三阶协变伽利略引力理论下的线性和非线性物质增长函数的计算

The linear and nonlinear growth functions in Cubic Galileon

本文介绍了ΛCDM标准宇宙学模型下的拉格朗日微扰论,并将其扩展到三阶协变伽利略引力模型(G3)下.利用二阶拉格朗日微扰论的方法计算了G3模型下宇宙物质密度的非线性增长模式.研究发现在G3模型下其有效引力常数具有标度不依赖性,并且其数值比传统的牛顿引力系数大.特别是在晚期暗能量为主时期,该理论下的有效引力常数是前者数值的2倍左右.基于该特性,G3模型下的线性以及非线性物质增长函数相对ΛCDM模型而言有较大幅度提升.这意味着该理论下的星系成团性比标准宇宙学模型所预言的结果要高.除此之外,研究还发现该模型中的二阶物质密度增长函数可以对动量依赖以及时间依赖部分进行变量分离.这使得仅需要在初始时刻对动量的角度依赖部分进行卷积计算,而在后面演化部分仅需进行时间积分.这一特性极大地提升了该模型的二阶增长函数的数值计算效率.

We introduce the Lagrangian perturbation theory under ΛCDM model, and extend it to the Cubic Galileon (G3) model.We present the second order growth function in G3 model based on the Lagrangian perturbation theory. We find that theeffective Newtonian constant in G3 model is almost scale independent. Its value is bigger than that of the ΛCDM model.In the late time dark energy dominated epoch, its value is enhanced by a factor about 2. Based on this, the linear andnonlinear growth functions in the structure formation for G3 model are larger than that of the ΛCDM model. It means G3model has stronger galaxy clustering effect than ΛCDM model. Besides of this, we find the second order growth functioncan be separated into spatial and temporal dependent parts. Hence, one only needs to convolve different momentumconfigurations at the initial stage. This will significantly accelerate the numerical calculation.