Cosmic string loop production functions

Abstract

Numerical simulations of Nambu-Goto cosmic strings in an expanding universe show that the loop distribution relaxes to an universal configuration, the so-called scaling regime, which is of power law shape on large scales. Precise estimations of the power law exponent are, however, still matter of debate while numerical simulations do not incorporate all the radiation and backreaction effects expected to affect the network dynamics at small scales. By using a Boltzmann approach, we show that the steepness of the loop production function with respect to loops size is associated with drastic changes in the cosmological loop distribution. For a scale factor varying as a(t) ∝ t ν , we find that sub-critical loop production functions, having a Polchinski-Rocha exponent χ < (3ν −1)/2, yield scaling loop distributions which are mostly insensitive to infra-red (IR) and ultra-violet (UV) assumptions about the cosmic string network. For those, cosmological predictions are expected to be relatively robust, in accordance with previous results. On the contrary, critical and super-critical loop production functions, having χ ≥ (3ν − 1)/2, are shown to be IR-physics dependent and this generically prevents the loop distribution to relax towards scaling. In the latter situation, we discuss the additional regularisations needed for convergence and show that, although a scaling regime can still be reached, the shape of the cosmological loop distribution is modified compared to the naive expectation. Finally, we discuss the implications of our findings.

Energy-conservation constraints on cosmic string loop production and distribution functions

“…Thus loop production functions of this form, and loop distribution functions arising from them, should not be used to calculate observable effects. this paper BOS [15] RSB [21] ARSS [19]…”

“…Reference [18] discusses loop production functions (further analyzed as part of Ref. [19]) which grow rapidly toward small scales until they are cut off at some value x c , which is intended to represent the effect of gravitational smoothing on long strings. Specifically, they consider the possibility that…”

“…Now suppose you consider, on the basis of a simulation, that f (x) ∼ x −β with β > 2, as Refs. [18,19] did on the basis of Ref. [21].…”

“…But the conclusion in that case is very different. We can get n(x) ∼ x −2.5 from a wide range of loop production functions, even a δ-function[1,16,19].…”

Constraints on Cosmic Strings Using Data from the Third Advanced LIGO–Virgo Observing Run

“…There is a qualitative difference between these two models, since in the latter, tiny loops are produced in a much larger amount than in the former. In addition, we will use a new model, based on [34] and labeled C, which extends and encompasses both models A and B. Similarly to model B, model C assumes that the scaling loop distribution is a power-law, but leaves its slope unspecified.…”