关于LTB宇宙模型中的Friedamann方程

On the Friedmann equation in the LTB cosmological model

Lematre-Tolman-Bondi(LTB)宇宙模型是对超新星亮度变暗的观测事实的另一种解释,其优点在于不再需要引入神秘的暗能量.在特殊情形下,LTB宇宙模型能够约化到通常的Friedmann-Robertson-Walker(FRW)宇宙模型.对于一般的LTB宇宙模型,通常的Friedmann方程必须作出相应的推广.由于LTB宇宙模型是非均匀但各向同性的,因而推广的Friedmann方程应含有两个哈勃参数.但在LTB的相关文献中,所讨论的是单哈勃参数的Friedmann方程,它无法完备地描述宇宙的演化.仅从牛顿引力理论即可导出单哈勃参数Friedmann方程,还进一步定义了LTB宇宙模型中无量纲参数,给出了双哈勃参数Friedmann方程的另一种形式.

Lematre-Tolman-Bondi （LTB） cosmological model is an alternative explanation to the observational fact of SNeIa dimming,while without the invocation of the mysterious dark energy.On a special occasion,the LTB model will reduce to the ordinary Friedmann-Robertson-Walker（FRW） model.For the discussion of the general LTB model,one should generalize the ordinary Friedmann equation,which should have two Hubble parameters,for the LTB model is inhomogeneous but isotropic.In pertinent literature,however,the discussions are all on the basis of the one-Hubble-parameter Friedmann equation,which cannot make a complete discription of the universe.In this paper,we have shown that the one-Hubble-parameter Friedmann equation can be derived just from the Newtonian gravitational theory.Furthermore,cosmological parameters are defined in the LTB model,and another form of the two-Hubble-parameter Friedmann equation are given.