作为回望时间函数的宇宙学标度因子的模型无关绘图
Model-Independent Plotting of the Cosmological Scale Factor as a Function of Lookback Time
摘要：
在目前的工作中，我们描述了一个独立于模型的方法，从通常的哈勃图的模量数据对红移的比例因子与回望时间的关系图。这是第一个这种类型的情节。我们遵循Daly和Djorgovski（2004）用于射电星系数据的独立模型方法。一旦数据图完成，任何模型都可以应用，并将按照标准文献中的描述进行相应显示。然后，我们通过结合Conley等人（2011）的SNLS 3的SNe Ia数据，Riess等人（2004）的High-z SNe数据和Daly & Djorgovski（2004）的射电星系数据来编辑一个z = 1.8的广泛数据集，用于验证新的图表。我们首先将这些数据显示在标准哈勃图上，以确认LCDM宇宙学的最佳拟合，从而验证连接的数据集。然后从数据中绘制比例因子图，并再次从最小二乘拟合中显示LCDM模型。拟合参数与哈勃图拟合一致，证实了新图的有效性。特别感兴趣的是宇宙的过渡时间，在标度因子图中，它将出现在数据集中的拐点。噪声在此演示中更明显，它对图上显示的任何模型的拐点特别敏感，不像在模数-z图上，其中没有拐点，并且通过检查转换-z根本不明显。我们得到了z >0.6的下限。从这个演示中可以明显看出，在z = 1-2的范围内缺乏SNe数据，这正是在z = 0.76附近确认LCDM跃迁-z所需的范围。
英文摘要：
In the present work we describe a model-independent method of developing a plot of scale factor versus lookback time from the usual Hubble diagram of modulus data against redshift. This is the first plot of this type. We follow the model-independent methodology of Daly and Djorgovski (2004) used for their radio-galaxy data. Once the data plot is completed, any model can be applied and will display accordingly as described in standard literature. We then compile an extensive data set to z = 1.8 by combining SNe Ia data from SNLS3 of Conley et al. (2011), High-z SNe data of Riess et al. (2004) and radio-galaxy data of Daly & Djorgovski (2004) to be used to validate the new plot. We first display these data on a standard Hubble diagram to confirm the best fit for LCDM cosmology and thus validate the joined data set. The scale factor plot is then developed from the data and the LCDM model is again displayed from a least-squares fit. The fit parameters are in agreement with the Hubble diagram fit confirming the validity of the new plot. Of special interest is the transition-time of the universe which in the scale factor plot will appear as an inflection point in the data set. Noise is more visible on this presentation which is particularly sensitive to inflection points of any model displayed on the plot unlike on a modulus-z diagram where there are no inflection points and the transition-z is not at all obvious by inspection. We obtain a lower limit of z >0.6. It is evident from this presentation that there is a dearth of SNe data in the range, z = 1-2, exactly the range necessary to confirm a LCDM transition-z in the neighborhood of z = 0.76.
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