https://doi.org/10.1140/epjc/s10052-025-14494-2
Regular Article - Theoretical Physics
Gravitational production of massive vectors non-minimally coupled to gravity
1
Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland
2
Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, 75005, Paris, France
a
bohdan.grzadkowski@fuw.edu.pl
Received:
20
March
2025
Accepted:
2
July
2025
Published online:
21
July
2025
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 
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 been calculated.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
