论文标题
标量调节理论的通胀平衡构型
Inflationary equilibrium configurations of scalar-tensor theories of gravity
论文作者
论文摘要
在本文中，我们研究了基于标量调节理论的通货膨胀宇宙学模型的渐近动力学。我们的主要目的是探索单场通货膨胀模型框架中相空间的全球结构。为此，我们强调了相位空间变量的足够选择。我们的结果表明，尽管单场通货膨胀是通用的，从某种意义上说，沿给定的相空间轨道（代表潜在的宇宙历史）存在相应的相位空间中的相应临界点，但通货膨胀阶段的发生却相当取决于初始条件。我们已经能够对初始条件的相对概率（RP）进行定量估计，从而导致缓慢的通货膨胀。对于具有$ ϕ^2 $ - 优势的非最小耦合模型，我们的粗略估计值几乎消失了相对概率：$ 10^{ - 13} \，\％\％\ sillesim rp \ ll 10^{ - 8} {-8} \ \％$。这些键在标量调整模型（包括Brans-Dicke理论）中得到了极大的改善，其中相对概率$ 1 \，\％\％\ lyssim rp \ leq 100 \，\％$。因此，缓慢的通胀确实是Brans-Dicke通货膨胀模型中宇宙扩张的自然阶段。同样也证实，具有任意势能的真空brans-dicke理论的动力学是非差异的。
In this paper we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of single-field inflation models. For this purpose we make emphasis in the adequate choice of the variables of the phase space. Our results indicate that, although single-field inflation is generic in the sense that the corresponding critical point in the phase space exists for a wide class of potentials, along given phase space orbits -- representing potential cosmic histories -- the occurrence of the inflationary stage is rather dependent on the initial conditions. We have been able to give quantitative estimates of the relative probability (RP) for initial conditions leading to slow-roll inflation. For the non-minimal coupling model with the $ϕ^2$-potential our rough estimates yield to an almost vanishing relative probability: $10^{-13}\,\%\lesssim RP\ll 10^{-8}\,\%$. These bonds are greatly improved in the scalar-tensor models, including the Brans-Dicke theory, where the relative probability $1\,\%\lesssim RP\leq 100\,\%$. Hence slow-roll inflation is indeed a natural stage of the cosmic expansion in Brans-Dicke models of inflation. It is confirmed as well that the dynamics of vacuum Brans-Dicke theories with arbitrary potentials are non-chaotic.
