Abstract: We discuss the feasibility of measuring the cosmological metric using the redshift space correlation function of the Lya forest in multiple lines of sight, as a function of angular and velocity separation. The geometric parameter that is measured is f(z) = H(z) D(z)/c, where H(z) is the Hubble constant and D(z) the angular diameter distance at redshift z. The correlation function is computed in linear theory. We describe a method to measure it from observations with the Gaussianization procedure of Croft et al (1998) to map the Lya forest transmitted flux to an approximation of the linear density field. The effect of peculiar velocities on the shape of the recovered power spectrum is pointed out. We estimate the error in recovering the f(z) factor from observations due to the variance in the Lya absorbers. We show that ~ 20 pairs of quasars (separations < 3') are needed to distinguish a flat \Omega_0=1 universe from a universe with \Omega_0=0.2, \Omega_\Lambda=0.8. A second parameter that is obtained from the correlation function of the Lya forest is \beta \simeq \Omega(z)^{0.6}/b (affecting the magnitude of the peculiar velocities), where b is a linear theory bias of the Lya forest. The statistical error of f(z) is reduced if b can be determined independently from numerical simulations, reducing the number of quasar pairs needed for constraining cosmology to approximately six. On small scales, where the correlation function is higher, f(z) should be measurable with fewer quasars, but non-linear effects must then be taken into account. The anisotropy of the non-linear redshift space correlation function as a function of scale should also provide a precise quantitative test of the gravitational instability theory of the Lya forest.

Abstract: It is well known that a combined analysis of the Sunyaev-Zel'dovich (SZ) effect and the X-ray emission observations can be used to determine the angular diameter distance to galaxy clusters, from which the Hubble constant is derived. The present values of the Hubble constant derived through the SZ/X-ray route have a broad distribution ranging from 30 to 70 km s^-1 Mpc^-1. We show that this broad distribution is primarily due to the projection effect of aspherical clusters, which have been modeled using spherical geometries. The projection effect is also expected to broaden the measured gas mass fraction of galaxy clusters. However, the projection effect either under- or overestimate the Hubble constant and the gas mass fraction in an opposite manner, producing an anticorrelation. Using the published data for SZ/X-ray clusters, we show that the current Hubble constant distribution is negatively correlated with the measured gas mass fraction for same clusters, suggesting that the projection effects are present in current results. If the gas mass fraction of galaxy clusters, when measured out to an outer hydrostatic radius is constant, it may be possible to account for the line of sight geometry of galaxy clusters. However, to perform such an analysis, an independent measurement of the total mass of galaxy clusters, such as from weak lensing, is needed. Using the weak lensing, optical velocity dispersion, SZ and X-ray data, we outline an alternative method to calculate the Hubble constant, which is subjected less to projection effects than the present method based on only the SZ and X-ray data. For A2163, the Hubble constant based on published SZ, X-ray and weak lensing observations is \sim 49 \pm 29 km s^-1 Mpc^-1.

Abstract: It is well known that a combined analysis of the Sunyaev-Zel'dovich (SZ) effect and the X-ray emission obser- vations can be used to determine the angular diameter distance to galaxy clusters, from which the Hubble constant is derived. The present values of the Hubble constant derived through the SZ/X-ray route have a broad distribution ranging from 30 to 70 km s 1 Mpc 1 . We show that this broad distribution is primar- ily due to the projection effect of aspherical clusters which have been modeled using spherical geometries. The projection ef- fect is also expected to broaden the measured gas mass fraction in galaxy clusters. However, the projection effect either under- or overestimate the Hubble constant and the gas mass fraction in an opposite manner, producing an anticorrelation. Using the published data for SZ/X-ray clusters, we show that the current Hubble constant distribution is negatively correlated with the measured gas mass fraction for same clusters, suggesting that the projection effects are present in current results. If the gas mass fraction of galaxy clusters, when measured out to an outer hydrostatic radius is constant, it may be possible to account for the line of sight geometry of galaxy clusters. However, to perform such an analysis, an independent measurement of the total mass of galaxy clusters, such as from weak lensing, is needed. Using the weak lensing, optical velocity dispersion, SZ and X-ray data, we outline an alternative method to calculate the Hubble constant, which is subjected less to projection effect than the present method based on only the SZ and X-ray data. For A2163, the Hubble constant based on published SZ, X-ray and weak lensing observations is 49 29 km s 1 Mpc 1 .

Abstract: The relation between the angular diameter distance and redshift ${(d}_{A}\ensuremath{-}z$ relation) in a spherically symmetric dust-shell universe is studied. We discover that the relation agrees with that of an appropriate Friedmann-Lema\^{\i}tre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks similar to a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. We also study the connection of the proper mass of a shell with the mass of gravitationally bound objects. Combining this with the results of the ${d}_{A}\ensuremath{-}z$ relation, we discuss an impact of the local inhomogeneities on the determination of the cosmological parameters through the observation of the locally inhomogeneous universe.

Abstract: Distance relations in a locally inhomogeneous universe are expected to behave like the Dyer-Roeder solution on small angular scales and the Friedmann-Robertson-Walker solution on large angular scales. Within a simple compact clump model the transition between these asymptotic behaviors is demonstrated and quantified. The redshift-dependent transition scale is of order a few arcseconds; this implies that it should have little influence on large angular scale cosmological tests such as the volume-redshift relation but possibly significant effects on arcsecond angular diameter measurements of radio galaxies and active galactic nuclei. For example, at z = 2 on arcsecond scales a clumpy flat universe mimics the angular diameter distance of a smooth Ω = 0.27 model.

Abstract: We present observations of 10 type Ia supernovae (SNe Ia) between 0.16 0) and a current acceleration of the expansion (i.e., q_0 0, the spectroscopically confirmed SNe Ia are consistent with q_0 0 at the 3.0 sigma and 4.0 sigma confidence levels, for two fitting methods respectively. Fixing a ``minimal'' mass density, Omega_M=0.2, results in the weakest detection, Omega_Lambda>0 at the 3.0 sigma confidence level. For a flat-Universe prior (Omega_M+Omega_Lambda=1), the spectroscopically confirmed SNe Ia require Omega_Lambda >0 at 7 sigma and 9 sigma level for the two fitting methods. A Universe closed by ordinary matter (i.e., Omega_M=1) is ruled out at the 7 sigma to 8 sigma level. We estimate the size of systematic errors, including evolution, extinction, sample selection bias, local flows, gravitational lensing, and sample contamination. Presently, none of these effects reconciles the data with Omega_Lambda=0 and q_0 > 0.