Spontaneous breaking of global symmetries and the consequent field ordering provide a mechanism for the formation of structure in the Universe. We compare the predictions of these theories with the cosmic microwave background (CMB) anisotropy recently detected by the Cosmic Background Explorer (COBE) and with recent observations of large-scale structure. In this paper we give a self-contained discussion of the analytical formalism, and numerical techniques required to simulate the texture, global monopole, global string, and nontopological texture scenarios. The Universe is assumed to have critical density and to be dominated by "cold" dark matter. Our main conclusions are that all of these scenarios are consistent with the reported amplitude, statistical properties, and multipole spectrum of the COBE signal, for a high bias factor $b\sim (2\mathrm{}\pm 1)h^{-1\mathrm{}}$. The distinctive non-Gaussian character of the CMB anisotropies produced in these theories is investigated, and the prospects for its detection are discussed. We also compare the theories with the recent data on the large-scale galaxy distribution. Like the "standard" inflationary scenarios, if $\Omega =1\mathrm{}$, $\Lambda =0\mathrm{}$, these theories may have insufficient power on large scales.

• Received 13 January 1993

DOI:https://doi.org/10.1103/PhysRevD.49.692