用$B$模的纯伪谱重建方法检测张量标量比
Detecting the tensor-to-scalar ratio with the pure pseudospectrum reconstruction of $B$-mode
摘要：
在这项工作中，我们采用纯伪形式主义设计的泄漏功率谱估计的方差的影响最小化，并讨论张量标量比，$r$，可以现实地设置由当前和即将到来的测量的$B$模式角功率谱的限制。我们将这些结果与使用其他方法获得的结果进行比较：天真模式计数，最小方差二次估计，并重新访问优化小规模亚轨道实验的天空覆盖范围的问题，以最大限度地提高检测$r$的统计意义。我们表明，优化的天空覆盖范围在很大程度上是不敏感的所采用的方法，至少对于合理紧凑的天空补丁。然而，我们发现，模式计数高估了检测的重要性的一个因素$\sim1.17$相比，无损的最大方差的方法和一个因素$\sim1.25$相比，有损的纯伪谱估计。在第二次，我们考虑更现实的实验配置。与纯伪谱重建的$B$模式，只考虑统计的不确定性，我们发现，检测$r\sim0.11$，$r\sim0.0051$和$r\sim0.0026$在99 $\%$的置信水平是在目前的亚轨道实验，未来的地面望远镜阵列和卫星任务，分别达到。这意味着，即使$E$到$B$的泄漏一直被包括在内，但在分析中被考虑在内，一组望远镜也足以区分大视场和小视场的暴胀模型。然而，将需要一个卫星任务来区分不同的小领域模型，这取决于e-折叠的数量。
英文摘要：
In this work we employ the pure-pseudo formalism devised to minimise the effects of the leakage on the variance of power spectrum estimates and discuss the limits on the tensor-to-scalar ratio, $r$, that could be realistically set by current and forthcoming measurements of the $B$-mode angular power spectrum. We compare those with the results obtained using other approaches: naïve mode-counting, minimum-variance quadratic estimators, and re-visit the question of optimizing the sky coverage of small-scale, suborbital experiments in order to maximize the statistical significance of the detection of $r$. We show that the optimized sky coverage is largely insensitive to the adopted approach at least for reasonably compact sky patches. We find, however, that the mode-counting overestimates the detection significance by a factor $\sim1.17$ as compared to the lossless maximum variance approach and by a factor $\sim1.25$ as compared to the lossy pure pseudo-spectrum estimator. In a second time, we consider more realistic experimental configurations. With a pure pseudospectrum reconstruction of $B$-modes and considering only statistical uncertainties, we find that a detection of $r\sim0.11$, $r\sim0.0051$ and $r\sim0.0026$ at 99$\%$ of confidence level is within the reach of current sub-orbital experiments, future arrays of ground-based telescopes and a satellite mission, respectively. This means that an array of telescopes could be sufficient to discriminate between large- and small-field models of inflation, even if the $E$-to-$B$ leakage is consistently included but accounted for in the analysis. However, a satellite mission will be required to distinguish between different small-field models depending on the number of e-folds.
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