PRISM: Sparse recovery of the primordial power spectrum
PRISM: Sparse recovery of the primordial power spectrum
复制标题
PRISM：原始功率谱的稀疏恢复
DOI：
10.1051/0004-6361/201322326
复制
发表时间：
2014
影响因子：
6.5
通讯作者：
J. Bobin
中科院分区：
文献类型：
--
作者：
P. Paykari;F. Lanusse;J. Starck;F. Sureau;J. Bobin
目标。原始功率谱描述了宇宙中最初的扰动，这些扰动最终发展成我们今天观察到的大尺度结构，从而提供了对暴胀或其他结构形成机制的间接探测。在这里，我们介绍了一种新的方法来估计这个频谱的宇宙微波背景图的经验功率谱。方法.提出了一种基于稀疏性的线性反演方法PRISM。该技术利用小波基中原始功率谱中的特征的稀疏性先验来正则化逆问题。这种非参数方法不假设原始功率谱形状的强先验，但能够正确重建其全局形状以及局部特征。这些优点使得该方法对于检测与当前受欢迎的尺度不变光谱的偏差是鲁棒的。结果我们调查的强度，这种方法的一组WMAP九年的模拟数据为三种类型的原始功率谱：近尺度不变的频谱，频谱与一个小的运行的频谱指数，频谱与本地化功能。这种技术证明，它可以很容易地检测偏离纯标度不变的功率谱，并适用于区分简单的模型的通货膨胀。我们处理的WMAP九年的数据，并没有发现显着偏离近scaleinvariant功率谱与谱指数ns = 0：972。结论.该方法可以重建出高分辨率的原始功率谱，任何强的局部偏差或小的全局偏差都可以很容易地从纯尺度不变谱中检测出来。
Aims. The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation mechanisms. Here, we introduce a new method to estimate this spectrum from the empirical power spectrum of cosmic microwave background maps. Methods. A sparsity-based linear inversion method, named PRISM, is presented. This technique leverages a sparsity prior on features in the primordial power spectrum in a wavelet basis to regularise the inverse problem. This non-parametric approach does not assume a strong prior on the shape of the primordial power spectrum, yet is able to correctly reconstruct its global shape as well as localised features. These advantages make this method robust for detecting deviations from the currently favoured scale-invariant spectrum. Results. We investigate the strength of this method on a set of WMAP nine-year simulated data for three types of primordial power spectra: a near scale-invariant spectrum, a spectrum with a small running of the spectral index, and a spectrum with a localised feature. This technique proves that it can easily detect deviations from a pure scale-invariant power spectrum and is suitable for distinguishing between simple models of the inflation. We process the WMAP nine-year data and find no significant departure from a near scaleinvariant power spectrum with the spectral index ns = 0:972. Conclusions. A high-resolution primordial power spectrum can be reconstructed with this technique, where any strong local deviations or small global deviations from a pure scale-invariant spectrum can easily be detected.