First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime. The perturbations, which are of perfect fluid type, include general scalar, vector and tensor modes and extend some previous works where vorticity perturbations were excluded. A harmonic decomposition is performed and the field equations are then reduced to a set of eight evolution equations for eight harmonic coefficients, representing perturbations in density, shear, vorticity and the Weyl tensor, in terms of which all other variables can be expressed algebraically. This system decouples into two sub-systems, one for five and one for three coefficients. As previously known, vorticity perturbations cannot be generated to any order in a barytopic perfect fluid. Hence the time development of existing first order vorticity perturbations are seen to be completely determined by the background. However, an already existing vorticity will act as source terms in the evolution equations for the other quantities. In the high frequency approximation the four independent Weyl tensor harmonics evolve as gravitational waves on the anisotropic background in the same manner as in the case without vorticity, whereas vorticity gives a first order disturbance of sonic waves.
This paper is a write-up of the ideas that were presented, developed and discussed at the third International Workshop on QCD Challenges from pp to A–A, which took place in August 2019 in Lund, Sweden (Workshop link: https://indico.lucas.lu.se/event/1214/). The goal of the workshop was to focus on some of the open questions in the field and try to come up with concrete suggestions for how to make progress on both the experimental and theoretical sides. The paper gives a brief introduction to each topic and then summarizes the primary results.
Motivated by recent interest in collectivity in small systems, we calculate the harmonic flow response to initial geometry deformations within weakly coupled QCD kinetic theory using the first correction to the free-streaming background. We derive a parametric scaling formula that relates harmonic flow in systems of different sizes and different generic initial gluon distributions. We comment on similarities and differences between the full QCD effective kinetic theory and the toy models used previously. Finally we calculate the centrality dependence of the integrated elliptic flow v2 in oxygen-oxygen, proton-lead and proton-proton collision systems.
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