Constraining the equation of state of the Universe from Distant Type Ia Supernovae and Cosmic Microwave Background Anisotropies

We analyse the constraints that can be placed on a cosmological constant or quintessence-like component by combining observations of Type Ia supernovae with measurements of anisotropies in the cosmic microwave background. We use the recent supernovae sample of Perlmutter et al and observations of the CMB anisotropies to constraint the equation of state (w_Q = p/rho) in quintessence-like models via a likelihood analysis. The 2 sigma upper limits are w_Q < -0.6 if the Universe is assumed to be spatially flat, and w_Q < -0.4 for universes of arbitrary spatial curvature. The upper limit derived for a spatially flat Universe is close to the lower limit (w_Q approx -0.7) allowed for simple potentials, implying that additional fine tuning may be required to construct a viable quintessence model.Comment: 9 pages, 8 Postscript figures, uses mn.sty. submitted to MNRA

Hybrid Estimation of CMB Polarization Power Spectra

This paper generalises the hybrid power spectrum estimator developed in Efstathiou (2004a) to the estimation of polarization power spectra of the cosmic microwave background radiation. The hybrid power spectrum estimator is unbiased and we show that it is close to optimal at all multipoles, provided the pixel noise satisfies certain reasonable constraints. Furthermore, the hybrid estimator is computationally fast and can easily be incorporated in a Monte-Carlo chain for Planck-sized data sets. Simple formulae are given for the covariance matrices, including instrumental noise, and these are tested extensively against numerical simulations. We compare the behaviour of simple pseudo-Cell estimates with maximum likelihood estimates at low multipoles. For realistic sky cuts, maximum likelihood estimates reduce very significantly the mixing of E and B modes. To achieve limits on the scalar-tensor ratio of r<<0.1 from sky maps with realistic sky cuts, maximum likelihood methods, or pseudo-Cell estimators based on unambiguous E and B modes, will be essential.Comment: 22 pages, 11 figures, submitted to MNRA

Power Spectrum Analysis of the Stromlo-APM Redshift Survey

We test estimators of the galaxy power spectrum $P(k)$ against simulated galaxy catalogues constructed from N-body simulations and we derive formulae to correct for biases. These estimators are then applied to compute the power spectrum of galaxies in the Stromlo-APM redshift survey. We test whether the amplitude of $P(k)$ depends on galaxy luminosity, but find no significant luminosity dependence except at absolute magnitudes brighter than M_{\bj} = -20.3, (H_{0} = 100 \kms) where there is some evidence for a rise in the amplitude of $P(k)$. By comparing the redshift space power spectrum of the Stromlo-APM survey with the real space power spectrum determined from the parent APM Galaxy Survey, we attempt to measure the distortion in the shape of $P(k)$ caused by galaxy peculiar motions. We find some evidence for an effect, but the errors are large and do not exclude a value of $\beta = \Omega^{0.6}/b = 1$, where $\Omega$ is the cosmological density parameter and $b$ is the linear biasing parameter relating galaxy fluctuations to those in the mass, $\left(\delta \rho/\rho\right)_{gal} = b \left(\delta \rho/\rho\right)_{m}$. The shape of the Stromlo-APM power spectrum is consistent with that determined from the CfA-2 survey, but has a slightly higher amplitude by a factor of about 1.4 than the power spectrum of IRAS galaxies.Comment: 14 pages, gziped and uuencoded postscript file. Submitted to MNRA

Reconstruction of cosmological initial conditions from galaxy redshift catalogues

We present and test a new method for the reconstruction of cosmological initial conditions from a full-sky galaxy catalogue. This method, called ZTRACE, is based on a self-consistent solution of the growing mode of gravitational instabilities according to the Zel'dovich approximation and higher order in Lagrangian perturbation theory. Given the evolved redshift-space density field, smoothed on some scale, ZTRACE finds via an iterative procedure, an approximation to the initial density field for any given set of cosmological parameters; real-space densities and peculiar velocities are also reconstructed. The method is tested by applying it to N-body simulations of an Einstein-de Sitter and an open cold dark matter universe. It is shown that errors in the estimate of the density contrast dominate the noise of the reconstruction. As a consequence, the reconstruction of real space density and peculiar velocity fields using non-linear algorithms is little improved over those based on linear theory. The use of a mass-preserving adaptive smoothing, equivalent to a smoothing in Lagrangian space, allows an unbiased (although noisy) reconstruction of initial conditions, as long as the (linearly extrapolated) density contrast does not exceed unity. The probability distribution function of the initial conditions is recovered to high precision, even for Gaussian smoothing scales of ~ 5 Mpc/h, except for the tail at delta >~ 1. This result is insensitive to the assumptions of the background cosmology.Comment: 19 pages, MN style, 12 figures included, revised version. MNRAS, in pres

How Stochastic is the Relative Bias Between Galaxy Types?

