Title: The Equation of State and Duration to Radiation Domination After Inflation Show Chinese title

Title: 状态方程与暴胀后辐射主导的持续时间

Abstract: We calculate the equation of state after inflation and provide an upper bound on the duration before radiation domination by taking the nonlinear dynamics of the fragmented inflaton field into account. A broad class of single-field inflationary models with observationally consistent flattening of the potential at a scale $M$ away from the origin, $V(\phi)\propto |\phi|^{2n}$ near the origin, and where the couplings to other fields are ignored are included in our analysis. We find that the equation of state parameter $w\rightarrow 0$ for $n=1$ and $w\rightarrow 1/3$ (after sufficient time) for $n\gtrsim 1$. We calculate how the number of $e$-folds to radiation domination depends on both $n$ and $M$ when $M\sim m_{\rm pl}$, whereas when $M\ll m_{\rm pl}$, we find that the duration to radiation domination is negligible. Our results are explained in terms of a linear instability analysis in an expanding universe, scaling arguments, and are supported by detailed 3+1 dimensional lattice simulations. We show how our work significantly reduces the uncertainty in inflationary observables, even after including couplings to additional light fields. Show Chinese abstract

Abstract: 我们计算了暴胀后的状态方程，并通过考虑碎片化暴胀场的非线性动力学，提供了辐射主导之前持续时间的上限。 一类广泛的单场暴胀模型被包含在我们的分析中，这些模型在距离原点$M$的尺度上观测一致的势能平坦化，在原点附近为$V(\phi)\propto |\phi|^{2n}$，并且忽略了与其他场的耦合。 我们发现状态方程参数$w\rightarrow 0$对于$n=1$和$w\rightarrow 1/3$（经过足够时间）对于$n\gtrsim 1$。 我们计算了当$M\sim m_{\rm pl}$时，$e$-folds 到辐射主导的数目如何依赖于$n$和$M$，而当$M\ll m_{\rm pl}$时，我们发现到辐射主导的时间是可忽略的。 我们的结果通过膨胀宇宙中的线性不稳定分析、标度论证进行解释，并得到了详细的3+1维晶格模拟的支持。 我们展示了我们的工作即使在考虑与额外轻场的耦合后，也能显著减少暴胀可观测量的不确定性。