Bose Fermi Supersymmetry with Bogoliubov transforms in Cosmology

TL;DR

This paper explores the use of Bogoliubov transforms in supersymmetric and Bose-Fermi frameworks to analyze vacuum expectation values in cosmological and black hole geometries, linking field theory with cosmological observations.

Contribution

It introduces a novel application of Bogoliubov transforms to supersymmetric and Bose-Fermi field theories in cosmology, providing new insights into vacuum states in dynamic geometries.

Findings

Derived conditions for mixed and distinct bosonic and fermionic representations.

Established differential equations for mode functions in Robertson Walker and Bianchi I geometries.

Linked supersymmetric field theory with cosmological and black hole vacuum states.

Abstract

Field theory including Supersymmetry and Bose Fermi Symmetry is an active subject of particle physics and cosmology. Recent and expected observational evidence gives indicators for the creation and destruction of normal and supersymmetric dark matter in the universe. This paper uses Bogoliubov transforms in supersymmetric and Bose Fermi form for obtaining the vaccuum expectation values at any two times in cosmological and black hole geometries. The isotropic Robertson Walker and slightly anisotropic Bianchi I geometry mode functions have a differential equation form analogous to the supersymmetric Hamiltonian. The condition for mixed and distinct representations for bosonic and fermionic fields of normal and supersymmetric partner particles are found.