Some effects of non-conservative gravity on cosmic string configurations

We investigate some consequences of a specific non-conservation of the energy-momentum tensor on the physics of certain cosmic string configurations. This non-conservation is induced by a new gravitational theory recently introduced as an attempt to incorporate dissipative systems in the gravity description. This model of gravity is endowed with a variational principle, where an action-dependence on the geometric sector is assumed. For the Abelian-Higgs string we derive the dynamical equations and provide the numerical solutions describing the behavior of the Higgs and gauge fields as well as the profile of the metric functions for different cases of the parameter that characterises the model. Additionally, from this numerical approach we find how the inner structure of the cosmic string is affected by this underlying gravitational theory, by analyzing the deviations both on the mass per unit length and the deficit angle of the string. Next, we proceed with an analytical treatment obtaining the solution close to the string axis and also the corresponding vacuum solution. Our analytical results are also complemented with the study of a thick cosmic string model, where the defect is endowed with finite core. In this case we have obtained the proper interior solution which joined together with the vacuum metric outside provides an exact solution for the exterior geometry which generalizes previous results and leads to a decreasing of the mass per unit length of the cosmic string.
12 pages, 8 figures. Improved version with more discussion added to the sections II, III.A and V.C. Matches version accepted in EPJC