Cosmic strings in an open universe: Quantitative evolution and observational consequences

The cosmic string scenario in an open universe is developed—including the equations of motion, a model of network evolution, the large angular scale cosmic microwave background (CMB) anisotropy, and the power spectrum of density fluctuations produced by cosmic strings with dark matter. We first derive the equations of motion for a cosmic string in an open Friedmann-Robertson-Walker (FRW) space-time. With these equations and the cosmic string stress-energy conservation law, we construct a quantitative model of the evolution of the gross features of a cosmic string network in a dust-dominated, $\Omega <1\mathrm{}$ FRW space-time. Second, we apply this model of network evolution to the results of a numerical simulation of cosmic strings in a dust-dominated, $\Omega =1\mathrm{}$ FRW space-time, in order to estimate the rms temperature anisotropy induced by cosmic strings in the CMB. By comparing to the COBE-DMR observations, we obtain the normalization for the cosmic string mass per unit length $\mu$ as a function of $\Omega$. Third, we consider the effects of the network evolution and normalization in an open universe on the large scale structure formation scenarios with either cold or hot dark matter (CDM, HDM). The string+HDM scenario for $\Omega <1\mathrm{}$ appears to produce too little power on scales $k\gtrsim 1$ $\Omega h^2/$Mpc. In a low density universe the string+CDM scenario is a better model for structure formation. We find that for cosmological parameters $\Gamma =\Omega h\sim 0.1$–0.2 in an open universe the string+CDM power spectrum fits the shape of the linear power spectrum inferred from various galaxy surveys. For $\Omega \sim 0.2$–0.4, the model requires a bias $b\gtrsim 2$ in the variance of the mass fluctuation on scales $8h^{-1}$ Mpc. In the presence of a cosmological constant, the spatially flat string+CDM power spectrum requires a slightly lower bias than for an open universe of the same matter density.