Cosmic string loop distribution on all length scales and at any redshift

TL;DR

This paper analytically derives the distribution of cosmic string loops across all scales and redshifts, showing how they evolve towards a scaling solution and providing bounds on their density and energy contribution today.

Contribution

It introduces an adjusted Polchinski-Rocha model combined with phenomenological backreaction to analytically predict cosmic string loop distributions over cosmic history.

Findings

Loop distribution reaches scaling in both radiation and matter eras.

Memory of initial conditions is erased before Big Bang Nucleosynthesis.

Loop density today is limited to less than 10^(-5) of the critical density.

Abstract

We analytically derive the expected number density distribution of Nambu-Goto cosmic string loops at any redshift soon after the time of string formation to today. Our approach is based on the Polchinski-Rocha model of loop formation from long strings which we adjust to fit numerical simulations and complement by a phenomenological modelling of gravitational backreaction. Cosmological evolution drives the loop distribution towards scaling on all length scales in both the radiation and matter era. Memory of any reasonable initial loop distribution in the radiation era is shown to be erased well before Big Bang Nucleosynthesis. In the matter era, the loop distribution reaches full scaling, up to some residual loops from the radiation era which may be present for extremely low string tension. Finally, the number density of loops below the gravitational cutoff is shown to be scale independent, proportional to a negative power of the string tension and insensitive to the details of the backreaction modelling. As an application, we show that the energy density parameter of loops today cannot exceed 10^(-5) for currently allowed string tension values, while the loop number density cannot be less than 10^(-6) per Mpc^3. Our result should provide a more robust basis for studying the cosmological consequences of cosmic string loops.