论文标题
部分可观测时空混沌系统的无模型预测
On Inflation and Reheating Features in the Higgs-$R^2$ Model
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We investigated inflation in the Higgs-$R^2$ model and assumed the trajectory to follow a single-field approximation called minimal two-field mode. Using this approximation, we tried to constrain the Higgs' non-minimal coupling $ξ$. During inflation, we investigated the effect of $ξ$ on the non-gaussianity. We found that $ξ$ could not provide the large non-gaussianity. In this paper, we divided the preheating stage to be quadratic regime and quartic regime. During the quadratic regime, the gauge bosons' production is the most dominant. However, it could not drain the whole inflaton's energy. Thus, we introduced a dark matter candidate with a large coupling that could drain the whole inflaton's energy. We also found that if $ξ<4.2$, the oscillation on the quadratic regime continued to the quartic regime. The reheating temperature obtained by this mode can be reached to be $\sim 10^{10}$ GeV and strongly depends on the remaining inflaton's energy density. On contrary, if $ξ>4.2$, the oscillation only happens at the quadratic regime. As we assumed the Pauli exclusion principle does exist during the quadratic regime, the instant decay of gauge bosons to fermions is restricted. Hence we expected, the reheating temperature to be low for about $\sim 10^9$ GeV.
