I am trying to find a reference for massive U(1) or "massive photon" during inflation (or de Sitter space) that derives or at least shows the mode functions for massive photon (with the different helicities as well).

Namely, I am trying to find a reference with something along the lines of the following setup. We are looking at inflation correlation functions that involve a massive photon. Since we are looking at inflation, the metric is given by \begin{align} ds^2 & = a^2(\eta)(-d\eta^2 + d\mathbf{x}^2)\nonumber\\ & = \frac{1}{H^2\eta^2}(-d\eta^2 + d\mathbf{x}^2) \end{align} where $a(\eta) = -1/(H\eta)$. We also consider the following action, \begin{equation} S = \int d^d\mathbf{x} d\eta\sqrt{-g}\:\left(-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} - \frac{1}{2}m^2A_\mu A^\mu + \mathcal{L}_\text{interaction}\right) + S_\text{other} \end{equation} where the field strength is $F_{\mu\nu} = \nabla_\mu A_\nu - \nabla_\nu A_\mu$ and the "other" part of the action can be any other fields the reference is considering.

I just need to find the mode functions for the free Proca-type action.

A textbook reference or any papers (preferably a paper) that could help, I would be immensely thankful.

I am trying to find a reference for massive $U(1)$ or "massive photon" during inflation (or de Sitter space) that derives or at least shows the mode functions for massive photon (with the different helicities as well).

Namely, I am trying to find a reference with something along the lines of the following setup. We are looking at inflation correlation functions that involve a massive photon. Since we are looking at inflation, the metric is given by \begin{align} ds^2 & = a^2(\eta)(-d\eta^2 + d\mathbf{x}^2)\nonumber\\ & = \frac{1}{H^2\eta^2}(-d\eta^2 + d\mathbf{x}^2) \end{align} where $a(\eta) = -1/(H\eta)$. We also consider the following action, \begin{equation} S = \int d^d\mathbf{x} d\eta\sqrt{-g}\:\left(-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} - \frac{1}{2}m^2A_\mu A^\mu + \mathcal{L}_\text{interaction}\right) + S_\text{other} \end{equation} where the field strength is $F_{\mu\nu} = \nabla_\mu A_\nu - \nabla_\nu A_\mu$ and the "other" part of the action can be any other fields the reference is considering.

I just need to find the mode functions for the free Proca-type action.

A textbook reference or any papers (preferably a paper) that could help, I would be immensely thankful.