During the radiation era, and when the correlation length is already growing with the Hubble radius, the texture field has energy density texture ~ ()2 ~ 2 / H-2, and remains a fixed fraction of the total density c ~ t-2 yielding texture ~ G 2. This is the scaling behavior for textures and thus we do not need to worry about textures dominating the universe.
But as we already mentioned, textures are unstable to collapse, and this collapse generates perturbations in the metric of spacetime that eventually lead to large scale structure formation. These perturbations in turn will affect the photon geodesics leading to CMB anisotropies, the clearest possible signature to probe the existence of these exotic objects being the appearance of hot and cold spots in the microwave maps. Due to their scaling behavior, the density fluctuations induced by textures on any scale at horizon crossing are given by ( / )H ~ G 2. CMB temperature anisotropies will be of the same amplitude. Numerically-simulated maps, with patterns smoothed over 10° angular scales, by Bennett & Rhie  yield, upon normalization to the COBE-DMR data, a dimensionless value G 2 ~ 10-6, in good agreement with a GUT phase transition energy scale. It is fair to say, however, that the texture scenario is having problems in matching current data on smaller scales [see, e.g., Durrer, 2000].