Vacuum polarisation of Dirac fermions in the cosmological de Sitter-global monopole spacetime

TL;DR

This paper investigates how a global monopole in de Sitter spacetime influences the vacuum polarization of Dirac fermions, deriving explicit mode solutions and computing related quantum expectation values.

Contribution

It provides a closed-form derivation of Dirac modes in this background and calculates the fermionic condensate and energy-momentum tensor with a novel regularisation approach.

Findings

Global monopole affects fermionic vacuum polarization in de Sitter space.

Explicit Dirac mode solutions are obtained in the monopole background.

Numerical analysis shows parameter dependence of vacuum expectation values.

Abstract

We study the vacuum polarisation effects of the Dirac fermionic field induced by a pointlike global monopole located in the cosmological de Sitter spacetime. First we derive the four orthonormal Dirac modes in this background in a closed form. Quantising the field using these modes, we then compute the fermionic condensate, $\langle 0| \overline{\Psi} \Psi | 0\rangle$, as well as the vacuum expectation value of the energy-momentum tensor for a massive Dirac field, regularised in a particular way. We have used the Abel-Plana summation formula in order to extract the global monopole contribution to these quantities and have investigated their variations numerically with respect to relevant parameters.