Strings, texture, and inflation

We examine mechanisms, several of which are proposed here, to generate structure formation, or to just add large-scale features, through either gauged or global cosmic strings or global texture, within the framework of inflation. We first explore the possibility that strings or texture form if there is no coupling between the topological theory and the inflaton or spacetime curvature, via (1) quantum creation, and (2) a sufficiently high reheat temperature. In addition, we examine the prospects for the inflaton field itself to generate strings or texture. Then, models with the string/texture field coupled to the curvature, and an equivalent model with coupling to the inflaton field, are considered in detail. The requirement that inflationary density fluctuations are not so large as to conflict with observations leads to a number of constraints on model parameters. We find that strings of relevance for structure formation can form in the absence of coupling to the inflaton or curvature through the process of quantum creation, but only if the strings are strongly type I, or if they are global strings. If formed after reheating, naturalness suggests that gauged cosmic strings correspond to a type-I superconductor. Similarly, gauged strings formed during inflation via conformal coupling $\ensuremath{\xi}=\frac{1}{6}$ to the spacetime curvature (in a model suggested by Yokoyama in order to evade the millisecond pulsar constraint on cosmic strings) are expected to be strongly type I. Type-II strings are possible if $\ensuremath{\xi}$ is large or if the strength of direct coupling between the string field and inflaton is chosen appropriately. We improve upon the understanding of the formation process of strings and texture during inflation, and find that the alternative fractal string scenario put forth by Vishniac et al. is further restricted in parameter space, but the model still turns out to be much more plausible than the authors had realized. The fractal model, as originally proposed, may in fact lead to ordinary scaling scenarios of structure formation. However, new structure formation scenarios still appear to be quite possible, especially for global strings. Gauged strings leading to nonstandard scenarios must be type I, and the quartic coupling for global texture should satisfy $\ensuremath{\lambda}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ if a new scenario of texture formation is to be possible. We find that the formation of strings and/or texture differs from the standard picture if $\ensuremath{\xi}\ensuremath{\lesssim}\frac{1}{12}$, and that the string and/or texture-curvature interaction is not sufficient to place the characteristic formation scale of texture or strings within the horizon if $\ensuremath{\xi}\ensuremath{\lesssim}0.002$. We estimate the likelihood $P$, in terms of model parameters, that structure in a universe of our size may be described by a nonstandard string or texture scenario. We find that $P$ can be of order unity.