RENORMALIZATION Of GRAVITATIONAL SELF INTERACTION FOR WIGGLY STRINGS

It is shown that for any elastic string model with energy density U and tension T , the divergent contribution from gravitational self interaction can be allowed for by an action renormalisation proportional to (U − T ). This formula is applied to the important special case of a bare model of the transonic type (characterised by a constant value of the product UT ) that represents the macroscopically averaged effect of shortwavelength wiggles on an underlying microscopic model of the Nambu-Goto type (characterised by U = T ). Although not so important for lightweight cosmic strings such as may may have been formed later on, for example at the time of electroweak symmetry breaking, gravitational self interaction is generally supposed to have played an essential role in the evolution of the cosmic strings that may have been formed earlier at the epoch of G.U.T. symmetry breaking. In the kind of scenario [1] originally proposed by Kibble an initial period during which the main damping mechanism was the friction exerted by the ambient thermal gas would be followed in by a period during the main damping mechanism would have been gravitational, at least for the local kind of strings to be considered here (in contrast with global strings for which axion radiation damping would have been more important). Nearly all the work that has been done [1] on gravitational self interaction in cosmic strings has been based on the use of a string model of the simplest kind, namely that of Nambu-Goto, in which (with the speed of light set to one) the energy density U and the tension T are both equal to a constant m, where m is a mass scale that will typically of the order of the mass associated with the Higgs field responsible for the relevant vacuum symmetry breaking. The use of such a simple model will be justifiable while gravitational self interaction is important, even in typical cases where the strings are of the current carrying kind whose likely relevance was first pointed out by Witten [2], since, at least a at the outset, the currents would be expected to be very weak so that their effects would be relatively negligible. At a later stage the currents in small loops would intensify as the loops contracted