Cosmic string lens phenomenology: Model of Poisson energy distribution

We present a novel approach for investigating lens phenomenology of cosmic strings in order to elaborate detection strategies in galaxy deep field images. To account for the complexity of the projected energy distribution of string networks we assume their lens effects to be similar to those of a straight string carrying a random energy distribution. In such a model we show that, unlike the case of uniform strings, critical phenomena naturally appear. We explore the properties of the critical lines and caustics. In particular, assuming that the energy coherence length along the string is much smaller than the observation scale, we succeed in computing the total length of critical lines per unit string length and find it to be 4/√3E(3/4). The length of the associated caustic lines can also be computed to be 16/(π√3)E(3/4). The picture we obtain here for the phenomenology of cosmic string detection is clearly at variance with common lore.