The growth of linear perturbations in generic defect models for structure formation

We study the growth of linear perturbations induced by a generic causal scaling source as a function of the cosmological parameters $h$, $\Omega^m_0$ and $\Omega^\Lambda_0$. We show that for wavenumbers k \gsim 0.01 h/Mpc the spectrum of density and velocity perturbations scale in a similar way to that found in inflationary models with primordial perturbations. We show that this result is independent of the more or less incoherent nature of the source, the small scale power spectrum of the source and of deviations from scaling which naturally occur at late times if $\Omega^m_0 \neq 1$.Comment: 4 pages, 2 figure

Dynamics of perfect fluid Unified Dark Energy models

In this paper we show that a \emph{one-to-one} correspondence exists between any dark energy model and an equivalent (from a cosmological point of view, in the absence of perturbations) quartessence model in which dark matter and dark energy are described by a single perfect fluid. We further show that if the density fluctuations are small, the evolution of the sound speed squared, $c_s^2$, is fully coupled to the evolution of the scale factor and that the transition from the dark matter to the dark energy dominated epoch is faster (slower) than in a standard $\Lambda$CDM model if $c_s^2 > 0$ ($c_s^2 < 0$). In particular, we show that the mapping of the simplest quintessence scenario with constant $w_Q \equiv p_Q/ \rho_Q$ into a unified dark energy model requires $c_s^2 -1$) contrasting to the Chaplygin gas scenario where one has $c_s^2 > 0$. However, we show that non-linear effects severely complicate the analysis, in particular rendering linear results invalid even on large cosmological scales. Although a detailed analysis of non-linear effects requires solving the full Einstein field equations, some general properties can be understood in simple terms. In particular, we find that in the context of Chaplygin gas models the transition from the dark matter to the dark energy dominated era may be anticipated with respect to linear expectations leading to a background evolution similar to that of standard $\Lambda$CDM models. On the other hand, in models with $c_s^2 > 0$ the expected transition from the decelerating to the accelerating phase may never happen.Comment: 5 page

Cosmic Numbers: A Physical Classification for Cosmological Models

We introduce the notion of the cosmic numbers of a cosmological model, and discuss how they can be used to naturally classify models according to their ability to solve some of the problems of the standard cosmological model.Comment: 3 pages, no figures. v2: Two references added, cosmetic changes. Version to appear in Phys. Rev. D (Brief reports

Cosmic strings, loops, and linear growth of matter perturbations

We describe the detailed study and results of high-resolution numerical simulations of string-induced structure formation in open universes and those with a non-zero cosmological constant. The effect from small loops generated from the string network has also been investigated. We provide a semi-analytical model which can reproduce these simulation results. A detailed study of cosmic string network properties regarding structure formation is also given, including the correlation time, the topological analysis of the source spectrum, the correlation between long strings and loops, and the evolution of long-string and loop energy densities. For models with $\Gamma=\Omega h=0.1--0.2 and a cold dark matter background, we show that the linear density fluctuation power spectrum induced by cosmic strings has both an amplitude at$8 h^{-1}$Mpc,$\sigma_8$, and an overall shape which are consistent within uncertainties with those currently inferred from galaxy surveys. The cosmic string scenario with hot dark matter requires a strongly scale-dependent bias in order to agree with observations.Comment: 60 pages, 24 figure