Comment: 4 pages, 2 figures, ApJL submitted; "Signal" discussed here is the extra covariance in astro-ph/050958

Problems with Pencils: Lensing Covariance of Supernova Distance Measurements

While luminosity distances from Type Ia supernovae (SNe) provide a powerful probe of cosmological parameters, the accuracy with which these distances can be measured is limited by cosmic magnification due to gravitational lensing by the intervening large-scale structure. Spatial clustering of foreground mass fluctuations leads to correlated errors in distance estimates from SNe. By including the full covariance matrix of supernova distance measurements, we show that a future survey covering more than a few square degrees on the sky, and assuming a total of ~2000 SNe, will be largely unaffected by covariance noise. ``Pencil beam'' surveys with small fields of view, however, will be prone to the lensing covariance, leading to potentially significant degradations in cosmological parameter estimates. For a survey with 30 arcmin mean separation between SNe, lensing covariance leads to a ~45% increase in the expected errors in dark energy parameters compared to fully neglecting lensing, and a ~20% increase compared to including just the lensing variance. Given that the lensing covariance is cosmology dependent and cannot be mapped out sufficiently accurately with direct weak lensing observations, surveys with small mean SN separation must incorporate the effects of lensing covariance, including its dependence on the cosmological parameters.Comment: 4 pages, 2 figures, PRL submitted; "Noise" discussed here is the "signal" in astro-ph/050957

Future supernovae data and quintessence models

The possibility to unambiguously determine the equation-of-state of the cosmic dark energy with existing and future supernovae data is investigated. We consider four evolution laws for this equation-of-state corresponding to four quintessential models, i.e. i) a cosmological constant, ii) a general barotropic fluid, iii) a perfect fluid with a linear equation-of-state and iv) a more physical model based on a pseudo-Nambu-Goldstone boson field. We explicitly show the degeneracies present not only within each model but also between the different models : they are caused by the multi-integral relation between the equation-of-state of dark energy and the luminosity distance. Present supernova observations are analysed using a standard $\chi^2$ method and the minimal $\chi^2$ values obtained for each model are compared. We confirm the difficulty to discriminate between these models using present SNeIa data only. By means of simulations, we then show that future SNAP observations will not remove all the degeneracies. For example, wrong estimations of $\Omega_m$ with a good value of $\chi^2_{min}$ could be found if the right cosmological model is not used to fit the data. We finally give some probabilities to obtain unambiguous results, free from degeneracies. In particular, the probability to confuse a cosmological constant with a true barotropic fluid with an equation-of-state different from -1 is shown to be 95% at a $2 \sigma$ level.Comment: 12 pages. This improved version has been accepted for publication in M.N.R.A.

Bias and high-order galaxy correlation functions in the APM Galaxy Survey

On large scales, the higher order moments of the mass distribution, S_J=\xibar_J/\xibar_2^{J-1}, e.g., the skewness $S_3$ and kurtosis $S_4$, can be predicted using non-linear perturbation theory. Comparison of these predictions with moments of the observed galaxy distribution probes the bias between galaxies and mass. Applying this method to models with initially Gaussian fluctuations and power spectra $P(k)$ similar to that of galaxies in the APM survey, we find that the predicted higher order moments $S_J(R)$ are in good agreement with those directly inferred from the APM survey {\it in the absence of bias}. We use this result to place limits on the linear and non-linear bias parameters. Models in which the extra power observed on large scales (with respect to standard CDM) is produced by scale-dependent bias match the APM higher order amplitudes only if non-linear bias (rather than non-linear gravity) generates the observed higher order moments. When normalized to COBE DMR, these models are significantly ruled out by the $S_3$ observations. The cold plus hot dark matter model normalized to COBE can reproduce the APM higher order correlations if one introduces non-linear bias terms, while the low-density CDM model with a cosmological constant does not require any bias to fit the large-scale amplitudes.Comment: 8 pages, 2 figures included, uuencoded postscript file (100 kB), Fermilab-Pub-94/207-

Lensing and Supernovae: Quantifying The Bias on the Dark Energy Equation of State

The gravitational magnification and demagnification of Type Ia supernovae (SNe) modify their positions on the Hubble diagram, shifting the distance estimates from the underlying luminosity-distance relation. This can introduce a systematic uncertainty in the dark energy equation of state (EOS) estimated from SNe, although this systematic is expected to average away for sufficiently large data sets. Using mock SN samples over the redshift range $0 < z \leq 1.7$ we quantify the lensing bias. We find that the bias on the dark energy EOS is less than half a percent for large datasets ($\gtrsim$ 2,000 SNe). However, if highly magnified events (SNe deviating by more than 2.5$\sigma$) are systematically removed from the analysis, the bias increases to $\sim$ 0.8%. Given that the EOS parameters measured from such a sample have a 1$\sigma$ uncertainty of 10%, the systematic bias related to lensing in SN data out to $z \sim 1.7$ can be safely ignored in future cosmological measurements.Comment: 5 pages, 4 figures; one figure and references added; minor modifications to text; reflects version accepted for publication in Ap

A Galaxy Photometric Redshift Catalog for the Sloan Digital Sky Survey Data Release 6

We present and describe a catalog of galaxy photometric redshifts (photo-z's) for the Sloan Digital Sky Survey (SDSS) Data Release 6 (DR6). We use the Artificial Neural Network (ANN) technique to calculate photo-z's and the Nearest Neighbor Error (NNE) method to estimate photo-z errors for ~ 77 million objects classified as galaxies in DR6 with r < 22. The photo-z and photo-z error estimators are trained and validated on a sample of ~ 640,000 galaxies that have SDSS photometry and spectroscopic redshifts measured by SDSS, 2SLAQ, CFRS, CNOC2, TKRS, DEEP, and DEEP2. For the two best ANN methods we have tried, we find that 68% of the galaxies in the validation set have a photo-z error smaller than sigma_{68} =0.021 or $0.024. After presenting our results and quality tests, we provide a short guide for users accessing the public data.Comment: 16 pages, 12 figure

The Projected Three-point Correlation Function: Theory and Observations

We report results for the angular three-point galaxy correlation function in the APM survey and compare them with theoretical expectations. For the first time, these measurements extend to sufficiently large scales to probe the weakly non-linear regime. On large scales, the results are in good agreement with the predictions of non-linear cosmological perturbation theory, for a model with initially Gaussian fluctuations and linear power spectrum $P(k)$ consistent with that inferred from the APM survey. These results reinforce the conclusion that large-scale structure is driven by non-linear gravitational instability and that APM galaxies are relatively unbiased tracers of the mass on large scales; they also provide stringent constraints upon models with non-Gaussian initial conditions and strongly exclude the standard cold dark matter model.Comment: 10 pages, latex, 2 figures, submited to ApJ Le