论文标题
相互作用的单样标量场电位和完美流体的动力学
Dynamics of interacting monomial scalar field potentials and perfect fluids
论文作者
论文摘要
由早期宇宙的宇宙学模型激励，我们分析了爱因斯坦方程的动力学，并具有最小的耦合标量场，具有单个潜力$ v（ϕ）= \ frac {（λϕ）^{（λϕ）^{2n}}}} {2n} {2n} {2n} $，$λ> 0 $，$λ> 0 $ n \ in \ nate \ n} $ n} $ p_ \ mathrm {pf} =（γ_\ Mathrm {pf} -1）ρ_\ Mathrm {pf} $，$γ_\ Mathrm {pf} \ in（0,2）$在Robertson-Robertson-Walker SpaceTimes中。交互是$γ（ϕ）= μϕ^{2p} $，$μ> 0 $，$ p \ in \ mathbb {n} \ cup \ cup \ {0 \} $的类似摩擦的术语。该分析依赖于引入新的常规三维动力系统对爱因斯坦方程在紧凑的状态空间上的表述，以及使用动态系统工具（例如准均匀爆炸）的使用，以及涉及时间依赖性扰动参数的平均方法。由于交互项的影响，我们发现$ P = N/2 $的分叉。总的来说，这个术语对$ p <n/2 $（$ p> n/2 $）的未来（过去）渐近造成更大的影响。对于$ p <n/2 $，我们发现可能未来的吸引子的复杂性，这取决于$ p =（n-1）/2 $还是$ p <（n-1）/2 $。在第一种情况下，未来的动态受liénard系统的约束。另一方面，当$ p =（n-2）/2 $ $时，通用的未来吸引子由以前在文献中未知的新解决方案组成，这些解决方案可以推动未来的加速，而情况$ p <（n-2）/2 $具有通用的未来吸引者De-Sitter解决方案。对于$ p = n/2 $，未来的渐近学可以是流体占主导地位或具有振荡行为，而在流体和标量场均不主导的情况下。对于$ p> n/2 $，未来的渐近学与没有互动的情况相似。最后，我们表明，无论参数如何，通货膨胀的准de-sitter解决方案始终存在于过去，因此，具有$ p \ leq（n-2）/2 $的案例可能会提供典型通货膨胀的新宇宙学模型。
Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $V(ϕ)=\frac{(λϕ)^{2n}}{2n}$, $λ>0$, $n\in\mathbb{N}$, interacting with a perfect fluid with linear equation of state $p_\mathrm{pf}=(γ_\mathrm{pf}-1)ρ_\mathrm{pf}$, $γ_\mathrm{pf}\in(0,2)$, in flat Robertson-Walker spacetimes. The interaction is a friction-like term of the form $Γ(ϕ)=μϕ^{2p}$, $μ>0$, $p\in\mathbb{N}\cup\{0\}$. The analysis relies on the introduction of a new regular 3-dimensional dynamical systems' formulation of the Einstein equations on a compact state space, and the use of dynamical systems' tools such as quasi-homogeneous blow-ups and averaging methods involving a time-dependent perturbation parameter. We find a bifurcation at $p=n/2$ due to the influence of the interaction term. In general, this term has more impact on the future (past) asymptotics for $p<n/2$ ($p>n/2$). For $p<n/2$ we find a complexity of possible future attractors, which depends on whether $p=(n-1)/2$ or $p<(n-1)/2$. In the first case the future dynamics is governed by Liénard systems. On the other hand when $p=(n-2)/2$ the generic future attractor consists of new solutions previously unknown in the literature which can drive future acceleration whereas the case $p<(n-2)/2$ has a generic future attractor de-Sitter solution. For $p=n/2$ the future asymptotics can be either fluid dominated or have an oscillatory behaviour where neither the fluid nor the scalar field dominates. For $p>n/2$ the future asymptotics is similar to the case with no interaction. Finally, we show that irrespective of the parameters, an inflationary quasi-de-Sitter solution always exists towards the past, and therefore the cases with $p\leq(n-2)/2$ may provide new cosmological models of quintessential inflation.
