In this paper, we study the perturbative regime in the static patch of de Sitter metric in the Regge–Wheeler formalism. After realizing that perturbative regime in a de Sitter spacetime depicted in terms of usual spherical coordinates cannot be extended up to the cosmological horizon, we study perturbative equations, in particular the axial ones, in terms of the tortoise coordinate $r_{\ast }$. We show that perturbative regime can be extended up to the cosmological horizon, provided that suitable boundary conditions are chosen. As an application, we explore the Regge–Wheeler equation at short distances by performing a Taylor expansion. In order to study some possible quantum effects at short distances, we impose to the equation so-obtained the same boundary conditions suitable for a quantum 3D harmonic oscillator. As a result, a discrete spectrum can be obtained. The aforementioned spectrum is analyzed and a relation with possible effects denoting quantum behavior of gravitons is suggested.

在本文中，我们研究了 Regge-Wheeler 形式主义中 de Sitter 度量的静态补丁中的微扰机制。在意识到用通常的球坐标描述的德西特时空中的微扰状态不能扩展到宇宙视界之后，我们研究了微扰方程，特别是轴向方程，根据乌龟坐标$r_{*}$. 我们表明，只要选择了合适的边界条件，微扰机制就可以扩展到宇宙视界。作为一个应用程序，我们通过执行泰勒展开来探索短距离的 Regge-Wheeler 方程。为了研究短距离内一些可能的量子效应，我们对方程施加了适用于量子 3D 谐振子的相同边界条件。结果，可以获得离散谱。分析了上述光谱，并提出了与表示引力子量子行为的可能效应的关系。