Statistical conformal Killing Vector Fields for FLRW Space-Time

TL;DR

This paper introduces a new perspective on conformal Killing vector fields in FLRW space-time, classifies statistical structures related to these fields, and explores affine connections with specific properties.

Contribution

It provides a novel classification of conformal Killing vector fields in FLRW space-time and analyzes associated statistical structures and affine connections.

Findings

Identified nine conformal vector fields in FLRW space-time.

Classified statistical structures based on these vector fields.

Derived conditions for affine connections with vanishing Lie derivatives.

Abstract

The classification of conformal Killing vector fields for FLRW space-time from Riemannian point of view was done by Maartens-Maharaj in \cite{Maartens1986}. In this paper, we introduce conformal Killing vector fields from a new point of view for the FLRW space-time. In particular, we consider three cases for the conformal factor. Then, it is shown that there exist nine conformal vector fields on FLRW in total, such that six of them are Killing and the rest being non-Killing conformal vector fields. Consequently, by recalling the concept of statistical conformal Killing vector fields introduced in \cite{SP}, we classify statistical structures with repsect to which these vector fields are conformal Killing. We also obtain the form of affine connections that feature a vanishing Lie derivative with respect to these conformal Killing vector fields. Imposing the torsion-free and the Codazzi conditions on these connections, we study statistical structures on FLRW. Finally, for torsionful connections we study the vanishing of the Lie derivative of the torsion tensor with respect to these conformal Killing vector fields and derive the conditions under which this is valid.