论文标题
关于在非单个bianchi-i空间中弹跳时的剪切和能量密度之间的新型关系
On a novel relationship between shear and energy density at the bounce in non-singular Bianchi-I spacetimes
论文作者
论文摘要
在经典的bianchi -i空间中，可以从广义的弗里德曼方程中很容易确定决定奇异性结构的基本条件 - 无论是各向异性剪切还是能量密度。然而，在非单明的各向异性模型中，这些见解很难在量子重力制度中获得，在量子重力状态下，根据初始条件，与普朗克体积相比，奇异性在非散布平均体积上解析，这可能是很大的。这样的非单明模型也可能缺乏通用的弗里德曼方程，从而使任务变得更加困难。我们在有效的循环量子宇宙学（LQC）的时空描述中解决了这个问题，其中能量密度和各向异性剪切因量子几何效应而普遍界定，但是由于潜在的复杂性，很难得出广义的弗里德曼方程。在LQC弹跳时，进行了有效的汉密尔顿动力学的广泛数值模拟，使能量密度与各向异性剪切之间存在令人惊讶的，看似普遍的关系。 For a variety of initial conditions for a massless scalar field, an inflationary potential, and two types of ekpyrotic potentials we find that the values of energy density and the anisotropic shear at the quantum bounce follow a novel parabolic relationship which reveals some surprising results about the anisotropic nature of the bounce, such as the maximum value of the anisotropic shear at the bounce is reached when the energy density reaches approximately half of its最大允许值。我们发现的关系对于发展反弹的各向异性程度，反弹后宇宙的各向异性以及在具有量子重力校正的Bianchi-I模型中发现了经过修改的广义Friedmann方程非常有用。
In classical Bianchi-I spacetimes, underlying conditions for what dictates the singularity structure - whether it is anisotropic shear or energy density, can be easily determined from the generalized Friedmann equation. However, in non-singular bouncing anisotropic models these insights are difficult to obtain in the quantum gravity regime where the singularity is resolved at a non-vanishing mean volume which can be large compared to the Planck volume, depending on the initial conditions. Such non-singular models may also lack a generalized Friedmann equation making the task even more difficult. We address this problem in an effective spacetime description of loop quantum cosmology (LQC) where energy density and anisotropic shear are universally bounded due to quantum geometry effects, but a generalized Friedmann equation has been difficult to derive due to the underlying complexity. Performing extensive numerical simulations of effective Hamiltonian dynamics, we bring to light a surprising, seemingly universal relationship between energy density and anisotropic shear at the bounce in LQC. For a variety of initial conditions for a massless scalar field, an inflationary potential, and two types of ekpyrotic potentials we find that the values of energy density and the anisotropic shear at the quantum bounce follow a novel parabolic relationship which reveals some surprising results about the anisotropic nature of the bounce, such as the maximum value of the anisotropic shear at the bounce is reached when the energy density reaches approximately half of its maximum allowed value. The relationship we find can prove very useful for developing our understanding of the degree of anisotropy of the bounce, isotropization of the post-bounce universe, and discovering the modified generalized Friedmann equation in Bianchi-I models with quantum gravity corrections.
