Using recent simulation results, we provide the mass and speed spectrum of cosmic string loops. This is the quantity of primary interest for many phenomenological signatures of cosmic strings, and it can be accurately predicted using recently acquired detailed knowledge of the loop production function. We emphasize that gravitational smoothing of long strings does not play any role in determining the total number of existing loops. We derive a bound on the string tension imposed by recent constraints on the stochastic gravitational wave background from pulsar timing arrays, finding Gµ ≤ 2.8 × 10 −9 . We also provide a derivation of the Boltzmann equation for cosmic string loops in the language of differential forms.

Using a new parallel computing technique, we have run the largest cosmic string simulations ever performed. Our results confirm the existence of a long transient period where a non-scaling distribution of small loops is produced at lengths depending on the initial correlation scale. As time passes, this initial population gives way to the true scaling regime, where loops of size approximately equal to one-twentieth the horizon distance become a significant component. We observe similar behavior in matter and radiation eras, as well as in flat space. In the matter era, the scaling population of large loops becomes the dominant component; we expect this to eventually happen in the other eras as well.

We analyze the gravitational wave signatures of a network of metastable cosmic strings. We consider the case of cosmic string instability to breakage, with no primordial population of monopoles. This scenario is well motivated from GUT and string theoretic models with an inflationary phase below the GUT/string scale. The network initially evolves according to a scaling solution, but with breakage events resulting from confined monopoles (beads) being pair produced and accelerated apart. We find these ultra-relativistic beads to be a potent source of gravitational waves bursts, detectable by Initial LIGO, Advanced LIGO, and LISA. Indeed, Advanced LIGO could observe bursts from strings with tensions as low as Gµ ∼ 10 −12 . In addition, we find that ultra-relativistic beads produce a scale-invariant stochastic background detectable by LIGO, LISA, and pulsar timing experiments. The stochastic background is scale invariant up to Planckian frequencies. This phenomenology provides new constraints and signatures of cosmic strings that disappear long before the present day.

Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.