Brans-Dicke引力下的宇宙微波背景：I.协变公式
Cosmic microwave background with Brans-Dicke Gravity: I. Covariant Formulation
摘要：
在协变的宇宙学扰动理论中，1+3分解保证了标架无关方程中的所有变量都是协变的，规范不变的，并且有明确的物理解释。我们在Brans-Dicke引力的情况下发展了这一方法，并将其应用于宇宙微波背景（CMB）各向异性和大尺度结构（LSS）的计算.我们修改了现有的Boltzmann程序CAMB，数值计算了背景扰动和绝热扰动的演化，得到了Brans-Dicke理论标量模和张量模的温度谱和偏振谱，首次数值计算了Brans-Dicke引力的张量模结果.我们首先详细介绍了我们的理论形式主义，然后明确描述了修改CAMB代码中使用的技术。这些技术对其它重力模型也是非常有用的。接下来，我们比较了Brans-Dicke理论和标准广义相对论理论中的CMB和LSS谱。最后，我们研究了Brans-Dicke理论中的ISW效应和CMB透镜效应。Brans-Dicke模型与当前观测数据的约束条件在配套文件（文件II）中提出。
英文摘要：
In the covariant cosmological perturbation theory, a 1+3 decomposition ensures that all variables in the frame-independent equations are covariant, gauge-invariant and have clear physical interpretations. We develop this formalism in the case of Brans-Dicke gravity, and apply this method to the calculation of cosmic microwave background (CMB) anisotropy and large scale structures (LSS). We modify the publicly available Boltzmann code CAMB to calculate numerically the evolution of the background and adiabatic perturbations, and obtain the temperature and polarization spectra of the Brans-Dicke theory for both scalar and tensor mode, the tensor mode result for the Brans-Dicke gravity are obtained numerically for the first time. We first present our theoretical formalism in detail, then explicitly describe the techniques used in modifying the CAMB code. These techniques are also very useful to other gravity models. Next we compare the CMB and LSS spectra in Brans-Dicke theory with those in the standard general relativity theory. At last, we investigate the ISW effect and the CMB lensing effect in the Brans-Dicke theory. Constraints on Brans-Dicke model with current observational data is presented in a companion paper (paper II).
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