Gravitational production of massive vectors non-minimally coupled to gravity

TL;DR

This paper develops a gauge-invariant quantum theory for massive vector bosons with non-minimal gravitational couplings, analyzing their potential as dark matter candidates through numerical solutions of mode equations in an evolving universe.

Contribution

It introduces a generalized Stuckelberg mechanism for non-minimally coupled massive vectors and explores their quantum production in cosmological backgrounds.

Findings

Identified conditions for consistent non-minimal couplings.

Derived and numerically solved mode equations for vector polarizations.

Calculated the spectral energy density and potential dark matter abundance.

Abstract

A quantum theory of massive Abelian vector bosons with non-minimal couplings to gravity has been studied within an evolving, isotropic, and homogeneous gravitational background. The vectors may play a role of dark matter if stabilizing $\mathbb{Z}_2$ symmetry is imposed. In order to construct a gauge invariant theory of massive vectors that couple to the Ricci scalar and Ricci tensor, a generalization of the Stuckelberg mechanism has been invoked. Constraints that ensure consistency of the model had been formulated and corresponding restrictions upon the space of non-minimal couplings have been found. Canonical quantization of the theory in evolving gravitational background was adopted. Mode equations for longitudinally and transversally-polarized vector bosons were derived and solved numerically. Regions of exponential growth in the solutions of the mode equations have been determined and discussed in detail. The spectral energy density for the three polarizations has been calculated, and the UV divergence of the integrated total energy density has been addressed. Finally, assuming their stability, the present abundance of the vector bosons has also been calculated.