A Bayesian analysis of the primordial power spectrum
A Bayesian analysis of the primordial power spectrum
复制标题
原始功率谱的贝叶斯分析
DOI：
10.1111/j.1365-2966.2006.10351.x
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发表时间：
2005
影响因子：
4.8
通讯作者：
M. Hobson
中科院分区：
文献类型：
--
作者：
M. Bridges;A. Lasenby;M. Hobson
我们提出了一个贝叶斯分析的大尺度结构（LSS）和宇宙微波背景数据约束的原始功率谱的形式。我们扩展了通常的尺度不变谱的假设，使之包括：（i）一个连续的谱指数;（ii）一个可能由潜在的驱动暴胀中断而产生的破碎谱;（iii）一个大尺度的功率截止，正如威尔金森微波各向异性探测器（WMAP）第一年的结果所显示的那样;以及（v）由Lasenby & Doran提出的宇宙学模型产生的光谱，该模型在非常大的尺度上自然地表现出幂指数下降。我们完整的贝叶斯分析的结果不仅包括后验概率分布，参数估计推断，但也贝叶斯证据。对于参数较少的模型，该证据值更大，除非更复杂的模型提供与数据的显著更好拟合，从而允许强大的模型选择方法。我们发现，这些模型表现出任何形式的大尺度上的功率切断一贯产生更高的证据比哈里森-泽尔多维奇或单谱指数谱。特别是，在最佳拟合的和谐宇宙学中，我们发现Lasenby & Doran谱显示出比其他模型更大的证据。
We present a Bayesian analysis of large-scale structure (LSS) and cosmic microwave background data to constrain the form of the primordial power spectrum. We have extended the usual presumption of a scale-invariant spectrum to include (i) a running spectral index; (ii) a broken spectrum arising perhaps from an interruption of the potential driving inflation; (iii) a large-scale cut-off in power as the first year Wilkinson Microwave Anisotropy Probe (WMAP) results appear to indicate; (iv) a reconstruction of the spectrum in eight bins in wavenumber; and (v) a spectrum resulting from a cosmological model proposed by Lasenby & Doran, which naturally exhibits an exponential drop in power on very large scales. The result of our complete Bayesian analysis includes not only the posterior probability distribution from which parameter estimates are inferred but also the Bayesian evidence. This evidence value is greater for a model with fewer parameters unless a more complicated model provides a significantly better fit to the data, thus allowing a powerful method of model selection. We find that those models exhibiting any form of cut-off in power on large scales consistently produce higher evidences than either the Harrison-Zel'dovich or single spectral index spectra. In particular, within the best-fitting concordance cosmology, we find the Lasenby & Doran spectrum to show significantly larger evidence as compared to the other models.