Observable Quantities in Cosmological Models with Strings

Abstract

The Friedman equation for the universe with arbitrary curvature $(k = 0, \pm 1)$, filled with mutually noninteracting pressureless dust, radiation, cosmological constant, and strings is considered. We assume the string domination scenario for the evolution of the latter component. Moreover, we discuss the simplest possibility for the scaling of the string energy density: $\varrho \propto R^{-2}$. For such models we write down the explicit solution of the Friedman equation. We realize that corresponding cosmological models do not essentially differ from those without strings. We find an analytic formula for the radial coordinate $χ$ of a galaxy with a redshift z and express it in terms of astronomical parameters. This relation is then used for the derivation of the astrophysical formulas such as luminosity distance, angular diameter, and source counts, which may serve for testing the string-dominated universe. It seems that the most sensitive test, at least from the formal point of view, is the formula for the number of galaxies $N(z)$ corresponding to a given value of the redshift. We show that the maximum of $N(z)$ strongly depends on the density of strings, especially if the density is large enough to explain the $Ω$ problem. Other tests are also proposed.