On the symmetry properties of the PT kernels and recurrence relations

TL;DR

This paper explores the symmetry properties of PT kernels in Large Scale Structure Cosmology, proposing new classes of subkernels with enhanced symmetry and recurrence relations for their construction.

Contribution

It introduces a novel decomposition of symmetrized PT kernels into subkernels and develops recurrence relations to generate these improved symmetric subkernels.

Findings

Decomposition of symmetrized kernels into subkernels

Construction of subkernels with improved symmetry

Recurrence relations for generating subkernels

Abstract

Perturbation Theory to Large Scale Structure Cosmology proposes corrections to the linearly evolved density contrast and velocity in terms of a series development in which all terms are integrals of powers of the linear density contrast multiplied by kernels. We discuss the symmetry properties of these kernels and show that their full symmetrized versions can be decomposed in different classes of subkernels. We will construct classes of subkernels with improved symmetry properties, and provide recurrence relations to generate them.