Equilibration and freeze-out of an expanding gas in a transport approach in a Friedmann–Robertson–Walker metric

J Tindall,J.M Torres-Rincon,J.B Rose,H Petersen

doi:10.1016/j.physletb.2017.04.080

Abstract

Motivated by a recent finding of an exact solution of the relativistic Boltzmann equation in a Friedmann–Robertson–Walker spacetime, we implement this metric into the newly developed transport approach Simulating Many Accelerated Strongly-interacting Hadrons (SMASH). We study the numerical solution of the transport equation and compare it to this exact solution for massless particles. We also compare a different initial condition, for which the transport equation can be independently solved numerically. Very nice agreement is observed in both cases. Having passed these checks for the SMASH code, we study a gas of massive particles within the same spacetime, where the particle decoupling is forced by the Hubble expansion. In this simple scenario we present an analysis of the freeze-out times, as function of the masses and cross sections of the particles. The results might be of interest for their potential application to relativistic heavy-ion collisions, for the characterization of the freeze-out process in terms of hadron properties.

Highlights

Kinetic theory [1] has been widely used to study the nonequilibrium evolution of fluids and plasmas, for ordinary substances and in the relativistic domain [2]
We study the numerical solution of the transport equation and compare it to this exact solution for massless particles
In this letter we have reported our results on the solutions of the Boltzmann equation for a relativistic gas in a FRW spacetime evolution using the Simulating Many Accelerated Strongly-interacting Hadrons (SMASH) transport approach

Summary

Introduction

Kinetic theory [1] has been widely used to study the nonequilibrium evolution of fluids and plasmas, for ordinary substances and in the relativistic domain [2]. We exploit the flexibility of SMASH to solve the transport equation in an expanding system of massive particles, generating a dynamical freeze-out (or decoupling) due to the Hubble expansion. This opens up the possibility to study more realistic systems of interest in cosmological scenarios, or in RHICs. In Sec. 2 we present the SMASH solution to the Boltzmann equation for massless particles using several initial conditions, in particular the one for which an exact analytical solution is known.

SMASH solution of the Boltzmann equation under a FRW spacetime

Dynamical decoupling of a relativistic massive gas

Conclusions and outlook