Super-horizon cosmic string correlations

Abstract

When gauged cosmic strings form in a symmetry-breaking phase transition, the gauge field configuration at the time becomes imprinted in the spatial string distribution by the flux trapping mechanism. Causality and flux conservation suggest that that quantum and thermal gauge field fluctuations give rise to long-range superhorizon correlations in the string network. Classical field theory simulations in the Abelian Higgs model confirm this finding. In contrast, the Kibble-Zurek mechanism which most cosmic string studies are based on, only gives rise to short-distance, subhorizon correlations. These results may have implications for cosmology, and it may also be possible to test them in superconductor experiments.

Cosmic Strings and Their Induced Non‐Gaussianities in the Cosmic Microwave Background

“…Its sign depends on the sign of c 0 defined in Eq. (71), and contrary to what one could naively expect c 0 = 0: the projected string velocity and curvature vectors are correlated. This can be shown by starting again from the equations of motion (29), but this time, in the light cone gauge.…”

“…From the Kibble's argument, one expects the phase of the Higgs field to be random and the resulting string path should be a self-avoiding random walk with a given correlation length [68]. Performing lattice simulations allows to probe in more details the string forming mechanism and gives a more accurate picture of a cosmic string network just after its formation [69,70,71,72]. Abelian Higgs simulations are also used to compute the cosmological evolution of such a network [73,74,75] (see Sec.…”

Correlations beyond the horizon

“…Long range correlations were predicted in the HR model [11,12]. However, these correlations should decay as r −4 , instead of r −1 which we observe and the predicted domain size is on a mm scale, 2 orders of magnitude larger than the few µm which we see.…”

“…Thus, the Kibble-Zurek model is a universal theory of defect formation whose applications range from phase transitions in grand unified theories of high-energy physics to phase transitions observed in different condensed-matter systems. An alternative mechanism of spontaneous vortex formation in superconductors was proposed by Hindmarsh and Rajantie [11,12] (HR). According to this mechanism, thermal fluctuations of the magnetic field freeze inside the superconductor during the transition, creating domains of magnetic flux with the same polarity and characteristic size.…”

The Kibble–Zurek mechanism in a subcritical bifurcation

“…In the framework represented in figure 1, quenches are performed with a linear dependence of the control parameter on the crossing rate ε(t) = µt along the transition through the threshold ε = 0 (see sketch in figure 4) from ε i = −0.5 to ε f = 0.01. To ensure valid equivalent initial states (conditions) [75], we prepare an amplified noisy state and we let it evolve freely, before imposing the quench, over six units of time, which is longer than the maximum relaxation time at ε i . This free evolution period sets a practical limit to the observation of the KZ-scaling regime at relatively high µ (in our case µ max.…”