论文标题
一类单一标量场弹跳解决方案的全球相空间分析
Global phase space analysis for a class of single scalar field bouncing solutions in general relativity
论文作者
论文摘要
我们对非规范标量场理论进行了紧凑的相空间分析，其拉格朗日是$ f（x）-v（ϕ）$在一般相对性中的形式。特别是，我们专注于$ f（x）=βx^m $的动力学术语，并具有功率定律的潜在$ v_0 ϕ^n $和指数电位$ v_0 e^{ - λϕ/m_ {pl}} $。这项工作的主要目的是研究这些模型中非弹跳的通用性，并研究弹跳宇宙学的宇宙未来。一种特别适合研究非弹跳宇宙学的全球动力系统公式用于进行分析。我们表明，当$ f（x）=βx^m $（$β<0 $）时，无挥发是通用的power law潜力$ v（ϕ）= v_0 ϕ^n $仅在参数范围内$ \ left \ left \ left \ lbrace \ lbrace \ frac \ frac {1} {1} {2} {2} {2} {2} <m <m <m <1，\，n <\ frac} $} $} $} $} $} = 2m} m。对于指数势$ v（ϕ）= v_0 e^{ - λϕ/m_ {pl}} $仅在参数范围内$ \ left \ left \ lbrace \ frac {1} {2} {2} <m \ leq1 \ leq1 \ leq1 \ leq1 \ right \ right \ rbrace $。除在这些情况下，由于全球过去或将来的吸引子的不存在，这些模型中的非弹跳并不是一般性的。我们的分析旨在显示全球阶段空间分析的重要性，以解决有关非弹跳解决方案的重要问题，即使在其他理论中，也必须采用这种解决方案的想法。
We carry out a compact phase space analysis of a non-canonical scalar field theory whose Lagrangian is of the form $F(X)-V(ϕ)$ within general relativity. In particular, we focus on a kinetic term of the form $F(X)=βX^m$ with power law potential $V_0 ϕ^n$ and exponential potential $V_0 e^{-λϕ/M_{Pl}}$ of the scalar field. The main aim of this work is to investigate the genericity of nonsingular bounce in these models and to investigate the cosmic future of the bouncing cosmologies when they are generic. A global dynamical system formulation that is particularly suitable for investigating nonsingular bouncing cosmologies is used to carry out the analysis. We show that when $F(X)=βX^m$ ($β<0$), nonsingular bounce is generic for a power law potential $V(ϕ) = V_0 ϕ^n$ only within the parameter range $\left\lbrace \frac{1}{2}<m<1,\,n<\frac{2m}{m-1}\right\rbrace$ and for an exponential potential $V(ϕ) = V_0 e^{-λϕ/M_{Pl}}$ only within the parameter range $\left\lbrace\frac{1}{2}<m\leq1\right\rbrace$. Except in these cases, nonsingular bounce in these models is not generic due to the non-existence of global past or future attractors. Our analysis serves to show the importance of a global phase space analysis to address important questions about nonsingular bouncing solutions, an idea that may and must be adopted for such solutions even in other theories.
