Building analytical three-field cosmological models

A difficult task to deal with is the analytical treatment of models composed by three real scalar fields, once their equations of motion are in general coupled and hard to be integrated. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is within inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.Comment: 11 pages, and 3 figures, updated version published in EPJ

The Peculiar Velocity Function of Galaxy Clusters

The peculiar velocity function of clusters of galaxies is determined using an accurate sample of cluster velocities based on Tully-Fisher distances of Sc galaxies (Giovanelli et al 1995b). In contrast with previous results based on samples with considerably larger velocity uncertainties, the observed velocity function does not exhibit a tail of high velocity clusters. The results indicate a low probability of $\lesssim$\,5\% of finding clusters with one-dimensional velocities greater than $\sim$ 600 {\kms}. The root-mean-square one-dimensional cluster velocity is 293$\pm$28 {\kms}. The observed cluster velocity function is compared with expectations from different cosmological models. The absence of a high velocity tail in the observed function is most consistent with a low mass-density ($\Omega \sim$0.3) CDM model, and is inconsistent at $\gtrsim 3 \sigma$ level with $\Omega$= 1.0 CDM and HDM models. The root-mean-square one-dimensional cluster velocities in these models correspond, respectively, to 314, 516, and 632 {\kms} (when convolved with the observational uncertainties). Comparison with the observed RMS cluster velocity of 293$\pm$28 {\kms} further supports the low-density CDM model.Comment: revised version accepted for publication in ApJ Letters, 18 pages, uuencoded PostScript with 3 figures included; complete paper available through WWW at http://www.astro.princeton.edu/~library/prep.htm

Cosmic homogeneity demonstrated with luminous red galaxies

We test the homogeneity of the Universe at $z\sim 0.3$ with the Luminous Red Galaxy (LRG) spectroscopic sample of the Sloan Digital Sky Survey. First, the mean number $N(R)$ of LRGs within completely surveyed LRG-centered spheres of comoving radius $R$ is shown to be proportional to $R^3$ at radii greater than $R\sim 70 h^{-1} \mathrm{Mpc}$. The test has the virtue that it does not rely on the assumption that the LRG sample has a finite mean density; its results show, however, that there \emph{is} such a mean density. Secondly, the survey sky area is divided into 10 disjoint solid angular regions and the fractional rms density variations of the LRG sample in the redshift range $0.2<z<0.35$ among these ($\sim 2\times10^7 h^{-3} \mathrm{Mpc^3}$) regions is found to be 7 percent of the mean density. This variance is consistent with typical biased \lcdm models and puts very strong constraints on the quality of SDSS photometric calibration.Comment: submitted to Ap

Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richness-dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with \Omega_m = 0.3 and, for comparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high redshift clusters are clustered more strongly (in comoving scale) than low redshift clusters of the same mass. The increased correlations with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation-scale versus cluster mean separation relation, R_0 - d, is found to be, remarkably, independent of redshift to z <~ 2 for LCDM and z <~ 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving R_0 - d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters so that the R_0 - d relation remains essentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ~ 0 and provide precise determination of cosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200