# Reply to the "Comment on Fermion production in a magnetic field in a de Sitter Universe"

## TL;DR

This paper investigates gauge invariance of first-order transition amplitudes in de Sitter QED within Coulomb gauge, demonstrating invariance under allowed gauge transformations and clarifying the applicability of previous comments.

## Contribution

It establishes that gauge invariance holds for first-order transition amplitudes in de Sitter QED under Coulomb gauge, clarifying the limitations of certain gauge transformations.

## Key findings

- Transition amplitudes are invariant under gradient-preserving gauge transformations.
- Allowed gauge transformations in Coulomb gauge are restricted to trivial ones.
- Previous comments do not apply due to gauge transformation constraints.

## Abstract

In this paper we study the problem of gauge invariance of the first order transition amplitudes in de Sitter QED in Coulomb gauge. We consider the gauge transformations which preserve the Coulomb gauge, that contain the gradient of the gauge function. The final results prove that the first order transition amplitudes do not change at a gradient transformation of the vector potential because the only allowed transformation is $\Lambda=0$. Our results suggest that the remarks made in the comment by Nicolaevici and Farkas {\em Phys. Rev. D} \textbf{95}, are not directly applicable to the results in our paper since their proposed gauge transformations do not preserve the Coulomb gauge.