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超新星对暗能量和光滑度参数的约束

Constraining the dark energy and smoothness-parameter with supernovae

R. C. Santos, J. V. Cunha, J. A. S. Lima

备注：
6 pages, 8 figures, typos corrected, paper matching the version published in Physical Review D
发表信息：
Phys.Rev.D77:023519,2008
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摘要：

不均匀性的存在通过引力透镜效应改变了宇宙距离，并且间接地影响了主要的宇宙学测试。假设暗能量是一个平滑的成分，解释成团影响的最简单方法是假设膨胀宇宙的平均演化是由总物质能量密度决定的，而光的聚焦只受$α$ Dyer-Roeder参数量化的总物质密度的一小部分影响。利用两个不同的Ia型SNe数据样本，通过应用Zeldovich-Kantowski-Dyer-Roeder（ZKDR）光度距离红移关系（$Λ$ CDM），对$Ω_m$和$α$参数进行了约束.使用Astier的115 SNe Ia数据的$χ^{2}$分析{\it et al.} sample（2006）将密度参数约束为$Ω_m=0.26_{-0.07}^{+0.17}$（$2σ$），而$α$参数受到弱限制（即使在1 $σ$时也允许所有值$\in [0,1]$）。然而，基于Riess的182 SNe Ia数据的类似分析{\it等人}（2007）将参数对约束为$Ω_m= 0.33^{+0.09}_{-0.07}$和$α\geq 0.42$（$2σ$）。基本上，这是因为Riess {\it et al.}样品延伸到明显更高的红移。作为一般结果，即使考虑到存在由平滑度$α$参数描述的不均匀性，Einstein-de Sitter模型也被具有高度统计置信度的两个样本（分别为$11.5σ$和$9.9σ$）排除。这里讨论的非均匀哈勃-桑德奇图突出了暗能量的必要性，并且还需要在$z\sim 0.5$处的过渡减速/加速阶段。

英文摘要：

The presence of inhomogeneities modifies the cosmic distances through the gravitational lensing effect, and, indirectly, must affect the main cosmological tests. Assuming that the dark energy is a smooth component, the simplest way to account for the influence of clustering is to suppose that the average evolution of the expanding Universe is governed by the total matter-energy density whereas the focusing of light is only affected by a fraction of the total matter density quantified by the $α$ Dyer-Roeder parameter. By using two different samples of SNe type Ia data, the $Ω_m$ and $α$ parameters are constrained by applying the Zeldovich-Kantowski-Dyer-Roeder (ZKDR) luminosity distance redshift relation for a flat ($Λ$CDM) model. A $χ^{2}$-analysis using the 115 SNe Ia data of Astier {\it et al.} sample (2006) constrains the density parameter to be $Ω_m=0.26_{-0.07}^{+0.17}$($2σ$) while the $α$ parameter is weakly limited (all the values $\in [0,1]$ are allowed even at 1$σ$). However, a similar analysis based the 182 SNe Ia data of Riess {\it et al.} (2007) constrains the pair of parameters to be $Ω_m= 0.33^{+0.09}_{-0.07}$ and $α\geq 0.42$ ($2σ$). Basically, this occurs because the Riess {\it et al.} sample extends to appreciably higher redshifts. As a general result, even considering the existence of inhomogeneities as described by the smoothness $α$ parameter, the Einstein-de Sitter model is ruled out by the two samples with a high degree of statistical confidence ($11.5σ$ and $9.9σ$, respectively). The inhomogeneous Hubble-Sandage diagram discussed here highlight the necessity of the dark energy, and a transition deceleration/accelerating phase at $z\sim 0.5$ is also required.

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