We have recently made public a rather technical paper in which we explicitly and unambiguously calculate the cosmic string loop number density distribution in our universe coming from various motivated loop production functions. Such a density distribution crucially determines the spectrum of their emitted gravitational waves, a smooking gun for their potential discovery.

Together with **Pierre Auclair**,
**Mairi Sakellariadou**
and **Danièle Steer**, we have
carefuly explored in Ref.[1] the consequences of
changing the slope of the Polchinski-Rocha loop production function to the actual
observable cosmic string loop distribution. This is the parameter
in the next plot:

For the cases we have referred to as “sub-critical”, , corresponding to steep slopes in the previous figure, we recover the results of Ref. [2]. The parameter encodes the growing rate of the scale factor , namely, we assume .

For shallower slopes, the so-called “critical” and “super-critical” cases, , we find that either the loop distribution incessantly grows, or, with some regularisation, reaches a stationnary distribution whose shape depends on what happens on the larger length scales. This is best illustrated by the following plot:

It compares the loop number density produced by assuming an infinitely
sharp loop production function peaked at (green
curve) with a (regularised) super-critical Polchinski-Rocha
distribution having (purple curve), in the radiation
era (). As this plot shows, the gravitational backreaction
scale, , at which the loop production function is
cut **always matters** and is responsible for the plateau on the
purple curve at small values. The existence of a second
plateau around comes from the Infra-Red
sensitivity of all super-critical loop production functions.