Although the search for azimutal patterns in cosmological surveys is useful to characterise some effects depending exclusively on an angular distance within the standard model, they are considered as a key distinguishing feature of some exotic scenarios, such as bubble collisions or conformal cyclic cosmology (CCC). In particular, the CCC is a non-stardard framework which predicts circular patterns on the CMB intensity fluctuations. Motivated by some previous works which explore the presence of radial gradients, we apply a methodology based on the radial derivatives to the latest release of \textit{Planck} data. The new approach allows exhaustive studies to be performed at all sky directions at a HEALPix resolution of $N_{\mathrm{side}} = 1024$. Specifically, two different analyses are performed focusing on weight functions in both small (up to a $5$-degree radius) and large scales. We present a comparison between our results and those shown by An et al. (2017), and An et al. (2018). In addition, a possible polarization counterpart of these circular patterns is also analysed for the most promising case. Taking into account the limitations to characterize the significance of the results, including the possibility of suffering a look-elsewhere effect, no strong evidence of the kind of circular patterns expected from CCC is found in the \textit{Planck} data for either the small or the large scales.

中文翻译：

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径向导数作为普朗克数据上大爆炸前事件的检验

尽管在宇宙学调查中寻找方位角模式有助于表征一些完全取决于标准模型内角距离的影响，但它们被认为是一些奇异场景的关键区别特征，例如气泡碰撞或共形循环宇宙学 (CCC) . 特别是，CCC 是一个非标准框架，它预测 CMB 强度波动的圆形图案。受之前一些探索径向梯度存在的工作的启发，我们将基于径向导数的方法应用于最新版本的 \textit{Planck} 数据。新方法允许以 $N_{\mathrm{side}} = 1024$ 的 HEALPix 分辨率在所有天空方向上进行详尽的研究。具体来说，进行了两种不同的分析，重点是小（高达 $5$ 度半径）和大尺度的权重函数。我们将我们的结果与 An 等人显示的结果进行了比较。(2017) 和 An 等人。(2018)。此外，还针对最有希望的情况分析了这些圆形图案的可能极化对应物。考虑到表征结果重要性的局限性，包括可能遭受别处效应，在 \textit{Planck} 数据中没有发现 CCC 预期的圆形图案类型的有力证据。或大尺度。对于最有希望的情况，还分析了这些圆形图案的可能极化对应物。考虑到表征结果重要性的局限性，包括可能遭受别处效应，在 \textit{Planck} 数据中没有发现 CCC 预期的圆形图案类型的有力证据。或大尺度。对于最有希望的情况，还分析了这些圆形图案的可能极化对应物。考虑到表征结果重要性的局限性，包括可能遭受别处效应，在 \textit{Planck} 数据中没有发现 CCC 预期的圆形图案类型的有力证据。或大尺度。