Correlation Function in Deep Redshift Space as a Cosmological Probe
Correlation Function in Deep Redshift Space as a Cosmological Probe
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DOI：
10.1086/424561
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发表时间：
2004-08
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通讯作者：
T. Matsubara
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作者：
T. Matsubara
星系调查的最新进展使我们能够研究深的、高红移的宇宙。在线性理论的框架下，定量地给出了深红移空间中可观测相关函数可提取的物理信息。相关函数取决于潜在的功率谱、速度畸变和Alcock-Paczyński （AP）效应。基础功率谱对宇宙中物质成分敏感，速度畸变对星系偏差和总物质量敏感，Alcock-Paczyński效应对暗能量成分敏感。利用相关函数中的重子特征测量暗能量是最有趣的应用之一。我们发现，在AP效应中，相关函数中的“重子脊”是一个统计上的圆形物体。为了充分约束暗能量成分，星系巡天的红移范围应该尽可能宽。在深红移时，天空上的观测区域应该比浅红移时小，以保持数字密度尽可能的高。我们举例说明了一个在宇宙学中有用的最佳调查设计。假设未来对z > 3的红移巡天在当前技术的范围内，可以通过计算费雪矩阵来估计宇宙学参数的可实现误差范围。根据图解设计，在偏差未知且被边缘化的情况下，暗能量状态方程的误差可以控制在±5%以内。即使同时确定所有其他宇宙学参数，状态方程的误差界也高达±10%。
Recent developments in galaxy surveys enable us to investigate the deep, high-redshift, universe. We quantitatively present the physical information extractable from the observable correlation function in deep redshift space in a framework of linear theory. The correlation function depends on the underlying power spectrum, velocity distortions, and the Alcock-Paczyński (AP) effect. The underlying power spectrum is sensitive to the constituents of matter in the universe, the velocity distortions are sensitive to the galaxy bias as well as the amount of total matter, and the Alcock-Paczyński effect is sensitive to the dark energy components. Measuring the dark energy by means of the baryonic feature in the correlation function is one of the most interesting applications. We show that the "baryon ridge" in the correlation function serves as a statistically circular object in the AP effect. In order to sufficiently constrain the dark energy components, the redshift range of the galaxy survey should be as broad as possible. The survey area on the sky should be smaller at deep redshifts than at shallow redshifts to keep the number density as dense as possible. We illustrate an optimal survey design that is useful in cosmology. Assuming future redshift surveys of z ≲ 3, which are within the reach of present-day technology, achievable error bounds on cosmological parameters are estimated by calculating the Fisher matrix. According to an illustrated design, the equation of state of dark energy can be constrained within ±5% error assuming that the bias is unknown and marginalized over. Even when all the other cosmological parameters should be simultaneously determined, the error bound for the equation of state is up to ±10%.