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. 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. . 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.