标题： 在Brans-Dicke理论中限制红移参数化参数：开放置信轮廓的演化 显示英文标题

标题： Constraining Red-shift Parametrization Parameters in Brans-Dicke Theory: Evolution of Open Confidence Contours

摘要： 在Brans Dicke引力理论中，从所考虑的标量场势的性质出发，结合不同观测预测的暗能量、暗物质、辐射密度以及宇宙的闭合性，我们可以确定我们的$\omega_{BD}$，即Brans Dicke参数，同时要记住从不同的太阳系约束来看，它必须大于$5\times 10^{5}$。 一旦我们手中有一个满足所需下限的值，我们继续设置不同暗能量模型的EoS参数的未知参数。 在本文中，我们使用三种广为人知的红移参数化方式来研究暗能量EoS。 为了限制Brans Dicke引力理论的自由参数，我们采用十二个红移与哈勃参数的数据点并进行$\chi^{2}$检验。 我们介绍了Stern、Stern+BAO和Stern+BAO+CMB观测的观测数据分析机制。 通过最小化$\chi^2$，我们得到最佳拟合值并绘制出不同的置信区间。 我们对这些区间进行物理分析。 同时，我们检查了我们理论模型的距离模数最佳拟合值与超新星I型Union2样本的比较。 对于Brans Dicke引力理论，与主流数据分析置信区间方法的不同之处在于，所演变的置信区间根本不是像圆或椭圆那样的闭合区间。 相反，它们被发现是开放区间，允许自由参数在参数空间的无限区域内浮动。 然而，负的EoS很可能从最佳拟合值演化而来。 显示英文摘要

摘要： In Brans Dicke theory of gravity, from the nature of the scalar field-potential considered, the dark energy, dark matter, radiation densities predicted by different observations and the closedness of the universe considered, we can fix our $\omega_{BD}$, the Brans Dicke parameter, keeping only the thing in mind that from different solar system constrains it must be greater than $5\times 10^{5}$. Once we have a value, satisfying the required lower boundary, in our hand we proceed for setting unknown parameters of the different dark energy models' EoS parameter. In this paper we work with three well known red shift parametrizations of dark energy EoS. To constrain their free parameters for Brans Dicke theory of gravity we take twelve point red shift vs Hubble's parameter data and perform $\chi^{2}$ test. We present the observational data analysis mechanism for Stern, Stern+BAO and Stern+BAO+CMB observations. Minimising $\chi^2$, we obtain the best fit values and draw different confidence contours. We analyze the contours physically. Also we examine the best fit of distance modulus for our theoretical models and the Supernovae Type Ia Union2 sample. For Brans Dicke theory of gravity the difference from the mainstream confidence contouring method of data analysis id that the confidence contours evolved are not at all closed contours like a circle or a ellipse. Rather they are found to be open contours allowing the free parameters to float inside a infinite region of parameter space. However, negative EoSs are likely to evolve from the best fit values.