Why We Don't See Cosmic Strings

Abstract

Cosmic strings can be formed in symmetry-b reaking phase transition in the early stage of the universe. They are topological defects, analogous to flux tubes in type-II superconductors, or to vortex filaments in superfluid heliu m. Cosmic strings consist of trapped regions of false vacuum in U(1) gauge theories with spontaneous symmetry breaking. Density perturbations that would be produced by these strings of GUT scale, Gμ = η 2 /Mpl 2 = 10 -6 , where G=1/Mpl 2 is Newton's constant, Mpl the Planck mass, μ the mass per unit length of the string and η the symmetry breaking scale, could have served as seeds for the formation of galaxies and clusters. However, recent observation of the cosmic microwave back-ground (CM B) radiat ion disfavored this scenario. The WAMP-data prove that cosmic strings can't contribute more than an insignificant proportion of the primo rdial density perturbation,Gμ ≤ 10 -6 . The space time around a cosmic string is conical, with an angle deficit ∆θ ~ μ. They should produce axially symmetric gravitational lensing effect, not found by observations. Recently, braneworld scenarios suggest the existence of fundamental strings, predicted by superstring theory. These super-massive cosmic strings, Gμ~1, could be produced when the universe underwent phase transitions at energies much higher than the GUT scale. To overcome the conflict with observational bounds, we present the "classical" Nielsen-Olesen string solution on a warped five d imensional space time, where we solved the effective four dimensional equations fro m the fivedimensional equations together with the junction and boundary conditions. Where the mass per unit length in the bulk can be of order of the Planck scale, in the brane it will be warped down to unobservable GUT scale. It turns out that the induced four dimensional space timedoes notshow asymptotic conical behaviour. So there is no angle deficit and the space time seems to be un-physical, at least under fairly weak assumptions on the stress-energy tensor and without a positive brane tension. The results are confirmed by numerical solutions of the field equations.