Next generation surveys will be capable of determining cosmological parameters beyond percent level. To match this precision, theoretical descriptions should look beyond the linear perturbations to approximate the observables in large scale structure. A quantity of interest is the Number density of galaxies detected by our instruments. This has been focus of interest recently, and several efforts have been made to explain relativistic effects theoretically, thereby testing the full theory. However, the results at nonlinear level from previous works are in disagreement. We present a new and independent approach to computing the relativistic galaxy number counts to second order in cosmological perturbation theory. We derive analytical expressions for the full second order relativistic observed redshift, for the angular diameter distance and for the volume spanned by a survey. Finally, we compare our results with previous works which compute the general distance-redshift relation, finding that our result is in agreement at linear order.

中文翻译：

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星系数量在二阶计数：一种独立的方法

下一代调查将能够确定超出百分比水平的宇宙学参数。为了匹配这种精度，理论描述应该超越线性扰动，以近似大规模结构中的可观测值。一个感兴趣的量是我们的仪器检测到的星系的数量密度。这一直是最近关注的焦点，并且已经做出了一些努力来从理论上解释相对论效应，从而测试完整的理论。然而，以前工作的非线性水平的结果存在分歧。我们提出了一种新的独立方法来计算宇宙学扰动理论中的二阶相对论星系数。我们推导出完整的二阶相对论观测红移的解析表达式，角直径距离和测量跨越的体积。最后，我们将我们的结果与之前计算一般距离-红移关系的工作进行比较，发现我们的结果在线性顺序上是一致的。