Examining the nature of the relative clustering of different galaxy types can help tell us how galaxies formed. To measure this relative clustering, I perform a joint counts-in-cells analysis of galaxies of different spectral types in the Las Campanas Redshift Survey (LCRS). I develop a maximum-likelihood technique to fit for the relationship between the density fields of early- and late-type galaxies. This technique can directly measure nonlinearity and stochasticity in the biasing relation. At high significance, a small amount of stochasticity is measured, corresponding to a correlation coefficient of about 0.87 on scales corresponding to 15 Mpc/h spheres. A large proportion of this signal appears to derive from errors in the selection function, and a more realistic estimate finds a correlation coefficient of about 0.95. These selection function errors probably account for the large stochasticity measured by Tegmark & Bromley (1999), and may have affected measurements of very large-scale structure in the LCRS. Analysis of the data and of mock catalogs shows that the peculiar geometry, variable flux limits, and central surface-brightness selection effects of the LCRS do not seem to cause the effect.Comment: 38 pages, 14 figures. Submitted to Apj. Modified from a chapter of my Ph.D. Thesis at Princeton University, available at http://www-astro-theory.fnal.gov/Personal/blanton/thesis/index.htm

The Beylkin-Cramer Summation Rule and A New Fast Algorithm of Cosmic Statistics for Large Data Sets

Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and operators within the framework of multi-resolution analysis (MRA), and realize theirs discrete representations. Accordingly, a homogenous point process could be equivalently described by a operation of a Toeplitz matrix on a vector, which is accomplished by making use of fast Fourier transformation. The algorithm could be applied widely in the cosmic statistics to tackle large data sets. Especially, we demonstrate this novel technique using the spherical, cubic and cylinder counts in cells respectively. The numerical test shows that the algorithm produces an excellent agreement with the expected results. Moreover, the algorithm introduces naturally a sharp-filter, which is capable of suppressing shot noise in weak signals. In the numerical procedures, the algorithm is somewhat similar to particle-mesh (PM) methods in N-body simulations. As scaled with $O(N\log N)$, it is significantly faster than the current particle-based methods, and its computational cost does not relies on shape or size of sampling cells. In addition, based on this technique, we propose further a simple fast scheme to compute the second statistics for cosmic density fields and justify it using simulation samples. Hopefully, the technique developed here allows us to make a comprehensive study of non-Guassianity of the cosmic fields in high precision cosmology. A specific implementation of the algorithm is publicly available upon request to the author.Comment: 27 pages, 9 figures included. revised version, changes include (a) adding a new fast algorithm for 2nd statistics (b) more numerical tests including counts in asymmetric cells, the two-point correlation functions and 2nd variances (c) more discussions on technic

The Correlation Function of Rich Clusters of Galaxies in CDM-like Models

We use ensembles of high-resolution CDM simulations to investigate the shape and amplitude of the two point correlation function of rich clusters. The standard scale-invariant CDM model with $\Omega=1$ provides a poor description of the clustering measured from the APM rich cluster redshift survey, which is better fitted by models with more power at large scales. The amplitudes of the rich cluster correlation functions measured from our models depend weakly on cluster richness. Analytic calculations of the clustering of peaks in a Gaussian density field overestimate the amplitude of the N-body cluster correlation functions, but reproduce qualitatively the weak trend with cluster richness. Our results suggest that the high amplitude measured for the correlation function of richness class $R \geq 2$ Abell clusters is either an artefact arising from incompleteness in the Abell catalogue, or an indication that the density perturbations in the early universe were very non-Gaussian.Comment: uuencoded compressed postscript ,MNRAS, in press, OUAST-93-1

First Structure Formation: A Simulation of Small Scale Structure at High Redshift

We describe the results of a simulation of collisionless cold dark matter in a LambdaCDM universe to examine the properties of objects collapsing at high redshift (z=10). We analyze the halos that form at these early times in this simulation and find that the results are similar to those of simulations of large scale structure formation at low redshift. In particular, we consider halo properties such as the mass function, density profile, halo shape, spin parameter, and angular momentum alignment with the minor axis. By understanding the properties of small scale structure formation at high redshift, we can better understand the nature of the first structures in the universe, such as Population III stars.Comment: 31 pages, 14 figures; accepted for publication in ApJ. Figure 1 can also be viewed at http://cfa-www.harvard.edu/~hjang/research