The number of cosmic string loops
  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 $G\mu \leq
2.8\times 10^{-9}$. We also provide a derivation of the Boltzmann equation for
cosmic string loops in the language of differential forms.
